CN108691938A - A kind of oscillation damping method, system and vibration absorber for low-frequency elastic wave - Google Patents

A kind of oscillation damping method, system and vibration absorber for low-frequency elastic wave Download PDF

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CN108691938A
CN108691938A CN201810373244.2A CN201810373244A CN108691938A CN 108691938 A CN108691938 A CN 108691938A CN 201810373244 A CN201810373244 A CN 201810373244A CN 108691938 A CN108691938 A CN 108691938A
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elastic wave
vibration absorber
vibration
infinitesimal
face
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CN108691938B (en
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高赫轩
向志海
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Tsinghua University
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Tsinghua University
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F7/00—Vibration-dampers; Shock-absorbers
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F2224/00—Materials; Material properties
    • F16F2224/02—Materials; Material properties solids
    • F16F2224/025—Elastomers
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F2228/00—Functional characteristics, e.g. variability, frequency-dependence
    • F16F2228/04—Frequency effects

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  • Engineering & Computer Science (AREA)
  • General Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Piezo-Electric Or Mechanical Vibrators, Or Delay Or Filter Circuits (AREA)

Abstract

The present invention provides a kind of oscillation damping method, system and vibration absorbers for low-frequency elastic wave.Technical scheme of the present invention constructs vibration absorber according to the feature and vibration damping demand of elastic wave, to the shape of vibration absorber, size and material parameter are designed, make when the communication space for using the vibration absorber as elastic wave, the transformation approximation of elastic wave governing equation meets invariance, to when carrying out vibration damping, elastic wave is located at elastic wave direction after the surface feeding sputtering on the path that insulator is propagated to the vibration absorber from the vibration absorber, the direction of propagation of elastic wave bends, elastic wave can be along the internal communication of the vibration absorber to another end face of the vibration absorber, to change the direction of propagation of elastic wave, reduction propagates to the elastic wave for waiting for insulator, to realize vibration damping.Technical scheme of the present invention has significant effectiveness in vibration suppression to the low-frequency elastic wave in 332-1800Hz frequency ranges.

Description

A kind of oscillation damping method, system and vibration absorber for low-frequency elastic wave
Technical field
The present invention relates to antivibration area, more particularly to a kind of oscillation damping method for low-frequency elastic wave, system with And vibration absorber.
Background technology
Vibration damping is in engineering to reduce influence that mechanical oscillation work normally machine, structure or instrumentation, prevent Hazard of vibration and the major measure taken.Vibration damping can be divided into active damping and passive vibration damping.Active damping is also known as positive vibration damping, It is mainly made of vibration detecting device, control device, the action elements such as device, when work consumes extra power, is filled by vibration detecting It sets and detects direction of vibration and kinetic energy first, vibration is offset in control device control action device work done.Passive vibration damping is also known as passiveness and subtracts It shakes, is mainly made of elastic element and damping unit, when work does not consume extra power, only dissipates or temporarily stores energy. Passive vibration damping has vibration isolation and absorbing etc..Vibration isolation can be divided into active vibration isolation and passive vibration isolation again.
When carrying out passive vibration isolation using conventional uniform material, homogeneous material enables itself first order resonance frequency far below excitation frequency Rate, to weaken the excitation from ground.Therefore, the support stiffness of homogeneous material is smaller, and first order resonance frequency is smaller, then subtracts The effect shaken is better.But in some practical engineering application occasions, such as supporting bridge, Payload Attach Fitting etc., it can not Reduction support stiffness simply, at this point, there are the contradictions between support stiffness and vibration damping degree.
The acoustics metamaterial (Acoustic Metamaterial) and phonon crystal of rising in recent years are shaken by being much smaller than The periodic distribution of the micro-structure of dynamic wavelength generates band gap using local resonance phenomenon and Bragg diffraction mechanism, realizes to shaking The isolation of a certain band segment in dynamic frequency spectrum.But this material has that the frequency band of isolation is narrow.
It is that distribution by designing material attribute in space changes the path of elastic wave propagation around wave method, it is enabled to bypass It needs the component of vibration isolation and realizes a kind of method of vibration damping.This method originates from electromagnetic wave and sound wave grinding around wave control aspect Study carefully, i.e., is transformed to original uniform field by transform method follow the bending field of geometric distortion.Due to electromagnetic wave and sound wave side Journey is remained unchanged in the front and back form of transformation, that is, has invariance, it is possible to pass through the one-to-one correspondence of equation before and after transformation Relationship come calculate deformation after material parameter, complete around wave material design.But elastic wave governing equation and electromagnetic wave It is different with the governing equation of sound wave, in uniform field to the transformation of bending field, the elastic wave governing equation form front and back in transformation It will change, that is, do not have the front and back invariance of transformation, so cannot be satisfied the design condition around wave material.Moreover, The frequency of elastic wave is lower, and equation is more unsatisfactory for the requirement of invariance.So traditional transform method is not particularly suited for designing Low-frequency elastic wave around wave material.
Therefore, there is an urgent need for a kind of oscillation damping methods and device suitable for low-frequency elastic wave, are ensureing to wait for needed for insulator Support stiffness while, can efficiently reduce and wait for insulator caused by the low-frequency elastic wave within the scope of broad frequency band Vibration.
Invention content
In view of the above problems, it is proposed that the present invention overcoming the above problem in order to provide one kind or solves at least partly State the oscillation damping method for low-frequency elastic wave of problem and corresponding device.
One side according to the ... of the embodiment of the present invention provides a kind of oscillation damping method for low-frequency elastic wave, suitable for subtracting The vibration for waiting for insulator caused by few elastic wave generated by driving source, including:
The vibration damping with appointed thickness is constructed according to the feature of the elastic wave and the vibration damping demand for waiting for insulator Any two cross section of device, the thickness direction of the vibration absorber is of similar shape, and the vibration absorber also has Two end faces, described two end faces are vertical with the cross section, when the elastic wave is from an end face in described two end faces Be incident to the vibration absorber, along the vibration absorber internal communication to another end face in described two end faces and from When another end face outgoing, the elastic wave is in the direction of propagation of one surface feeding sputtering and the elastic wave in institute The direction of propagation for stating the outgoing of another end face is different;Also, the vibration absorber is made of non-uniform rod material, institute Any cross section for stating the thickness direction of vibration absorber is made of multiple infinitesimals, will be in the multiple infinitesimal in each infinitesimal Material be equivalent to homogeneous material, then the material parameter in each infinitesimal meets the following conditions:Enable the elastic wave from one surface feeding sputtering to the vibration absorber along The internal communication of the vibration absorber another end face described in, wherein λ and G is the equivalent Lame of material in the infinitesimal respectively Lam é first constants and equivalent Lam é second constants, A are that rectangle two-dimensional space is converted into described by conformal mapping The introduced center position pair with the infinitesimal of two-dimensional space of the shape of any cross section of the thickness direction of vibration absorber The characteristic size answered, L ' are the wavelength of the elastic wave;
By the vibration absorber be arranged the elastic wave driving source and it is described wait for insulator between, make the vibration damping At least one of described two end faces of device are located on the path for waiting for insulator propagation described in the elastic wave direction, and make The elastic wave is filled from the surface feeding sputtering on the propagation path of the elastic wave to the vibration damping of the vibration absorber It sets;
Make the elastic wave from the end face of elastic wave incidence by the vibration absorber, along the vibration absorber Internal communication is to another end face of the vibration absorber, and to change the direction of propagation of the elastic wave, reduction propagates to institute The elastic wave for waiting for insulator is stated, to realize the vibration damping to the component.
Optionally, the shape of any cross section of the thickness direction of the vibration absorber includes curved annular.
Optionally, the shape of any cross section of the thickness direction of the vibration absorber is semi-annular shape, the vibration damping dress Each infinitesimal in the multiple infinitesimal in any cross section for the thickness direction set is by each finger in the semicircular ring Determine curved annular region obtained from the corresponding region of segment angle is radially divided, the material parameter in each described infinitesimal Meet the following conditions:Wherein, λ and G is that the equivalent Lam é first of material in the infinitesimal are normal respectively Number and equivalent Lam é second constants, R be the infinitesimal in the cross section central point apart from the center of circle of the semicircular ring away from From L ' is the wavelength of the elastic wave.
Optionally, each in the multiple infinitesimal in any cross section of the thickness direction of the vibration absorber is micro- Member is:
The central angle of the semicircular ring is subjected to m deciles and obtains m segment angle, then will be corresponding to each segment angle Region radially curved annular region obtained from n deciles, wherein m and n is the positive integer more than or equal to 2.
Optionally, the material includes rubber.
Optionally, the vibration absorber is constructed in the following manner:
The first rubber is chosen, the Lam é first constants and Lam é second constants of first rubber are respectively λ1,G1;
The second rubber is chosen, the Lam é first constants and Lam é second constants of second rubber are respectively λ2,G2, wherein λ2≠λ1, G2≠G1;
First rubber and second rubber are kneaded and are molded according to predetermined mixing rule, is obtained by non-equal The vibration absorber with appointed thickness of even isotropic material composition, wherein the thickness direction of the vibration absorber The material parameter in each infinitesimal in any cross section is satisfied by the following conditions:λ=R2λ1, G=R2G1,
Optionally, the vibration absorber is constructed in the following manner:
It chooses the first rubber and by first rubber-moulding, obtains the semi-annular shape matrix with appointed thickness, wherein The Lam é first constants and Lam é second constants of first rubber are respectively λ1,G1;
The second rubber is chosen, the Lam é first constants and Lam é second constants of second rubber are respectively λ2,G2, wherein λ2≠λ1, G2≠G1;
Form multiple hollow micro-structures on the matrix according to pre-defined rule;
Second rubber is fed into the micro-structure, obtain by non-uniform rod material form described in subtract Vibrating device, wherein the material parameter in each infinitesimal in any cross section of the thickness direction of the vibration absorber is full Sufficient the following conditions:λ=R2λ1, G=R2G1,
Optionally, the micro-structure is through-hole or slot.
Another aspect according to the ... of the embodiment of the present invention additionally provides a kind of vibration absorber for low-frequency elastic wave, is applicable in In the vibration for waiting for insulator caused by the elastic wave that reduction is generated by driving source, the vibration absorber is according to the elasticity The feature of wave and the vibration damping demand for waiting for insulator construct, and have appointed thickness, the thickness side of the vibration absorber To any two cross section be of similar shape, the vibration absorber also has there are two end face, described two end faces and institute State that cross section is vertical, when the elastic wave is from a surface feeding sputtering in described two end faces to the vibration absorber, along described The internal communication of vibration absorber is described to another end face in described two end faces and when being emitted from another described end face The direction of propagation that elastic wave is emitted in the direction of propagation of one surface feeding sputtering and the elastic wave in another described end face It is different;Also, the vibration absorber is made of non-uniform rod material, any of the thickness direction of the vibration absorber Cross section is made of multiple infinitesimals, and the material in the multiple infinitesimal in each infinitesimal is equivalent to homogeneous material, then this is every Material parameter in one infinitesimal meets the following conditions:So that from one surface feeding sputtering to The elastic wave of the vibration absorber can be along the internal communication of the vibration absorber another end face described in, wherein λ and G is the equivalent Lam é first constants of material in the infinitesimal and equivalent Lam é second constants respectively, and A is will by conformal mapping Rectangle two-dimensional space is converted into the two-dimensional space institute of the shape of any cross section of the thickness direction with the vibration absorber The characteristic size corresponding with the center position of the infinitesimal introduced, L ' is the wavelength of the elastic wave;
When carrying out vibration damping, by the vibration absorber be arranged driving source in the elastic wave with it is described wait for insulator it Between, so that at least one of described two end faces of the vibration absorber is located at described in the elastic wave direction and waits for that insulator is propagated Path on, and make surface feeding sputtering positioned at the propagation path of the elastic wave on of the elastic wave from the vibration absorber To the vibration absorber, makes the elastic wave from the end face of elastic wave incidence by the vibration absorber, subtract along described The internal communication of vibrating device is to another end face of the vibration absorber, to change the direction of propagation of the elastic wave, reduces The elastic wave for waiting for insulator is propagated to, to realize the vibration damping to the component.
Another aspect according to the ... of the embodiment of the present invention additionally provides a kind of vibration insulating system for low-frequency elastic wave, is applicable in In the vibration for waiting for insulator caused by the elastic wave that reduction is generated by driving source, the vibration insulating system includes:
Structural unit is suitable for:Had according to the feature of the elastic wave and the vibration damping demand construction for waiting for insulator Any two cross section of the vibration absorber of appointed thickness, the thickness direction of the vibration absorber is of similar shape, described Vibration absorber also has there are two end face, and described two end faces are vertical with the cross section, when the elastic wave is from described two ends A surface feeding sputtering in face is to the vibration absorber, along the internal communication to described two end faces of the vibration absorber Another end face and when being emitted from another described end face, the elastic wave the direction of propagation of one surface feeding sputtering with The elastic wave is different in the direction of propagation that another described end face is emitted;Also, the vibration absorber is from non-homogeneous respectively to same Property material composition, any cross section of the thickness direction of the vibration absorber is made of multiple infinitesimals, will be in the multiple infinitesimal Material in each infinitesimal is equivalent to homogeneous material, then the material parameter in each infinitesimal meets the following conditions:Enable the elastic wave from one surface feeding sputtering to the vibration absorber along The internal communication of the vibration absorber another end face described in, wherein λ and G is the equivalent Lam é of material in the infinitesimal respectively First constant and equivalent Lam é second constants, A are that rectangle two-dimensional space is converted into the vibration damping by conformal mapping The two-dimensional space of the shape of any cross section of the thickness direction of device is introduced corresponding with the center position of the infinitesimal Characteristic size, L ' are the wavelength of the elastic wave;
Setting unit is suitable for:The driving source in the elastic wave is arranged in the vibration absorber and waits for insulator with described Between, so that at least one of described two end faces of the vibration absorber is located at described in the elastic wave direction and waits for that insulator passes On the path broadcast, and the elastic wave is made to enter from the end face on the propagation path of the elastic wave of the vibration absorber It is incident upon the vibration absorber;And
The direction of propagation changes unit, is suitable for:Make the elastic wave from elastic wave incidence by the vibration absorber End face, along the internal communication of the vibration absorber to another end face of the vibration absorber, to change the elastic wave The direction of propagation, reduce and propagate to the elastic wave for waiting for insulator, to realize the vibration damping to the component.
Optionally, the shape of any cross section of the thickness direction of the vibration absorber includes curved annular.
Optionally, the shape of any cross section of the thickness direction of the vibration absorber is semi-annular shape, the vibration damping dress Each infinitesimal in the multiple infinitesimal in any cross section for the thickness direction set is by each finger in the semicircular ring Determine curved annular region obtained from the corresponding region of segment angle is radially divided, the material parameter in each described infinitesimal Meet the following conditions:Wherein, λ and G is the equivalent Lam é first constants of material in the infinitesimal respectively With equivalent Lam é second constants, R be the infinitesimal in the cross section central point apart from the center of circle of the semicircular ring away from From L ' is the wavelength of the elastic wave.
Optionally, each in the multiple infinitesimal in any cross section of the thickness direction of the vibration absorber is micro- Member is:
The central angle of the semicircular ring is subjected to m deciles and obtains m segment angle, then will be corresponding to each segment angle Region radially curved annular region obtained from n deciles, wherein m and n is the positive integer more than or equal to 2.
Optionally, the material includes rubber.
Optionally, the structural unit is further adapted for:
The first rubber is chosen, the Lam é first constants and Lam é second constants of first rubber are respectively λ1,G1;
The second rubber is chosen, the Lam é first constants and Lam é second constants of second rubber are respectively λ2,G2, wherein λ2≠λ1, G2≠G1;
First rubber and second rubber are kneaded and are molded according to predetermined mixing rule, is obtained by non-equal The vibration absorber with appointed thickness of even isotropic material composition, wherein the thickness direction of the vibration absorber The material parameter in each infinitesimal in any cross section is satisfied by the following conditions:λ=R2λ1, G=R2G1,
Optionally, the structural unit is further adapted for:
It chooses the first rubber and by first rubber-moulding, obtains the semi-annular shape matrix with appointed thickness, wherein The Lam é first constants and Lam é second constants of first rubber are respectively λ1,G1;
The second rubber is chosen, the Lam é first constants and Lam é second constants of second rubber are respectively λ2,G2, wherein λ2≠λ1, G2≠G1;
Form multiple hollow micro-structures on the matrix according to pre-defined rule;
Second rubber is poured into the micro-structure, the vibration damping being made of non-uniform rod material is obtained Device, wherein the material parameter in each infinitesimal in any cross section of the thickness direction of the vibration absorber is satisfied by The following conditions:λ=R2λ1, G=R2G1,
Optionally, the micro-structure is through-hole or slot.
The technical solution of the embodiment of the present invention is suitable for the vibration damping environment of low-frequency elastic wave.According to the feature of elastic wave and Vibration damping demand constructs vibration absorber, is designed to the shape, size and material parameter of vibration absorber so that described in use When communication space of the vibration absorber as elastic wave, the transformation approximation of elastic wave governing equation meets invariance, and then is carrying out When vibration damping, the vibration absorber is arranged in the driving source of elastic wave and between waiting for insulator, the vibration absorber is made to have At least one of two end faces be located on the path that elastic wave direction waits for that insulator is propagated, and make elastic wave from the vibration damping Device after the surface feeding sputtering to the vibration absorber on the propagation path of elastic wave, the direction of propagation of elastic wave occurs Bending, elastic wave can be along the internal communication of the vibration absorber to another end face, to change the propagation side of elastic wave To reduction propagates to the elastic wave for waiting for insulator, to realize vibration damping.Statistics indicate that the technical solution of the embodiment of the present invention with The scheme that vibration damping is carried out using the homogeneous material of same support stiffness is compared, to the low frequency bullet in 332-1800Hz frequency ranges Property wave have significant effectiveness in vibration suppression.
Above description is only the general introduction of technical solution of the present invention, in order to better understand the technical means of the present invention, And can be implemented in accordance with the contents of the specification, and in order to allow above and other objects of the present invention, feature and advantage can It is clearer and more comprehensible, below the special specific implementation mode for lifting the present invention.
According to the following detailed description of specific embodiments of the present invention in conjunction with the accompanying drawings, those skilled in the art will be brighter The above and other objects, advantages and features of the present invention.
Description of the drawings
By reading the detailed description of hereafter preferred embodiment, various other advantages and benefit are common for this field Technical staff will become clear.Attached drawing only for the purpose of illustrating preferred embodiments, and is not considered as to the present invention Limitation.And throughout the drawings, the same reference numbers will be used to refer to the same parts.In the accompanying drawings:
Fig. 1 is the schematic diagram for the field u ' for converting front and back uniform field u and bending;
Fig. 2 is the two-dimentional object of the rectangle two-dimensional virtual space that conformal mapping is related in the embodiment of the present invention and arbitrary shape Manage the schematic diagram in space;
Fig. 3 shows the flow chart of the oscillation damping method according to an embodiment of the invention for low-frequency elastic wave;
Fig. 4 shows the stereoscopic schematic diagram of the vibration absorber constructed according to one embodiment of the invention;
Fig. 5 is the schematic diagram of any cross section of the thickness direction of vibration absorber shown in Fig. 4;
Fig. 6 shows the schematic diagram that elastic wave longitudinal wave is propagated in uniform rectangle Virtual Space, and is meeting Under conditions of propagate in the semi-annular shape two-dimensional physical space of elastic wave longitudinal wave after transformation show It is intended to;
Fig. 7 shows multiple in any semi-annular shape cross section of the thickness direction of the vibration absorber of one embodiment of the invention The distribution schematic diagram of infinitesimal;
Fig. 8 shows the multiple row of the radial arrangement formed on semi-annular shape matrix according to pre-defined rule in embodiment 2 The distribution schematic diagram of through-hole;
Fig. 9 show in embodiment 3 formed on semi-annular shape matrix according to pre-defined rule it is arranged in parallel multiple rows of logical The distribution schematic diagram in hole;
Figure 10 shows the distribution signal of the multiple slots formed on semi-annular shape matrix according to pre-defined rule in embodiment 4 Figure;
Figure 11 shows a kind of showing for concrete application scene of the oscillation damping method for low-frequency elastic wave according to embodiment 4 It is intended to;
Figure 12 is the comparison diagram of the time-domain signal after the scheme of embodiment 4 and comparative example carries out vibration damping;
Figure 13 is the comparison diagram of the frequency-region signal after the scheme of embodiment 4 and comparative example carries out vibration damping;And
Figure 14 shows the structural schematic diagram of the vibration insulating system according to an embodiment of the invention for low-frequency elastic wave.
Specific implementation mode
The exemplary embodiment of the disclosure is more fully described below with reference to accompanying drawings.Although showing the disclosure in attached drawing Exemplary embodiment, it being understood, however, that may be realized in various forms the disclosure without should be by embodiments set forth here It is limited.On the contrary, these embodiments are provided to facilitate a more thoroughly understanding of the present invention, and can be by the model of the disclosure It encloses and is completely communicated to those skilled in the art.
In the prior art, damper is one of most common vibration damping means.But in the vibration damping environment of low-frequency elastic wave In, since the wavelength of low-frequency elastic wave is larger, diffraction phenomenon may occur for elastic wave and damping is very low, to make damper Due effectiveness in vibration suppression can not be played.
It can change the path of elastic wave propagation by controlling attribute or the structure of material around wave method, enable it around needing It wants the component of vibration isolation and realizes vibration damping.But due to the complexity of elastic wave, the propagation for controlling elastic wave is a rhetorical question for being difficult Topic.Inventor has found, the propagation problem of the transform method occurred in recent years elastic wave in order to control, which provides a kind of new solution, to be thought Road.If borrowing the theory of Continuum Mechanics to describe the deformation in space, transform method is that the field that can be measured is enabled to become It is constant to measure the covariant component of u ' and u in the embedded curvilinear coordinate system of the front and back Lagrange (Lagrange) of transformation, i.e. ui'= ui, physical significance is that and then coordinate grid distorts vector u together.By this transformation, original uniform field u is made to follow Geometric distortion becomes the field u ' of bending.The field of the front and back uniform field u of transformation (as shown in (a)) and bending is shown in Fig. 1 The schematic diagram of u ' (as shown in (b)).Shown in the front and back equation expression formula such as formula (1) of transformation:
Wherein, GiAnd giThe front and back curvilinear coordinate base vector of transformation is indicated respectively.At this point, if equation is in transformation front and back Form is constant, so that it may to calculate the material parameter after deformation by one-to-one relationship, to complete the design around wave material.
But the governing equation of elastic wave and do not have this formal fixity.In order to by being carried out to elastic wave The method of transformation come solve the problem of how the propagation that designing material controls elastic wave, need to make the control of elastic wave by processing Equation approximation processed meets invariance.
LN equations (Lam é-Navier Equation, Lame-navier's equation) are elastic waves using displacement as the control of independent variable Equation processed.Inventor has found, the corresponding functional variation equations of finite element scheme of LN equations can more easily handle it is non- Even and anisotropic problem.Shown in the functional variation equation such as formula (2) of above-mentioned LN equations:
Wherein, ε indicates that strain tensor, D indicate that elasticity tensor, ρ indicate that density, μ indicate that damped coefficient, f indicate muscle power, T Expression face power.
The functional variation equation of LN equations shown in formula (2) is derived below in transformation u '=F-TEquation expression formula after u.
In transformation u '=F-TIn u, F is deformation gradient, and component of the transformation in rectangular coordinate system in space is
Relationship before and after the transformation for the field variable u that determination can be observed firstIt will transformation With constitutive relation Dijkl=λ δijδkl+G(δikδjl+δilδjk) substitute into formula (2) obtain the equation as shown in formula (3):
In above formula (3), Extra is the redundant term of the equation (3) after transformation, shown in the expression formula such as formula (4) of redundant term:
Wherein, Bsδur=δ ur,s+δus,r。
By the condition for introducing conformal mappingWithExtra can be reduced to one, As shown in formula (5):
Comparison expression (2) with formula (3) it is found that Extra compared with other in equation (3) after transformation, equation after the conversion (3) shared proportion is smaller in, then the form of equation (3) and transformation front journey (2) is closer to consistent after converting.It may be used Its remainder weighs the size of Extra proportions with Extra ratio in equation (3) after transformation, particularly preferably, Using first item δ ε ' in equation after transformation (3)ijD′ijklε′klThe big of Extra proportions is weighed with Extra ratio It is small.δε′ijD′ijklε′klExpansion such as following formula (6) shown in:
δε′ijD′ijklε′kl=λ ' ε 'iiδε′kk+G′(ε′ijδε′ij+ε′ijδε′ji) (6)
Determine after transformation its remainder in equation (3) with Extra ratio by what factor below by magnitude Analysis It influences.Particularly, by first item δ ε ' in equation after transformation (3)ijD′ijklδ′klRatio with Extra carries out magnitude point Analysis, the results show that the δ ε ' as shown in formula (6)ijD′ijklε′klExpansion in two λ ' ε 'iiδε′kkWith G ' (ε 'ijδε′ij + ε′ijδε′ji) respectively with shown in Extra ratio such as formulas (7):
Wherein,Related with the form of conformal mapping, this is 1 in the problem of the present invention.λ and G is material respectively Lam é (Lame) first constants and Lam é second constants, they are similar with Poisson's ratio v with the elastic modulus E of material two A unrelated amount.Shown in the specific conversion relation such as formula (8) and formula (9) of λ and G and elastic modulus E and Poisson's ratio v:
A is the characteristic size that conformal mapping introduces, and L ' is the wavelength of elastic wave.Conformal mapping is to meet conditionWithA kind of transformation, x=AC (X) can be write, wherein X be homogeneous material constitute Rectangle two-dimensional virtual space dimensionless coordinate, x is that the two-dimensional physical for the arbitrary shape being made of material to be designed is empty Between space coordinate, change commanders after two-dimensional virtual spatial alternation to two-dimensional physical space by C changes, the use of characteristic size A be two Tie up the length unit of the coordinate imparting of physical space physically.Characteristic size A is scalar related with coordinate position, Ke Yishi Rice, millimeter or certain specific length.The rectangle two-dimensional virtual space referred to Fig. 2 shows above-mentioned conformal mapping and arbitrary shape The schematic diagram in the two-dimensional physical space of shape.It should be noted that the shape in two-dimensional physical space shown in fig. 2 is only shown Meaning property, in practical applications, the shape in two-dimensional physical space can be the arbitrary shape obtained by conformal mapping.
As it can be seen thatWithThe two ratios are bigger, illustrate that the proportion shared by Extra is smaller, convert the shape of front and back equation Formula more approaches unanimously, and the effect of transformation is better.Therefore, it is reasonable to be carried out by material parameter to vibration absorber and shape, size Design, makeThe requirement to transform effect can be met, make elastic wave in designed vibration damping Propagation path bends and realizes vibration damping when being propagated in device.Especially in the environment for requiring low frequency vibration damping, due to low frequency The wavelength of elastic wave is larger, as the λ > > of material, can farthest ensure the effect of transformation.
Based on above-mentioned technical concept, the embodiment of the present invention proposes a kind of oscillation damping method for low-frequency elastic wave, is applicable in In the vibration for waiting for insulator caused by the elastic wave that reduction is generated by driving source.Fig. 3 is shown to be implemented according to the present invention one The flow chart of the oscillation damping method for low-frequency elastic wave of example.Referring to Fig. 3, which may comprise steps of S302 To step S306.
Step S302 according to the feature of elastic wave and waits for that the vibration damping demand of insulator constructs the vibration damping with appointed thickness Any two cross section of device, the thickness direction of vibration absorber is of similar shape, vibration absorber also have there are two end Face, two end faces are vertical with the cross section, when elastic wave is from a surface feeding sputtering in two end faces to vibration absorber, edge The internal communication of vibration absorber from another end face to another end face in two end faces and when being emitted, and elastic wave is at one The direction of propagation of surface feeding sputtering is different from the direction of propagation that elastic wave is emitted in another end face;Also, vibration absorber is by non-equal Even isotropic material composition, any cross section of the thickness direction of vibration absorber are made of multiple infinitesimals, will be in multiple infinitesimals Material in each infinitesimal is equivalent to homogeneous material, then the material parameter in each infinitesimal meets the following conditions:Enable elastic wave from a surface feeding sputtering to vibration absorber along the inside of vibration absorber Travel to another end face, wherein λ and G is the equivalent Lam é first constants and equivalent Lam é second of material in the infinitesimal respectively Constant, A are any cross sections that rectangle two-dimensional space is converted into the thickness direction with vibration absorber by conformal mapping Shape the introduced characteristic size corresponding with the center position of the infinitesimal of two-dimensional space, L ' is the wavelength of elastic wave.
Vibration absorber is arranged in the driving source of elastic wave and between waiting for insulator, makes vibration absorber by step S304 At least one of two end faces are located on the path that elastic wave direction waits for that insulator is propagated, and make elastic wave from vibration absorber Surface feeding sputtering on the propagation path of elastic wave is to vibration absorber.
Step S306 makes elastic wave from the end face of elastic wave incidence, is passed along the inside of vibration absorber by vibration absorber It is multicast to another end face of vibration absorber, to change the direction of propagation of elastic wave, reduction propagates to the elasticity for waiting for insulator Wave, to realize the vibration damping to the component.
The oscillation damping method of the embodiment of the present invention is suitable for the vibration damping environment of low-frequency elastic wave.According to the feature of elastic wave and Vibration damping demand constructs vibration absorber, is designed to the shape, size and material parameter of vibration absorber so that subtract when using this When communication space of the vibrating device as elastic wave, the transformation approximation of elastic wave governing equation meets invariance, and then is being subtracted When shaking, the vibration absorber constructed is arranged in the driving source of elastic wave and between waiting for insulator, vibration absorber is made to be had At least one of two end faces be located on the path that elastic wave direction waits for that insulator is propagated, and make elastic wave from vibration absorber After the surface feeding sputtering to vibration absorber on the propagation path of elastic wave, the direction of propagation of elastic wave bends, elasticity The enough internal communications along vibration absorber of wave energy are to another end face, and to change the direction of propagation of elastic wave, reduction propagates to The elastic wave for waiting for insulator, to realize vibration damping.
In above step S302, vibration absorber is constructed according to the feature of elastic wave and vibration damping demand, to the shape of vibration absorber Shape, size and material parameter are designed.The feature of elastic wave includes frequency, wavelength, spread speed etc..Fig. 4 shows basis The stereoscopic schematic diagram of the vibration absorber 400 of construction of the embodiment of the present invention.Shown in Figure 4, vibration absorber 400 has specified thickness Degree, the numerical value of thickness depend on the requirement to the enabling capabilities of vibration absorber 400.The thickness direction of vibration absorber 400 is (herein Thickness direction is y-axis direction shown in Fig. 4) any two cross section be of similar shape.Vibration absorber 400 also has There are two end face 401 and 402, end face 401 and 402 is vertical with above-mentioned cross section.The shape of vibration absorber 400 designs so that working as From a surface feeding sputtering in end face 401 and 402 to vibration absorber 400, the internal communication along vibration absorber 400 arrives elastic wave Another end face in end face 401 and 402 and when being emitted from another end face, elastic wave is in the propagation side of a surface feeding sputtering It is different to the direction of propagation being emitted in another end face from elastic wave.Also, vibration absorber 400 is by non-uniform rod material Material composition.In practical applications, for the ease of design, any cross section of the thickness direction of vibration absorber 400 is divided into multiple Infinitesimal, the material in each infinitesimal are equivalent to homogeneous material.Above mentioned infinitesimal is the thickness direction of vibration absorber 400 Any cross section on tiny area, the cross section of the division of infinitesimal depending on the thickness direction of vibration absorber 400 The direction of propagation of shape and desirable elastic wave in vibration absorber 400.Multiple infinitesimal is along desirable elastic wave The direction of propagation in vibration absorber 400, the close-packed arrays between end face 401 and 402.Pass through the material to each infinitesimal The design of parameter so that the material parameter in each infinitesimal in any cross section of the thickness direction of vibration absorber 400 Meet So that from a surface feeding sputtering in end face 401 and 402 to vibration absorber 400 Elastic wave can be along the internal communication of vibration absorber 400 to another end face.In a kind of optional embodiment, this refers to Fixed number value is in the range of 10 to 100 so that is converted into vibration absorber by the field variable in rectangle two-dimensional space During field variable in the two-dimensional space of the shape of any cross section of 400 thickness direction, the LN equations of elastic wave Functional variation equation is constant in the front and back formal approximation of transformation, to make the propagation path of elastic wave along vibration absorber 400 Inside bends, and changes the direction of propagation of elastic wave.
Fig. 5 shows the schematic diagram of any cross section of the thickness direction of vibration absorber 400 shown in Fig. 4.In Fig. 5 also with Dotted line shows several infinitesimals in above-mentioned multiple infinitesimals.It should be noted that vibration damping dress shown in fig. 5 The shape for setting the cross section of 400 thickness direction (that is, y-axis direction shown in Fig. 4) is only illustrative, in practical application In, the shape of the cross section can meet the arbitrary shape for making the direction of propagation of elastic wave change.Correspondingly, in Fig. 5 Shown in quantity, shape and the arrangement mode of infinitesimal be also only illustrative, in practical applications, the division of infinitesimal can root It is flexibly carried out according to the shape of the cross section of the thickness direction of vibration absorber and the direction of propagation of desirable elastic wave.
In a preferred embodiment, the shape of the cross section of the thickness direction of vibration absorber 400 includes arc ring Shape, for example, fan-shaped annulus etc..
In a kind of preferred embodiment, the shape of the cross section of the thickness direction of vibration absorber 400 is semicircular ring Shape.
The case where shape below for the cross section of the thickness direction of vibration absorber 400 is semi-annular shape discusses and how to set Count the material parameter of vibration absorber 400.
Consider one block of uniform rectangle material as Virtual Space, incident and outgoing both sides boundaries in two-dimensional space Exact Solution is arranged, and waveform does not change when so that elastic wave longitudinal wave is propagated from left to right, and reaching right end.Pass through Conformal mapping ζ (z)=ezAbove-mentioned uniform rectangle Virtual Space is transformed into the thickness direction with vibration absorber 400 The two-dimensional physical space of the shape of semi-annular shape cross section, at this point, after the functional variation equation transformation of the LN equations of elastic wave Its remainder as shown in formula (7) and the form that embodies of Extra ratio are converted into as shown in formula (10):
Wherein, λ and G is the Lam é first of material at every bit in the semi-annular shape two-dimensional physical space after transformation respectively Constant and Lam é second constants, R are that distance of this apart from the center of circle, L ' are elastic waves in semi-annular shape two-dimensional physical space Wavelength.
In order to which make still can be as one in rectangle Virtual Space in the two-dimensional physical space of elastic wave after transformation Sample passes through propagation, and waveform does not change, that is, the invariance for meeting transformation needs to reduce transformation to the greatest extent The influence of the Extra items of generation.It is more than specified numerical value by any one of formula (10), the LN equations of elastic wave can be made Functional variation equation approximation meet transformation invariance.Under low frequency environments, due to the λ > > of material, then Always it is more thanIt is therefore preferable that enablingOptionally, the specified range of the numerical value 10 to 100 It is interior.At this point, i.e. it is believed that Extra influences can be ignored, in the two-dimensional physical space of elastic wave after transformation still Can so pass through propagation, and waveform does not change.It is calculated to simplify, by ratioSimplify ForFig. 6 shows the schematic diagram that elastic wave longitudinal wave is propagated in uniform rectangle Virtual Space, and full FootUnder conditions of propagate in the semi-annular shape two-dimensional physical space of elastic wave longitudinal wave after transformation Schematic diagram.Although it should be noted that being only discussed in the case of longitudinal wave propagation above, (also known as shear wave For shearing wave) it is equally applicable.
Under conditions of the functional variation equation approximation of the LN equations of elastic wave meets the invariance of transformation, it can obtain State the relativeness such as formula between the material parameter in the two-dimensional physical space after uniform rectangle Virtual Space and transformation (11) shown in:
Wherein, λ0,G0,ρ0It is Lam é first constants, Lam é second constants and the density of material in Virtual Space, ρ respectively It is the density of material in physical space, the meaning of λ, G and R are same as above.Physics sky is arbitrarily chosen according to the proportionate relationship in formula (11) Between in λ, G and ρ, and ensureThe functional variation equation of the LN equations of elastic wave can be made close Like the invariance for meeting transformation, to complete the design and construction of vibration absorber.
In λ, G and ρ in choosing physical space, it is contemplated that density of material not malleable can set ρ=ρ0, then basis The relativeness of formula (11) can derive λ=R2λ0, G=R2G0, then can be in this, as the parameter distribution mode of material The functional variation equation approximation for designing the LN equations for elastic wave of sening as an envoy to meets the non-uniform rod material of the invariance converted.
In actual non-uniform rod design of material, for the ease of design, by the thickness direction of vibration absorber Any cross section is divided into multiple infinitesimals, and the material in each infinitesimal is equivalent to homogeneous material.In the thickness direction of vibration absorber Any cross section shape be semi-annular shape in the case of, each infinitesimal in above-mentioned multiple infinitesimals is by the semicircular ring Curved annular region obtained from the corresponding region of interior each specified segment angle is radially divided.It is highly preferred that above-mentioned multiple micro- Each infinitesimal in member is:The central angle of the semicircular ring is subjected to m deciles and obtains m segment angle, then by each segment angle institute Corresponding region radially curved annular region obtained from n deciles, wherein m and n is the positive integer more than or equal to 2.It is logical Cross the design to the material parameter of each infinitesimal so that the material parameter in each infinitesimal meets λ=R2λ0, G=R2G0, ρ=ρ0, andThe functional variation equation of the LN equations for elastic wave of sening as an envoy to can easily be designed Approximation meets the non-uniform rod material of the invariance of transformation.At this point, λ and G be respectively in each infinitesimal material etc. It is the central point range semicircle ring of each infinitesimal in the cross section to imitate Lam é first constants and equivalent Lam é second constants, R The center of circle distance, L ' is the wavelength of elastic wave.Fig. 7 shows that any semi-annular shape of the thickness direction of vibration absorber is transversal The distribution schematic diagram of multiple infinitesimals in face, wherein by a plurality of circumferential dotted line and a plurality of radial dotted line by the semi-annular shape cross section It is divided into multiple arcs annular section, each curved annular region represents an infinitesimal.It should be noted that in the figure 7 Shown in infinitesimal quantity and size be only illustrative, be not construed as limiting the invention, in practical applications can root According to actual design requirement flexible configuration.
In the alternative embodiment of the present invention, non-uniform rod material includes rubber.
It is mentioned above, as the λ > > of material, Extra influences can be reduced to the greatest extent, make the LN equations of elastic wave Functional variation equation approximation meets the invariance of transformation.It is non-since the Poisson's ratio v of rubber type of material is generally between 0.45-0.5 Very close to 0.5, according to formula (8) and formula (9) it is found that the λ > > of ordinary rubber.Further, due to the rubber of most of types Density all in 1.0-1.3kg/m3Between, the density of different types of rubber is sufficiently close to and the difference of their elasticity modulus It Xiang Bi not can be ignored, substantially meet the constant setting of above-mentioned density.Therefore, a variety of rubber is selected to construct the present invention The vibration absorber being made of non-uniform rod material is more advantageous to the effect for meeting transformation, to change the biography of elastic wave Path is broadcast to realize vibration damping.Preferably, by being distributed come structure using the different ratio of two kinds of rubber in the direction of propagation of elastic wave It makes and meets the non-uniform rod material that the above material parameter requires.It specifically, can be by being kneaded, punching perfusion, cut slot The modes such as perfusion realize on the direction of propagation of elastic wave the different volumes ratio distribution of two kinds of rubber.
In the alternative embodiment of the present invention, rubber used includes silicon rubber, natural rubber etc..
In the alternative embodiment of the present invention, it can construct and to be made of non-uniform rod material in the following manner Vibration absorber:
The first rubber is chosen, the Lam é first constants and Lam é second constants of the first rubber are respectively λ1,G1;
The second rubber is chosen, the Lam é first constants and Lam é second constants of the second rubber are respectively λ2,G2, wherein λ2≠ λ1, G2≠G1;
The first rubber and the second rubber are kneaded and are molded according to predetermined mixing rule, is obtained from non-homogeneous respectively to same Property material composition the vibration absorber with appointed thickness, it is wherein every in any cross section of the thickness direction of vibration absorber Material parameter in one infinitesimal is satisfied by the following conditions:λ=R2λ1, G=R2G1,
In another alternative embodiment of the present invention, it can also construct in the following manner by non-uniform rod material The vibration absorber of composition:
It chooses the first rubber and by the first rubber-moulding, the semi-annular shape matrix with appointed thickness is obtained, wherein first The Lam é first constants and Lam é second constants of rubber are respectively λ1,G1;
The second rubber is chosen, the Lam é first constants and Lam é second constants of the second rubber are respectively λ2,G2, wherein λ2≠ λ1, G2≠G1;
Multiple hollow micro-structures are formed on matrix according to pre-defined rule;
Second rubber is fed into multiple micro-structures, the vibration absorber being made of non-uniform rod material is obtained, The material parameter in each infinitesimal wherein in any cross section of the thickness direction of vibration absorber is satisfied by the following conditions:λ =R2λ1, G=R2G1,
Optionally, which is through-hole or slot.
In above step S304, by the vibration absorber constructed be arranged elastic wave driving source and wait for insulator it Between, so that at least one of two end faces of vibration absorber is located on the path that elastic wave direction waits for that insulator is propagated, and make elasticity Wave is from the surface feeding sputtering on the propagation path of elastic wave of vibration absorber to vibration absorber.Herein, the incidence angle of elastic wave Degree, that is, angle of the elastic wave between the direction of propagation of its incident endface and the normal of its incident end face, can be 0 It spends to any angle within the scope of 90 degree, the invention is not limited in this regard.
In above step S306, make elastic wave from the end face of elastic wave incidence by vibration absorber, along vibration absorber Internal communication is to another end face of vibration absorber.After elastic wave reaches another end face, it will usually which some is transmitted Vibration absorber, a part are reflected back vibration absorber.After reaching incident end face usually again part can occur for reflected elastic wave Transmission and part are reflected.Therefore, elastic wave can constantly turn back in vibration absorber, to make elastic wave constantly decay.
A variety of realization methods of the links of embodiment illustrated in fig. 3 are described above, specific embodiment will be passed through below The realization process of the oscillation damping method for low-frequency elastic wave of the invention is discussed in detail.
Embodiment 1
The oscillation damping method for low-frequency elastic wave of the embodiment of the present invention is suitable for reducing the elastic wave generated by driving source The caused vibration for waiting for insulator, concrete scheme include the following steps a) to step c).
A) according to the feature of elastic wave and waiting for that the vibration damping demand of insulator constructs the vibration absorber with appointed thickness, subtract Any two cross section of the thickness direction of vibrating device is of similar shape, and the shape of the cross section is semi-annular shape, is subtracted Vibrating device also has there are two end face, and two end faces are vertical with the cross section, when elastic wave is from an end face in two end faces It is incident to vibration absorber, the internal communication along vibration absorber goes out to another end face in two end faces and from another end face When penetrating, elastic wave is different from the direction of propagation that elastic wave is emitted in another end face in the direction of propagation of a surface feeding sputtering;And And vibration absorber is made of non-uniform rod rubber, any cross section of the thickness direction of vibration absorber is by multiple infinitesimals It forms, each infinitesimal in multiple infinitesimal is that semicircular ring is first obtained 18 segment angles by central angle 18 deciles of progress to be 10 ° of fan-shaped ring region, then by each fan-shaped ring region radially obtained curved annular region of 12 deciles, it will Material in each infinitesimal is equivalent to homogeneous material, then the material parameter in each infinitesimal meets the following conditions:Enable elastic wave from a surface feeding sputtering to vibration absorber along vibration absorber internal communication to Another end face, wherein λ and G is the equivalent Lam é first constants of material in the infinitesimal and equivalent Lam é second constants, R respectively It is the distance in the center of circle of the central point range semicircle ring of the infinitesimal in the cross section, L ' is the wavelength of elastic wave.
B) vibration absorber constructed is arranged in the driving source of elastic wave and between waiting for insulator, makes vibration absorber At least one of two end faces are located on the path that elastic wave direction waits for that insulator is propagated, and make elastic wave from vibration absorber End face vertical incidence on the propagation path of elastic wave is to vibration absorber.
C) make elastic wave from the end face of elastic wave incidence by vibration absorber, along the internal communication of vibration absorber to vibration damping Another end face of device, to change the direction of propagation of elastic wave, reduction propagates to the elastic wave for waiting for insulator, with reality Now to the vibration damping of the component.
Specifically, the vibration absorber is constructed in the embodiment of the present invention in the following manner:
The first step chooses the first rubber, and the Lam é first constants and Lam é second constants of first rubber are respectively λ1, G1。
Second step chooses the second rubber, and the Lam é first constants and Lam é second constants of second rubber are respectively λ2, G2, wherein λ2≠λ1, G2≠G1。
Third walks, and according to the material parameter of two kinds of rubber, chooses the mixing of 12 groups of specific first rubber and the second rubber Volume ratio is kneaded, and a series of rubber compounds are obtained, and the effective material parameters λ and G between these rubber compounds are different.
These rubber compounds are collapsed into type according to certain regular place Min layers, obtain the vibration damping with appointed thickness by the 4th step Device, on any cross section of the thickness direction of the vibration absorber, the effective material parameters λ and G of infinitesimal are inside from outer toroid The direction of annulus is gradually reduced, and the material in each infinitesimal in any cross section of the thickness direction of vibration absorber Parameter is satisfied by the following conditions:λ=R2λ1, G=R2G1,
Embodiment 2
The concrete scheme of the oscillation damping method for low-frequency elastic wave of the embodiment of the present invention is same as Example 1, only in addition to Vibration absorber is constructed in the present embodiment in the following manner:
The first step chooses the first rubber and by the first rubber-moulding, obtains the semi-annular shape matrix with appointed thickness, In the first rubber Lam é first constants and Lam é second constants be respectively λ1,G1。
Second step chooses the second rubber, and the Lam é first constants and Lam é second constants of the second rubber are respectively λ2,G2, Wherein λ2<λ1, G2<G1。
Third walks, and forms the multiple row through-hole radially arranged on semi-annular shape matrix according to pre-defined rule.
Fig. 8 shows that the distribution of the multiple row through-hole formed on semi-annular shape matrix according to pre-defined rule in the present embodiment is shown It is intended to.Shown in Figure 8, the multiple row through-hole is radially evenly distributed, and each row are made of multiple through-holes, each through-hole edge The thickness direction of semi-annular shape matrix extends, in each column, according to the side in the center of circle of the thoughtful semicircular ring of outer circle from semicircular ring To the diameter of through-hole gradually increases, and the distance between two neighboring through-hole is gradually reduced.
Second rubber is fed into multiple through-hole by the 4th step, obtains being subtracted by what non-uniform rod material formed Vibrating device, the wherein material parameter in each infinitesimal in any cross section of the thickness direction of vibration absorber be satisfied by with Lower condition:λ=R2λ1, G=R2G1,
Embodiment 3
The concrete scheme of the oscillation damping method for low-frequency elastic wave of the embodiment of the present invention is same as Example 1, only in addition to Vibration absorber is constructed in the present embodiment in the following manner:
The first step chooses the first rubber and by the first rubber-moulding, obtains the semi-annular shape matrix with appointed thickness, In the first rubber Lam é first constants and Lam é second constants be respectively λ1,G1。
Second step chooses the second rubber, Lam é first constants of the second rubber and be respectively λ with Lam é second constants2, G2, wherein λ2<λ1, G2<G1。
Third walks, and forms multiple rows of through-hole arranged in parallel on semi-annular shape matrix according to pre-defined rule.
Fig. 9 shows that the distribution of the multiple rows of through-hole formed on semi-annular shape matrix according to pre-defined rule in the present embodiment is shown It is intended to.Shown in Figure 9, each row in multiple rows of through-hole is parallel with two end faces of semi-annular shape matrix, each through-hole edge The thickness direction of semi-annular shape matrix extends in each row, and the diameter of through-hole is with the through-hole at a distance from the center of circle of semicircular ring Increase and reduce, and the distance between two neighboring through-hole remains unchanged.
Second rubber is fed into multiple through-hole by the 4th step, obtains being subtracted by what non-uniform rod material formed Vibrating device, the wherein material parameter in each infinitesimal in any cross section of the thickness direction of vibration absorber be satisfied by with Lower condition:λ=R2λ1, G=R2G1,
Embodiment 4
The concrete scheme of the oscillation damping method for low-frequency elastic wave of the embodiment of the present invention is same as Example 1, only in addition to Vibration absorber is constructed in the present embodiment in the following manner:
The first step chooses the first rubber and by the first rubber-moulding, obtains the semi-annular shape matrix with appointed thickness, In the first rubber Lam é first constants and Lam é second constants be respectively λ1,G1。
Second step chooses the second rubber, and the Lam é first constants and Lam é second constants of the second rubber are respectively λ2,G2, Wherein λ2<λ1, G2<G1。
Third walks, and multiple slots are formed on semi-annular shape matrix according to pre-defined rule.
Figure 10 shows that the distribution of the multiple slots formed on semi-annular shape matrix according to pre-defined rule in the present embodiment is shown It is intended to.Shown in Figure 10, multiple slot is radially distributed, and each slot runs through on the thickness direction of semi-annular shape matrix The semi-annular shape matrix, each slot extend along the radial direction of semi-annular shape matrix, and each slot is in the width of circumferencial direction Gradually increase according to the direction of the inner periphery of the thoughtful semicircular ring of outer circle from semicircular ring.
Second rubber is fed into multiple slot by the 4th step, obtains the vibration damping formed by non-uniform rod material Device, the wherein material parameter in each infinitesimal in any cross section of the thickness direction of vibration absorber are satisfied by following Condition:λ=R2λ1, G=R2G1,
In the present embodiment, specifically, the first rubber is natural rubber, and the second rubber is silicon rubber.
Several specific embodiments of the oscillation damping method for low-frequency elastic wave of the present invention are described above, but the present invention is simultaneously It is without being limited thereto.By be kneaded, punch perfusion, cut slot perfusion etc. modes construct vibration absorber when, can also according to used in The material parameter of rubber correspondingly adopts the distribution mode of other through-holes or slot, for example, the multiple row through-hole of radial arrangement In, the through-hole diameter in each row is gradually reduced according to the direction in the center of circle of the thoughtful semicircular ring of outer circle from semicircular ring;Parallel In multiple rows of through-hole of row, the through-hole diameter in each row increases at a distance from the center of circle of semicircular ring with the through-hole and is increased;Radiation Shape distribution multiple slots in, each slot circumferencial direction width according to the thoughtful semicircular ring of outer circle from semicircular ring inner periphery Direction be gradually reduced, will not enumerate herein.
Illustrate oscillation damping method of the invention below by the comparison of the effectiveness in vibration suppression of the scheme and comparative example of embodiment 4 Effect.
Figure 11 shows a kind of signal of concrete application scene of the oscillation damping method for low-frequency elastic wave of embodiment 4 Figure.It is shown in Figure 11, wait for that insulator is supported on the top of semi-annular shape vibration absorber, the elastic wave that driving source generates It is incident to semi-annular shape vibration absorber from two ends of semi-annular shape vibration absorber, and is passed in semi-annular shape vibration absorber It broadcasts.
In the comparative example, in addition to using the vibration absorber being made of natural rubber homogeneous material instead of structure in embodiment 4 Except the vibration absorber made, remaining operation is identical as the concrete scheme of embodiment 4, wherein the vibration damping dress of homogeneous material composition The shape and support stiffness set are identical as the vibration absorber constructed in embodiment 4.
By measuring the original excitation signal of driving source and waiting for vibration signal at insulator (that is, by vibration absorber Signal after vibration damping), to evaluate the effectiveness in vibration suppression of embodiment 4 and comparative example.
The measurement method of above-mentioned support stiffness is as follows:It is support with two end faces of semi-annular shape vibration absorber, Apply downward power F in the middle position at the top of semi-annular shape vibration absorber, measures the displacement d at top, then it can be under Formula calculates support stiffness K:
K=F/d.
Figure 12 is the comparison diagram of the time-domain signal after the scheme of embodiment 4 and comparative example carries out vibration damping.In fig. 12, horizontal Coordinate is time T (unit:Second, s) ordinate was voltage U (units:Volt V).As shown in Figure 12, figure (a) is original sharp The time domain waveform of signal is encouraged, figure (b) is the time domain waveform of the signal after the scheme of embodiment 4 carries out vibration damping, is schemed (c) It is the time domain waveform that the scheme of example by contrast carries out the signal after vibration damping.
Figure 13 is the comparison diagram of the frequency-region signal after the scheme of embodiment 4 and comparative example carries out vibration damping, and wherein A indicates warp The scheme of embodiment 4 carries out the frequency-region signal after vibration damping, and B indicates that the scheme of example by contrast carries out the frequency-region signal after vibration damping. In Figure 13, abscissa is frequency f (units:Hz), ordinate is the Fen Bei &#124 of the relatively primitive pumping signal of signal after vibration damping;P1 (f)&#124;(unit:DB), calculation &#124;P1(f)&#124;=10log (XA(B)/XE), wherein XAAnd XBGeneration is respectively referred to through embodiment 4 The power spectral amplitude ratio of the signal after vibration damping, X are carried out with the scheme of comparative exampleERefer to the power spectral amplitude ratio of original excitation signal.
According to the comparative analysis of Figure 12 and Figure 13 as it can be seen that while ensureing the support stiffness of vibration absorber, the present invention is real The technical solution for applying example has significant effectiveness in vibration suppression to the low-frequency elastic wave in 332-1800Hz frequency ranges.
It should be noted that in practical application, combination may be used in above-mentioned all optional embodiments arbitrary group of mode It closes, forms the alternative embodiment of the present invention, this is no longer going to repeat them.
Based on same inventive concept, the embodiment of the present invention additionally provides a kind of vibration absorber for low-frequency elastic wave, fits For reducing the vibration for waiting for insulator caused by the elastic wave generated by driving source.
The structure of vibration absorber is shown in Figure 4.The vibration absorber is according to the feature of elastic wave and waits for subtracting for insulator The demand of shaking constructs, and has appointed thickness, any two cross section shape having the same of the thickness direction of vibration absorber Shape, vibration absorber also have there are two end face, and two end faces are vertical with the cross section, when elastic wave is from one in two end faces A surface feeding sputtering to vibration absorber, along vibration absorber internal communication to another end face in two end faces and from another When end face is emitted, elastic wave is in the direction of propagation that the direction of propagation of a surface feeding sputtering and elastic wave are emitted in another end face It is different;Also, vibration absorber is made of non-uniform rod material, any cross section of the thickness direction of vibration absorber by Multiple infinitesimal compositions, are equivalent to homogeneous material, then in each infinitesimal by the material in multiple infinitesimals in each infinitesimal Material parameter meets the following conditions:So that the elastic wave from a surface feeding sputtering to vibration absorber It can be along the internal communication of vibration absorber to another end face, wherein λ and G is the equivalent Lam é of material in the infinitesimal respectively First constant and equivalent Lam é second constants, A are that rectangle two-dimensional space is converted into vibration absorber by conformal mapping Thickness direction any cross section shape the introduced feature corresponding with the center position of the infinitesimal of two-dimensional space Size, L ' are the wavelength of elastic wave.
When carrying out vibration damping, which is arranged in the driving source of elastic wave and between waiting for insulator, vibration damping is made At least one of two end faces of device are located on the path that elastic wave direction waits for that insulator is propagated, and make elastic wave from vibration damping The surface feeding sputtering on the propagation path of elastic wave of device makes elastic wave from elasticity to vibration absorber by vibration absorber The end face of wave incidence, along the internal communication of vibration absorber to another end face of vibration absorber, to change the biography of elastic wave Direction is broadcast, reduction propagates to the elastic wave for waiting for insulator, to realize the vibration damping to the component.
In an alternative embodiment, the shape of any cross section of the thickness direction of vibration absorber includes arc ring Shape.
In an alternative embodiment, the shape of any cross section of the thickness direction of vibration absorber is semi-annular shape, Each infinitesimal in multiple infinitesimals in any cross section of the thickness direction of vibration absorber is first by the central angle of semicircular ring It carries out m deciles and obtains m segment angle, then by curved annular obtained from the region corresponding to each segment angle radially n deciles Region, wherein m and n is the positive integer more than or equal to 2;And it is every in any cross section of the thickness direction of vibration absorber Material parameter in one infinitesimal meets the following conditions:Wherein, λ and G is material in the infinitesimal respectively The equivalent Lam é first constants and equivalent Lam é second constants, R of material are the central point range semicircles of the infinitesimal in the cross section The distance in the center of circle of ring, L ' are the wavelength of elastic wave.
An optional embodiment or in, non-uniform rod material includes rubber.
Based on same inventive concept, the embodiment of the present invention additionally provides a kind of vibration insulating system for low-frequency elastic wave, uses In the oscillation damping method for low-frequency elastic wave for supporting that any one above-mentioned embodiment or combinations thereof is provided.Figure 14 is shown The structural schematic diagram of vibration insulating system according to an embodiment of the invention for low-frequency elastic wave.Referring to Figure 14, the vibration insulating system At least may include:Structural unit 1410, setting unit 1420 and the direction of propagation change unit 1430.
Now introduce each composition of the vibration insulating system for low-frequency elastic wave of the embodiment of the present invention or the function of device and Connection relation between each section:
Structural unit 1410, is suitable for:According to the feature of elastic wave and wait for the vibration damping demand construction of insulator with specified Any two cross section of the vibration absorber of thickness, the thickness direction of vibration absorber is of similar shape, and vibration absorber also has There are two end faces, and two end faces are vertical with the cross section, when elastic wave is from a surface feeding sputtering in two end faces to vibration damping Device, the internal communication along vibration absorber is to another end face in two end faces and when being emitted from another end face, elastic wave It is different from the direction of propagation that elastic wave is emitted in another end face in the direction of propagation of a surface feeding sputtering;Also, vibration absorber It is made of non-uniform rod material, any cross section of the thickness direction of vibration absorber is made of multiple infinitesimals, will be multiple Material in infinitesimal in each infinitesimal is equivalent to homogeneous material, then the material parameter in each infinitesimal meets following item Part: Enable elastic wave from a surface feeding sputtering to vibration absorber along in vibration absorber Portion travels to another end face, wherein λ and G is the equivalent Lam é first constants and equivalent Lam é of material in the infinitesimal respectively Two constants, A are that rectangle two-dimensional space is converted into any transversal of the thickness direction with vibration absorber by conformal mapping The introduced characteristic size corresponding with the center position of the infinitesimal of two-dimensional space of the shape in face, L ' is the wave of elastic wave It is long.
Setting unit 1420, is suitable for:Vibration absorber is arranged in the driving source of elastic wave and between waiting for insulator, makes to subtract At least one of two end faces of vibrating device are located on the path that elastic wave direction waits for that insulator is propagated, and make elastic wave from subtracting The surface feeding sputtering on the propagation path of elastic wave of vibrating device is to vibration absorber.
The direction of propagation changes unit 1430, is suitable for:Make elastic wave from the end face of elastic wave incidence by vibration absorber, along The internal communication of vibration absorber is to another end face of vibration absorber, and to change the direction of propagation of elastic wave, reduction propagates to The elastic wave for waiting for insulator, to realize the vibration damping to the component.
According to the combination of any one above-mentioned alternative embodiment or multiple alternative embodiments, the embodiment of the present invention can reach Following advantageous effect:
Oscillation damping method, system and the vibration absorber for low-frequency elastic wave of the embodiment of the present invention are suitable for low frequency bullet The vibration damping environment of property wave.Vibration absorber, shape, size to vibration absorber are constructed according to the feature of elastic wave and vibration damping demand It is designed with material parameter so that when using communication space of the vibration absorber as elastic wave, elastic wave controlling party The transformation approximation of journey meets invariance, and then when carrying out vibration damping, by the vibration absorber be arranged driving source in elastic wave with Between waiting for insulator, so that at least one of two end faces that the vibration absorber has is located at elastic wave direction and wait for insulator On the path of propagation, and make elastic wave from the surface feeding sputtering on the propagation path of elastic wave of the vibration absorber to institute After stating vibration absorber, the direction of propagation of elastic wave bends, and elastic wave can be arrived along the internal communication of the vibration absorber Another end face, to change the direction of propagation of elastic wave, reduction propagates to the elastic wave for waiting for insulator, to realize vibration damping. Statistics indicate that the technical solution of the embodiment of the present invention has significantly the low-frequency elastic wave in 332-1800Hz frequency ranges Effectiveness in vibration suppression.
Finally it should be noted that:The above embodiments are only used to illustrate the technical solution of the present invention., rather than its limitations;To the greatest extent Present invention has been described in detail with reference to the aforementioned embodiments for pipe, it will be understood by those of ordinary skill in the art that:At this It, still can be with technical scheme described in the above embodiments is modified or right within the spirit and principle of invention Which part or all technical features carry out equivalent replacement;And these modifications or replacements, do not make corresponding technical solution de- From protection scope of the present invention.

Claims (10)

1. a kind of oscillation damping method for low-frequency elastic wave, suitable for reduce caused by the elastic wave generated by driving source wait for every It shakes the vibration of component, including:
The vibration absorber with appointed thickness is constructed according to the feature of the elastic wave and the vibration damping demand for waiting for insulator, Any two cross section of the thickness direction of the vibration absorber is of similar shape, the vibration absorber also have there are two end Face, described two end faces are vertical with the cross section, when the elastic wave from a surface feeding sputtering in described two end faces to The vibration absorber, the internal communication along the vibration absorber is to another end face in described two end faces and from described another When a end face outgoing, the elastic wave is in the direction of propagation of one surface feeding sputtering and the elastic wave at another described end The direction of propagation of face outgoing is different;Also, the vibration absorber is made of non-uniform rod material, the vibration absorber Any cross section of thickness direction is made of multiple infinitesimals, and the material in the multiple infinitesimal in each infinitesimal is equivalent to Even material, then the material parameter in each infinitesimal meet the following conditions:So that from described one The elastic wave of a surface feeding sputtering to the vibration absorber can be along the internal communication of the vibration absorber to described another A end face, wherein λ and G be respectively material in the infinitesimal equivalent Lame Lam é first constants and equivalent Lame Lam é second it is normal Number, A is that rectangle two-dimensional space is converted into any transversal of the thickness direction with the vibration absorber by conformal mapping The introduced characteristic size corresponding with the center position of the infinitesimal of two-dimensional space of the shape in face, L ' is the elastic wave Wavelength;
By the vibration absorber be arranged the elastic wave driving source and it is described wait for insulator between, make the vibration absorber At least one of described two end faces be located at and waited for described in the elastic wave direction on path that insulator is propagated, and make the bullet Property wave is from the surface feeding sputtering on the propagation path of the elastic wave of the vibration absorber to the vibration absorber;
Make the elastic wave from the end face of elastic wave incidence by the vibration absorber, along the inside of the vibration absorber Another end face for traveling to the vibration absorber, to change the direction of propagation of the elastic wave, reduction propagates to described wait for The elastic wave of insulator, to realize the vibration damping to the component.
2. according to the method described in claim 1, wherein, the shape packet of any cross section of the thickness direction of the vibration absorber Bracket is cyclic annular.
3. according to the method described in claim 2, wherein, the shape of any cross section of the thickness direction of the vibration absorber is Semi-annular shape, each infinitesimal in the multiple infinitesimal in any cross section of the thickness direction of the vibration absorber is will Curved annular region obtained from the corresponding region of each specified segment angle is radially divided in the semicircular ring, it is described each Material parameter in infinitesimal meets the following conditions:Wherein, λ and G is material in the infinitesimal respectively Equivalent Lam é first constants and equivalent Lam é second constants, R are the central points of the infinitesimal in the cross section apart from described half The distance in the center of circle of annulus, L ' are the wavelength of the elastic wave.
4. described in any cross section of the thickness direction of the vibration absorber according to the method described in claim 3, wherein Each infinitesimal in multiple infinitesimals is:
The central angle of the semicircular ring is subjected to m deciles and obtains m segment angle, then by the region corresponding to each segment angle Radially curved annular region obtained from n deciles, wherein m and n is the positive integer more than or equal to 2.
5. according to the method described in claim 4, wherein, the material includes rubber.
6. according to the method described in claim 5, wherein, constructing the vibration absorber in the following manner:
The first rubber is chosen, the Lam é first constants and Lam é second constants of first rubber are respectively λ1,G1;
The second rubber is chosen, the Lam é first constants and Lam é second constants of second rubber are respectively λ2,G2, wherein λ2≠ λ1, G2≠G1;
First rubber and second rubber are kneaded and are molded according to predetermined mixing rule, is obtained by non-homogeneous each The vibration absorber with appointed thickness formed to isotropic material, wherein any cross of the thickness direction of the vibration absorber The material parameter in each infinitesimal in section is satisfied by the following conditions:λ=R2λ1, G=R2G1,
7. according to the method described in claim 5, wherein, constructing the vibration absorber in the following manner:
It chooses the first rubber and by first rubber-moulding, obtains the semi-annular shape matrix with appointed thickness, wherein described The Lam é first constants and Lam é second constants of first rubber are respectively λ1,G1;
The second rubber is chosen, the Lam é first constants and Lam é second constants of second rubber are respectively λ2,G2, wherein λ2≠ λ1, G2≠G1;
Form multiple hollow micro-structures on the matrix according to pre-defined rule;
Second rubber is fed into the micro-structure, the vibration damping dress being made of non-uniform rod material is obtained Set, wherein the material parameter in each infinitesimal in any cross section of the thickness direction of the vibration absorber be satisfied by it is following Condition:λ=R2λ1, G=R2G1,
8. according to the method described in claim 7, wherein, the micro-structure is through-hole or slot.
9. a kind of vibration absorber for low-frequency elastic wave, suitable for reduce caused by the elastic wave generated by driving source wait for every Shake the vibration of component, the vibration absorber according to the feature and the vibration damping demand construction for waiting for insulator of the elastic wave and At with appointed thickness, any two cross section of the thickness direction of the vibration absorber is of similar shape, the vibration damping Device also has there are two end face, and described two end faces are vertical with the cross section, when the elastic wave is from described two end faces A surface feeding sputtering to the vibration absorber, the internal communication along the vibration absorber is to another in described two end faces End face and when being emitted from another described end face, the elastic wave is in the direction of propagation of one surface feeding sputtering and the elasticity Wave is different in the direction of propagation that another described end face is emitted;Also, the vibration absorber is by non-uniform rod material group At any cross section of the thickness direction of the vibration absorber is made of multiple infinitesimals, each in the multiple infinitesimal is micro- Material in member is equivalent to homogeneous material, then the material parameter in each infinitesimal meets the following conditions:Enable the elastic wave from one surface feeding sputtering to the vibration absorber along institute The internal communication of vibration absorber is stated to another described end face, wherein λ and G is the equivalent Lam é the of material in the infinitesimal respectively One constant and equivalent Lam é second constants, A are to be converted into rectangle two-dimensional space by conformal mapping to fill with the vibration damping The introduced spy corresponding with the center position of the infinitesimal of two-dimensional space of the shape of any cross section for the thickness direction set Size is levied, L ' is the wavelength of the elastic wave;
When carrying out vibration damping, by the vibration absorber be arranged the elastic wave driving source and it is described wait for insulator between, So that at least one of described two end faces of the vibration absorber is located at described in the elastic wave direction and waits for the road that insulator is propagated On diameter, and make the elastic wave from the surface feeding sputtering on the propagation path of the elastic wave of the vibration absorber to described Vibration absorber makes the elastic wave from the end face of elastic wave incidence, along the vibration absorber by the vibration absorber Internal communication to another end face of the vibration absorber, to change the direction of propagation of the elastic wave, reduction propagates to The elastic wave for waiting for insulator, to realize the vibration damping to the component.
10. a kind of vibration insulating system for low-frequency elastic wave is waited for suitable for reducing caused by the elastic wave generated by driving source The vibration of insulator, the vibration insulating system include:
Structural unit is suitable for:Had according to the feature of the elastic wave and the vibration damping demand construction for waiting for insulator specified Any two cross section of the vibration absorber of thickness, the thickness direction of the vibration absorber is of similar shape, the vibration damping Device also has there are two end face, and described two end faces are vertical with the cross section, when the elastic wave is from described two end faces A surface feeding sputtering to the vibration absorber, the internal communication along the vibration absorber is to another in described two end faces End face and when being emitted from another described end face, the elastic wave is in the direction of propagation of one surface feeding sputtering and the elasticity Wave is different in the direction of propagation that another described end face is emitted;Also, the vibration absorber is by non-uniform rod material group At any cross section of the thickness direction of the vibration absorber is made of multiple infinitesimals, each in the multiple infinitesimal is micro- Material in member is equivalent to homogeneous material, then the material parameter in each infinitesimal meets the following conditions:Enable the elastic wave from one surface feeding sputtering to the vibration absorber along institute The internal communication of vibration absorber is stated to another described end face, wherein λ and G is the equivalent Lam é the of material in the infinitesimal respectively One constant and equivalent Lam é second constants, A are to be converted into rectangle two-dimensional space by conformal mapping to fill with the vibration damping The introduced spy corresponding with the center position of the infinitesimal of two-dimensional space of the shape of any cross section for the thickness direction set Size is levied, L ' is the wavelength of the elastic wave;
Setting unit is suitable for:By the vibration absorber be arranged the elastic wave driving source and it is described wait for insulator between, So that at least one of described two end faces of the vibration absorber is located at described in the elastic wave direction and waits for the road that insulator is propagated On diameter, and make the elastic wave from the surface feeding sputtering on the propagation path of the elastic wave of the vibration absorber to described Vibration absorber;And
The direction of propagation changes unit, is suitable for:Make the elastic wave from the end face of elastic wave incidence by the vibration absorber, Along the internal communication of the vibration absorber to another end face of the vibration absorber, to change the propagation of the elastic wave Direction reduces and propagates to the elastic wave for waiting for insulator, to realize the vibration damping to the component.
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