CN110472287A - A kind of control method of periodic structure Propagation of Elastic Wave characteristic - Google Patents
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Abstract
This disclosure relates to Structural Dynamics field, provide a kind of control method of periodic structure Propagation of Elastic Wave characteristic, by applying propagation characteristic of the elastic wave in the periodic structure described in Temperature Field Control, wherein, the control method of periodic structure Propagation of Elastic Wave characteristic includes: a single cell model to be obtained from the periodic structure, and obtain the corresponding stiffness matrix of the single cell model and mass matrix；According to the stiffness matrix and mass matrix, the frequency and wave vector equation of the single cell model are obtained；According to the frequency of the single cell model and wave vector equation, the band gap properties of the elastic wave are obtained.The control method of periodic structure Propagation of Elastic Wave characteristic in the disclosure provides a kind of new control method for the regulation of periodic structure medium wave propagation, can be realized flexible, autonomous regulation.
Description
Technical field
This disclosure relates to Structural Dynamics technical field, in particular to a kind of control of periodic structure Propagation of Elastic Wave characteristic
Control device, computer storage medium and the electronic equipment of method processed, periodic structure Propagation of Elastic Wave characteristic.
Background technique
Structural vibration problem is widely present in each engineering field such as aerospace, ship, vehicular traffic, inhibits structure
Nuisance vibration and noise be always problem in the urgent need to address in engineering technology.Basically, the vibration in structure
It with noise is propagated in the medium in the form of elastic wave.Therefore, based on the wave propagation characteristic in periodic structure, regulation wave is established
The method of propagation characteristic realizes being precisely controlled for elastic wave propagation characteristic, has great importance to the damping noise reduction of structure.
Currently, the inclined field of shear stress, electromagnetic field etc. are applied to periodic structure generally by perfect analysis model is established,
To regulate and control the wave propagation characteristic in periodic structure.But these methods are typically necessary to be pre-processed when making component, meeting
A large amount of human and material resources are expended, need to do a large amount of manual working.Thus, it takes time and effort, higher cost.
In consideration of it, this field needs to develop the control method and dress of a kind of new periodic structure Propagation of Elastic Wave characteristic
It sets.
It should be noted that information disclosed in above-mentioned background technology part is only used for reinforcing the reason to the background of the disclosure
Solution.
Summary of the invention
In a kind of control method for being designed to provide periodic structure Propagation of Elastic Wave characteristic of the disclosure, periodic structure
Control method device, computer storage medium and the electronic equipment of elastic wave propagation characteristic, and then keep away at least to a certain extent
The control method for having exempted from periodic structure Propagation of Elastic Wave characteristic in the prior art takes time and effort, the defect of higher cost.
Other characteristics and advantages of the disclosure will be apparent from by the following detailed description, or partially by the disclosure
Practice and acquistion.
According to the disclosure in a first aspect, provide a kind of control method of periodic structure Propagation of Elastic Wave characteristic, pass through
Apply propagation characteristic of the elastic wave in the periodic structure described in Temperature Field Control, which comprises from periodic structure
A single cell model is obtained, and obtains the corresponding stiffness matrix of the single cell model and mass matrix；According to the stiffness matrix with
Mass matrix obtains the frequency and wave vector equation of the single cell model；According to the frequency of the single cell model and wave vector equation, obtain
Take the band gap properties of the elastic wave.
In an exemplary embodiment of the disclosure, described to obtain the corresponding stiffness matrix of the single cell model and moment of mass
Battle array, comprising: the single cell model is divided by multiple identical beam elements according to dynamic model；According to the movement of the beam element
The axial force that governing equation and the single cell model generate under the temperature field action, obtains the corresponding matter of the beam element
Moment matrix and stiffness matrix；Mass matrix and stiffness matrix to the beam element carry out unit assembling, to obtain the unit cell
The corresponding mass matrix of model and stiffness matrix.
In an exemplary embodiment of the disclosure, the motion control equation and the unit cell according to the beam element
The axial force that model generates under the temperature field action obtains the corresponding mass matrix of the beam element and stiffness matrix, packet
It includes: the axial direction generated under the temperature field action according to the motion control equation of the beam element and the single cell model
Power obtains the parameter value of the beam element correspondingly-shaped function；According to the parameter value of the beam element correspondingly-shaped function, it is based on
The golden method of gal the Liao Dynasty, obtains the corresponding mass matrix of the beam element and stiffness matrix.
In an exemplary embodiment of the disclosure, the single cell model is divided by multiple phases according to dynamic model described
Before same beam element, the method also includes: the dynamic model is established according to timoshenko beam theory.
In an exemplary embodiment of the disclosure, described according to the stiffness matrix and mass matrix, obtain the unit cell
The frequency and wave vector equation of model, comprising: according to the stiffness matrix and mass matrix, establish the movement side of the single cell model
Journey；According to Bloch theorem, the relation equation of displacement vector Yu freedom degree condensation matrix is obtained；According to the equation of motion and institute
Relation equation is stated, the frequency and wave vector equation of the single cell model are obtained.
In an exemplary embodiment of the disclosure, the frequency according to the single cell model and wave vector equation obtain institute
State the band gap properties of elastic wave, comprising: according to the frequency of the single cell model and wave vector equation, obtain institute in the single cell model
State the natural frequency of vibration of elastic wave；According to the natural frequency of vibration, the band gap properties of the elastic wave are obtained.
In an exemplary embodiment of the disclosure, the method also includes: according to the band gap properties of the elastic wave regulate and control
The propagation of elastic wave described in the periodic structure.
According to the second aspect of the disclosure, a kind of control device of periodic structure Propagation of Elastic Wave characteristic is provided, is passed through
Apply propagation characteristic of the elastic wave in the periodic structure described in Temperature Field Control, comprising: first obtains module, is used for from institute
It states and obtains a single cell model in periodic structure, and obtain the corresponding stiffness matrix of the single cell model and mass matrix；Second obtains
Modulus block, for obtaining the frequency and wave vector equation of the single cell model according to the stiffness matrix and mass matrix；Third obtains
Modulus block obtains the band gap properties of the elastic wave for the frequency and wave vector equation according to the single cell model.
According to the third aspect of the disclosure, a kind of computer storage medium is provided, is stored thereon with computer program, it is described
The control of periodic structure Propagation of Elastic Wave characteristic described in above-mentioned first aspect is realized when computer program is executed by processor
Method.
According to the fourth aspect of the disclosure, a kind of electronic equipment is provided, comprising: processor；And memory, for storing
The executable instruction of the processor；Wherein, the processor is configured to above-mentioned to execute via the executable instruction is executed
The control method of periodic structure Propagation of Elastic Wave characteristic described in first aspect.
As shown from the above technical solution, the control of the periodic structure Propagation of Elastic Wave characteristic in disclosure exemplary embodiment
Method processed, periodic structure Propagation of Elastic Wave characteristic control device, computer storage medium and electronic equipment at least have with
Lower advantage and good effect:
In the technical solution provided by some embodiments of the present disclosure, on the one hand, by obtaining one from periodic structure
Single cell model, and obtain the corresponding stiffness matrix of single cell model and mass matrix；According to stiffness matrix and mass matrix, obtain single
The frequency and wave vector equation of born of the same parents' model；In turn, according to the frequency of single cell model and wave vector equation, can know under Influence of Temperature Field
The band gap properties of elastic wave control propagation of the elastic wave in periodic structure, energy according to the band gap properties of above-mentioned elastic wave in turn
It enough provides a kind of new, is different from the prior art and middle expend a large amount of manpower and material resources the inclined field of shear stress, electromagnetism are applied to periodic structure
Etc. come the method that controls wave propagation characteristic, thus, it is possible to realize flexible, autonomous regulation.
The disclosure it should be understood that more than general description and following detailed description be only exemplary and explanatory
, it does not limit the disclosure.
Detailed description of the invention
The drawings herein are incorporated into the specification and forms part of this specification, and shows the implementation for meeting the disclosure
Example, and together with specification for explaining the principles of this disclosure.It should be evident that the accompanying drawings in the following description is only the disclosure
Some embodiments for those of ordinary skill in the art without creative efforts, can also basis
These attached drawings obtain other attached drawings.
Fig. 1 shows the process of the control method of periodic structure Propagation of Elastic Wave characteristic in one exemplary embodiment of the disclosure
Schematic diagram；
Fig. 2 shows the models of the control method of periodic structure Propagation of Elastic Wave characteristic in one exemplary embodiment of the disclosure
Schematic diagram；
Fig. 3 shows the mould of the control method of periodic structure Propagation of Elastic Wave characteristic in disclosure another exemplary embodiment
Type schematic diagram；
Fig. 4 shows the mould of the control method of periodic structure Propagation of Elastic Wave characteristic in the another exemplary embodiment of the disclosure
Type schematic diagram；
Fig. 5 shows the stream of the control method of periodic structure Propagation of Elastic Wave characteristic in disclosure another exemplary embodiment
Journey schematic diagram；
Fig. 6 shows the stream of the control method of periodic structure Propagation of Elastic Wave characteristic in the another exemplary embodiment of the disclosure
Journey schematic diagram；
Fig. 7 shows the mould of the control method of periodic structure Propagation of Elastic Wave characteristic in disclosure another exemplary embodiment
Type schematic diagram；
Fig. 8 shows the stream of the control method of periodic structure Propagation of Elastic Wave characteristic in disclosure another exemplary embodiment
Journey schematic diagram；
Fig. 9 shows the process of the control method of periodic structure Propagation of Elastic Wave characteristic in one exemplary embodiment of the disclosure
Schematic diagram；
Figure 10 shows the structure of the control device of periodic structure Propagation of Elastic Wave characteristic in disclosure exemplary embodiment
Schematic diagram；
Figure 11 shows the structural schematic diagram of computer storage medium in disclosure exemplary embodiment；
Figure 12 shows the structural schematic diagram of electronic equipment in disclosure exemplary embodiment.
Specific embodiment
Example embodiment is described more fully with reference to the drawings.However, example embodiment can be with a variety of shapes
Formula is implemented, and is not understood as limited to example set forth herein；On the contrary, thesing embodiments are provided so that the disclosure will more
Fully and completely, and by the design of example embodiment comprehensively it is communicated to those skilled in the art.Described feature, knot
Structure or characteristic can be incorporated in any suitable manner in one or more embodiments.In the following description, it provides perhaps
More details fully understand embodiment of the present disclosure to provide.It will be appreciated, however, by one skilled in the art that can
It is omitted with technical solution of the disclosure one or more in the specific detail, or others side can be used
Method, constituent element, device, step etc..In other cases, be not shown in detail or describe known solution to avoid a presumptuous guest usurps the role of the host and
So that all aspects of this disclosure thicken.
In this specification using term "one", " one ", "the" and " described " to indicate there are one or more elements/
Component part/etc.；Term " comprising " and " having " is to indicate the open meaning being included and refer in addition to listing
Element/component part/also may be present except waiting other element/component part/etc.；Term " first " and " second " etc. are only made
It is used for label, is not the quantity limitation to its object.
In addition, attached drawing is only the schematic illustrations of the disclosure, it is not necessarily drawn to scale.Identical attached drawing mark in figure
Note indicates same or similar part, thus will omit repetition thereof.Some block diagrams shown in the drawings are function
Energy entity, not necessarily must be corresponding with physically or logically independent entity.
Currently, the inclined field of shear stress, electromagnetic field etc. are applied to periodic structure generally by perfect analysis model is established,
To regulate and control the wave propagation characteristic in periodic structure.But these methods are typically necessary to be pre-processed when making component, meeting
A large amount of human and material resources are expended, need to do a large amount of manual working.Thus, it takes time and effort, higher cost.
In embodiment of the disclosure, a kind of control method of periodic structure Propagation of Elastic Wave characteristic is provided firstly,
The control method time-consuming of the periodic structure Propagation of Elastic Wave characteristic provided in the prior art is overcome to consume at least to a certain extent
Power, the defect of higher cost.
Fig. 1 shows the process of the control method of periodic structure Propagation of Elastic Wave characteristic in one exemplary embodiment of the disclosure
Schematic diagram.
With reference to Fig. 1, according to the control method packet of the periodic structure Propagation of Elastic Wave characteristic of one embodiment of the disclosure
Include following steps:
Step S110 obtains a single cell model from periodic structure, and obtains the corresponding stiffness matrix of the single cell model
With mass matrix；
Step S120 obtains the frequency and wave vector equation of the single cell model according to the stiffness matrix and mass matrix；
Step S130 obtains the band gap properties of the elastic wave according to the frequency of the single cell model and wave vector equation.
In technical solution provided by embodiment shown in Fig. 1, on the one hand, by obtaining a unit cell mould from periodic structure
Type, and obtain the corresponding stiffness matrix of single cell model and mass matrix；According to stiffness matrix and mass matrix, single cell model is obtained
Frequency and wave vector equation；In turn, according to the frequency of single cell model and wave vector equation, it can know elastic wave under Influence of Temperature Field
Band gap properties control propagation of the elastic wave in periodic structure in turn according to the band gap properties of above-mentioned elastic wave, be capable of providing
It is a kind of new, it is different from the prior art and middle expends a large amount of manpower and material resources and apply the inclined field of shear stress, electromagnetic field etc. to periodic structure
The method for controlling wave propagation characteristic, thus, it is possible to realize flexible, autonomous regulation.
The specific implementation process of each step in Fig. 1 is described in detail below:
In step s 110, a single cell model is obtained from periodic structure, and obtains the corresponding rigidity of the single cell model
Matrix and mass matrix.
In an exemplary embodiment of the disclosure, elastic wave is one kind of stress wave, is answered caused by disturbance or external force
The form that power and strain are transmitted in elastic fluid.Elastic force in elastic fluid between particle there is interaction.Work as somewhere
Material particle leaves equilbrium position, that is, when straining, which vibrates under the action of elastic force, while causing week again
The strain and vibration of particle are enclosed, communication process of the vibration formed in this way in elastic fluid is known as " elastic wave ".Pass through application
Propagation characteristic (band gap locations, path, the energy of elastic wave propagation of the elastic wave described in Temperature Field Control in the periodic structure
Distribution etc.), it is capable of providing a kind of new, is different from the prior art and middle expend a large amount of manpower and material resources shear stress is applied to periodic structure
Inclined field, electromagnetic field etc. take time and effort come the method for controlling wave propagation characteristic thus, it is possible to solve the prior art, higher cost
Technical problem reduces cost of labor, realizes flexible, autonomous regulation.
In an exemplary embodiment of the disclosure, a single cell model can be first obtained from periodic structure, and obtains unit cell
The stiffness matrix and mass matrix of model.
In an exemplary embodiment of the disclosure, periodic structure i.e. engineering in practice, overall structure constitute have repeat
Property, the structure being successively spliced by same parts, i.e., the elements such as several beams, bar, rope, plate are connected in one direction by certain way
Connect the structure of composition.Such as: the skeleton of multispan beam, Large Flexible Space Structures, large-sized solar battery windsurfing, regular hexagon week
Phase structure etc. is periodic structure.Illustratively, Fig. 2 can be referred to, Fig. 2 is schematically shown in one exemplary embodiment of the disclosure
The model schematic of the control method of periodic structure Propagation of Elastic Wave characteristic, specifically illustrates by taking regular hexagon periodic structure as an example
Periodic structure model schematic.
In an exemplary embodiment of the disclosure, single cell model is the model separated from above-mentioned periodic structure, i.e.,
Single cell model is a part of above-mentioned periodic structure.Illustratively, Fig. 3 can be referred to, Fig. 3 schematically show that the disclosure is another to be shown
The model schematic of the control method of periodic structure Propagation of Elastic Wave characteristic, specifically illustrates above-mentioned unit cell mould in example property embodiment
The model schematic of type.As shown in figure 3, the dotted portion in circular frame is the unit cell mould separated from above-mentioned periodic structure
Type.Illustratively, Fig. 4 can also be referred to, Fig. 4 schematically shows elastic in periodic structure in the another exemplary embodiment of the disclosure
The model schematic of the control method of wave propagation characteristic specifically illustrates the above-mentioned unit cell mould separated from above-mentioned periodic structure
The schematic diagram of type.
In an exemplary embodiment of the disclosure, when getting above-mentioned single cell model, available above-mentioned single cell model
Mass matrix and stiffness matrix.
In an exemplary embodiment of the disclosure, Fig. 5 schematically shows period knot in disclosure another exemplary embodiment
The flow diagram of the control method of structure Propagation of Elastic Wave characteristic, specifically illustrate obtain the mass matrix of above-mentioned single cell model with
The flow diagram of stiffness matrix explains step S110 below in conjunction with Fig. 5.
In step S501, the single cell model is divided by multiple identical beam elements according to dynamic model.
In an exemplary embodiment of the disclosure, beam refers to that, by bearing support, the external force of receiving is with cross force and shearing
It is main, to be bent into the component of primary deformable.
It in an exemplary embodiment of the disclosure, can theoretical (timoshenko beam can exactly consider according to timoshenko beam
Shear-deformable beam, specifically, its displacement and sectional twisting angle are independent interpolations, rather than the derivative by being displaced is asked
.) establish dynamic model.
In an exemplary embodiment of the disclosure, dynamic model is the mould that above-mentioned periodic structure can be divided into beam element
Type.After establishing above-mentioned dynamic model, above-mentioned single cell model can be divided into according to above-mentioned dynamic model multiple identical
Beam element.
In step S502, according to the motion control equation of the beam element and the single cell model in the temperature field
The lower axial force generated of effect, obtains the corresponding mass matrix of the beam element and stiffness matrix.
In an exemplary embodiment of the disclosure, Fig. 6 schematically shows period knot in the another exemplary embodiment of the disclosure
The flow diagram of the control method of structure Propagation of Elastic Wave characteristic, specifically illustrate according to the motion control equation of beam element and
The axial force that single cell model generates under temperature field action obtains the mass matrix of above-mentioned single cell model and the process of stiffness matrix
Schematic diagram explains step S502 below in conjunction with Fig. 6.
In step s 601, according to the motion control equation of the beam element and the single cell model in the temperature field
The lower axial force generated of effect, obtains the parameter value of the beam element correspondingly-shaped function.
It in an exemplary embodiment of the disclosure, can be according to the motion control equation and single cell model of beam element in temperature
The axial force generated under degree field action, obtains the parameter value of beam element correspondingly-shaped function.
In an exemplary embodiment of the disclosure, axial force refers on structure caused by effect or a certain normal section of component
Reversal interlocking relay or pressure.Illustratively, when applying temperature field to periodic structure, due to the thermal characteristics of structural material, Liang Huisui
The variation of temperature and deformation occurs.However due between Liang Yuliang rigid connection and effect of contraction, beam cannot freely stretch
It contracts and generates additional internal force, thus, when the temperature increases, beam can only axially deform, and generate axial force p, and axial force p's is big
It is small to beα is the thermal expansion coefficient of material, and E is the elasticity modulus of material, and A is the area of section of beam,It is i.e. warm
Spend the temperature value that field applies.
In an exemplary embodiment of the disclosure, shape function is the continuous letter for indicating a certain node coordinate inside unit
Number illustratively can be the continuous function N (x) for indicating a certain node coordinate inside beam element, specifically, can refer to down
State the relevant explanation of step.
In an exemplary embodiment of the disclosure, beam element is divided into two nodes, and each node has three degree of freedom, i.e.,
Axial displacement με, vertical displacement ωτAnd swing offsetIllustratively, Fig. 7 can be referred to, Fig. 7 schematically shows the disclosure again
The model schematic of the control method of periodic structure Propagation of Elastic Wave characteristic, specifically illustrates each beam in one exemplary embodiment
Unit corresponding three nodes (axial displacement μ ε, vertical displacement ωτAnd swing offset) direction relations schematic diagram.Only examine
Consider vertical displacement ωτAnd swing offsetRelationship, obtain the motion control equation of beam element are as follows:
In an exemplary embodiment of the disclosure, the motion control equation of above-mentioned beam element illustrates axial force p and vertical
It is displaced ωτAnd swing offsetRelationship, ω, that is, vertical displacement ω in formulaτ, in formulaThat is swing offsetIts
In, k is shear factor related with beam element cross sectional shape, and G indicates the modulus of shearing of material, and ρ is the density of material, and A is beam
Area of section, I be beam section polar moment of inertia, E is the elasticity modulus of material, p, that is, above-mentioned axial force.X indicates each beam element
The node location of node, t indicate to apply the time in temperature field.ω " indicates second dervative of the ω about x,It indicatesAbout x's
First derivative, ω ' indicate first derivative of the ω about x.Indicate second dervative of the ω about t,It indicatesAbout t's
Second dervative.
In an exemplary embodiment of the disclosure, with continued reference to Fig. 7, vertical displacement ωτAnd swing offsetIt can be by
It is expressed as motion vectorQ=a, b.Further, motion vector can be represented as wq=N (x) we,
Wherein, we=[wa wb]T, N (x)=[N1 N2]T, N (x) is shape function, N1=[N11 N12 N13 N14]T, N2=[N21 N22 N23
N24]T。
It in an exemplary embodiment of the disclosure, can be first by above-mentioned vertical displacement ωτAnd swing offsetIt is represented as
wq=N (x) we.In turn, according to the motion control equation of above-mentioned beam element and above-mentioned axial forceIt can calculate
The parameter N of above-mentioned shape function out1And N2。
In step S602, institute is obtained based on the golden method of gal the Liao Dynasty according to the parameter value of the beam element correspondingly-shaped function
State the corresponding mass matrix of beam element and stiffness matrix.
It in an exemplary embodiment of the disclosure, can be according to the parameter value of the corresponding shape function of above-mentioned beam element, base
In the golden method of gal the Liao Dynasty, the corresponding mass matrix of beam element and stiffness matrix are obtained.
In an exemplary embodiment of the disclosure, the golden method of gal the Liao Dynasty is a kind of numerical analysis method, limited more by choosing
Formula function (also known as shape function), they are superimposed, then requirement result is solving in domain and borderline weighted integral (Quan Han
Number is trial function itself) meet original equation, one group of linear algebraic equation for being easy to solve, and natural boundary conditions can be obtained
(refer to admissible function in the case of the value on fixed boundary is without restriction, extremal function due to making first variation be zero and
The condition that must satisfy on boundary.) can meet automatically.
In an exemplary embodiment of the disclosure, in the parameter N for obtaining above-mentioned shape function1And N2Later, gal can be based on
Distant gold method, integrates above-mentioned beam element, to obtain the corresponding mass matrix M of above-mentioned beam elementeWith stiffness matrix Ke.Show
Example property, the mass matrix for obtaining beam element isObtain the rigidity of beam element
Matrix isWherein, l
For the length of beam element.
In step S503, mass matrix and stiffness matrix to the beam element carry out unit assembling, described in obtaining
The corresponding mass matrix of single cell model and stiffness matrix.
In an exemplary embodiment of the disclosure, in the mass matrix M for obtaining above-mentioned beam elementeWith stiffness matrix KeLater,
Can mass matrix to above-mentioned beam element and stiffness matrix carry out unit assembling, to obtain the corresponding mass matrix of single cell model
M and stiffness matrix K.
In the step s 120, according to the stiffness matrix and mass matrix, the frequency and wave vector of the single cell model are obtained
Equation.
In an exemplary embodiment of the disclosure, single cell model can be obtained according to above-mentioned stiffness matrix and mass matrix
Frequency and wave vector equation.
In an exemplary embodiment of the disclosure, the number that wave source vibrates in frequency, that is, unit time.Wave vector is a kind of table
The method of the vector of oscillography, wave vector are a vectors, and size indicates angular wave number, and direction indicates the direction that wave is propagated.Frequency
It is the equation for characterizing said frequencies and wave vector relationship with wave vector equation.
In an exemplary embodiment of the disclosure, Fig. 8 schematically shows period knot in disclosure another exemplary embodiment
The flow diagram of the control method of structure Propagation of Elastic Wave characteristic is specifically illustrated according to stiffness matrix and mass matrix, is obtained
The frequency of single cell model and the flow diagram of wave vector equation, explain step S120 below in conjunction with Fig. 8.
In step S801, according to the stiffness matrix and mass matrix, the equation of motion of the single cell model is established.
Disclosed in this public affairs in exemplary embodiment, the stiffness matrix and mass matrix for obtaining above-mentioned single cell model it
Afterwards, can be discrete to the progress of above-mentioned single cell model according to FInite Element, to establish the equation of motion of single cell model, specifically, building
The vertical equation of motion isWherein, q indicates the displacement vector of unit, q={ q1 q2 q3 q4 qi}T.F indicates single
The node force vector of member, f={ f1 f2 f3 f4 0}T。
In an exemplary embodiment of the disclosure, abbreviation first can be carried out to the above-mentioned equation of motion, under normal circumstances, freely
Vibration considers f=0.It is assumed that this movement is simple harmonic motion, then the solution form of q are as follows: q (t)=qsin (ω t+ θ), wherein q is
Vibration shape vector, θ are phase angle.Second derivative is taken to q (t), is obtainedThis formula is substituted into above-mentioned movement
EquationIn available-M ω2Qsin (ω t+ θ)+Kqsin (ω t+ θ)=0, abbreviation obtains Kq- ω2Mq=0.
In step S802, according to Bloch theorem, the relation equation of displacement vector Yu freedom degree condensation matrix is obtained.
In an exemplary embodiment of the disclosure, displacement vector q and freedom degree can be obtained according to Bloch theorem
The relation equation of condensation matrix Q.That is q=Qqr, wherein qr={ qi q1 q2}T。
In step S803, according to the equation of motion and the relation equation, obtain the frequency of the single cell model with
Wave vector equation.
In an exemplary embodiment of the disclosure, with reference to the relevant explanation of above-mentioned steps S801, above-mentioned relation side is being obtained
Formula Kq- ω after journey, after above-mentioned relation equation can be substituted into above-mentioned abbreviation2In Mq=0, in turn, available KQqr-
ω2MQqr=0, in turn, due to the orthogonality of mass matrix M and stiffness matrix K, to above formula premultiplication orthogonal matrix QHIt obtains
QHKQqr-ω2QHMQqr=0, coordinate (k1, k2) the i.e. wave vector of series of points is chosen, final frequency and wave can be obtained in substitution
Arrow equation is [K (k1, k2)-ω2M(k1, k2)]μr=0, wherein μrQ i.e. in above-mentioned formular。
In step s 130, according to the frequency of the single cell model and wave vector equation, the band gap for obtaining the elastic wave is special
Property.
In an exemplary embodiment of the disclosure, Fig. 9 schematically shows periodic structure in one exemplary embodiment of the disclosure
The flow diagram of the control method of Propagation of Elastic Wave characteristic specifically illustrates frequency and wave vector equation according to single cell model,
The flow diagram for obtaining the band gap properties of elastic wave, explains step S130 below in conjunction with Fig. 9.
In step S901, according to the frequency of single cell model and wave vector equation, elastic wave described in single cell model is obtained
The natural frequency of vibration.
It in an exemplary embodiment of the disclosure, can be with after the frequency that obtains above-mentioned single cell model and wave vector equation
Enable the det ([K (k in above-mentioned equation1, k2)])=0, in turn, when choosing different wave vector K (k1, k2), it can be obtained corresponding
Different ω, according to ω, the phase velocity of available elastic wave propagationU is a unit direction vector, along wave vector K
Direction.And the group velocity of available elastic wave propagationIt is available with phase velocity by group velocity
The direction of propagation of elastic wave.
In step S902, according to the natural frequency of vibration, the band gap properties of the elastic wave are obtained.
In an exemplary embodiment of the disclosure, periodic structure has important vibration characteristics, i.e. band gap properties, works as elasticity
When wave is propagated in periodic structure, the elastic wave in certain frequency ranges cannot pass through, referred to as band gap.Band gap properties, that is, unit cell
The frequency of the elastic wave passed through in model and the corresponding relationship of wave vector.
In an exemplary embodiment of the disclosure, with reference to the relevant explanation of above-mentioned steps S901, according to different ω from it is different
The corresponding relationship of wave vector K (k1, k2), the band gap properties of available elastic wave.
It in an exemplary embodiment of the disclosure, can be according to elasticity after the band gap properties for obtaining above-mentioned elastic wave
The propagation of the band gap properties regulation periodic structure Elastic Wave of wave.Specifically, period knot can be controlled according to above-mentioned band gap properties
In structure can by elastic wave frequency.Both it can control above-mentioned periodic structure and generated new band gap, in new frequency range
Interior prevention wave is propagated；Or the bandgap range of script is reduced, to reach different requirements.It is realized indirectly pair by adjusting temperature
The adjusting of elastic wave propagation characteristic cuts periodic structure application thus, it is possible to solve to expend a large amount of manpower and material resources in the prior art
The inclined field of stress, electromagnetic field etc. control wave propagation characteristic, caused by the technical issues of taking time and effort, realize flexibly, it is autonomous
Regulation.
The disclosure additionally provides a kind of control device of periodic structure Propagation of Elastic Wave characteristic, by applying temperature field control
Propagation characteristic of the elastic wave in the periodic structure is made, Figure 10 is shown in disclosure exemplary embodiment in periodic structure
The structural schematic diagram of the control device of elastic wave propagation characteristic；As shown in Figure 10, the control of periodic structure Propagation of Elastic Wave characteristic
Device 1000 processed may include that the first acquisition module 1001, second obtains module 1002 and third acquisition module 1003.Wherein:
First obtains module 1001, for obtaining a single cell model from the periodic structure, and obtains the unit cell mould
The corresponding stiffness matrix of type and mass matrix.
In an exemplary embodiment of the disclosure, single cell model for being divided by the first acquisition module according to dynamic model
Multiple identical beam elements；The axial direction generated under temperature field action according to the motion control equation of beam element and single cell model
Power obtains the corresponding mass matrix of beam element and stiffness matrix；Mass matrix and stiffness matrix to beam element carry out unit group
Dress, to obtain the corresponding mass matrix of single cell model and stiffness matrix.
In an exemplary embodiment of the disclosure, first acquisition module be also used to according to the motion control equation of beam element with
And the axial force that single cell model generates under temperature field action, obtain the parameter value of beam element correspondingly-shaped function；According to beam list
The parameter value of first correspondingly-shaped function obtains the corresponding mass matrix of beam element and stiffness matrix based on the golden method of gal the Liao Dynasty.
In an exemplary embodiment of the disclosure, the first acquisition module is also used to according to the foundation of timoshenko beam theory
Dynamic model.
Second obtains module 1002, for obtaining the frequency of the single cell model according to the stiffness matrix and mass matrix
Rate and wave vector equation.
In an exemplary embodiment of the disclosure, second module is obtained for establishing according to stiffness matrix and mass matrix
The equation of motion of single cell model；According to Bloch theorem, the relation equation of displacement vector Yu freedom degree condensation matrix is obtained；According to
The equation of motion and the relation equation obtain the frequency and wave vector equation of single cell model.
Third obtains module 1003, for the frequency and wave vector equation according to the single cell model, obtains the elastic wave
Band gap properties.
In an exemplary embodiment of the disclosure, third acquisition module is used for frequency and wave vector side according to single cell model
Journey obtains the natural frequency of vibration of elastic wave described in single cell model；According to the natural frequency of vibration, the band gap properties of elastic wave are obtained.
In an exemplary embodiment of the disclosure, third obtains module and is also used to regulate and control week according to the band gap properties of elastic wave
The propagation of phase structure Elastic Wave.
The detail of each module is corresponding in the control device of above-mentioned periodic structure Propagation of Elastic Wave characteristic
It is described in detail in the control method of periodic structure Propagation of Elastic Wave characteristic, therefore details are not described herein again.
It should be noted that although being referred to several modules or list for acting the equipment executed in the above detailed description
Member, but this division is not enforceable.In fact, according to embodiment of the present disclosure, it is above-described two or more
Module or the feature and function of unit can embody in a module or unit.Conversely, an above-described mould
The feature and function of block or unit can be to be embodied by multiple modules or unit with further division.
In addition, although describing each step of method in the disclosure in the accompanying drawings with particular order, this does not really want
These steps must be executed in this particular order by asking or implying, or having to carry out step shown in whole could realize
Desired result.Additional or alternative, it is convenient to omit multiple steps are merged into a step and executed by certain steps, and/
Or a step is decomposed into execution of multiple steps etc..
Through the above description of the embodiments, those skilled in the art is it can be readily appreciated that example described herein is implemented
Mode can also be realized by software realization in such a way that software is in conjunction with necessary hardware.Therefore, according to the disclosure
The technical solution of embodiment can be embodied in the form of software products, which can store non-volatile at one
Property storage medium (can be CD-ROM, USB flash disk, mobile hard disk etc.) in or network on, including some instructions are so that a calculating
Equipment (can be personal computer, server, mobile terminal or network equipment etc.) is executed according to disclosure embodiment
Method.
In disclosure illustrative embodiments, a kind of computer storage Jie that can be realized the above method is additionally provided
Matter.It is stored thereon with the program product that can be realized this specification above method.In some possible embodiments, the disclosure
Various aspects are also implemented as a kind of form of program product comprising program code, when described program product is set in terminal
When standby upper operation, said program code is retouched in above-mentioned " illustrative methods " part of this specification for executing the terminal device
The step of illustrative embodiments various according to the disclosure stated.
With reference to shown in Figure 11, the program product for realizing the above method according to embodiment of the present disclosure is described
1100, can using portable compact disc read only memory (CD-ROM) and including program code, and can in terminal device,
Such as it is run on PC.However, the program product of the disclosure is without being limited thereto, in this document, readable storage medium storing program for executing can be with
To be any include or the tangible medium of storage program, the program can be commanded execution system, device or device use or
It is in connection.
Described program product can be using any combination of one or more readable mediums.Readable medium can be readable letter
Number medium or readable storage medium storing program for executing.Readable storage medium storing program for executing for example can be but be not limited to electricity, magnetic, optical, electromagnetic, infrared ray or
System, device or the device of semiconductor, or any above combination.The more specific example of readable storage medium storing program for executing is (non exhaustive
List) include: electrical connection with one or more conducting wires, portable disc, hard disk, random access memory (RAM), read-only
Memory (ROM), erasable programmable read only memory (EPROM or flash memory), optical fiber, portable compact disc read only memory
(CD-ROM), light storage device, magnetic memory device or above-mentioned any appropriate combination.
Computer-readable signal media may include in a base band or as carrier wave a part propagate data-signal,
In carry readable program code.The data-signal of this propagation can take various forms, including but not limited to electromagnetic signal,
Optical signal or above-mentioned any appropriate combination.Readable signal medium can also be any readable Jie other than readable storage medium storing program for executing
Matter, the readable medium can send, propagate or transmit for by instruction execution system, device or device use or and its
The program of combined use.
The program code for including on readable medium can transmit with any suitable medium, including but not limited to wirelessly, have
Line, optical cable, RF etc. or above-mentioned any appropriate combination.
Can with any combination of one or more programming languages come write for execute the disclosure operation program
Code, described program design language include object oriented program language-Java, C++ etc., further include conventional
Procedural programming language-such as " C " language or similar programming language.Program code can be fully in user
It calculates and executes in equipment, partly executes on a user device, being executed as an independent software package, partially in user's calculating
Upper side point is executed on a remote computing or is executed in remote computing device or server completely.It is being related to far
Journey calculates in the situation of equipment, and remote computing device can pass through the network of any kind, including local area network (LAN) or wide area network
(WAN), it is connected to user calculating equipment, or, it may be connected to external computing device (such as utilize ISP
To be connected by internet).
In addition, in an exemplary embodiment of the disclosure, additionally providing a kind of electronic equipment that can be realized the above method.
Person of ordinary skill in the field it is understood that various aspects of the disclosure can be implemented as system, method or
Program product.Therefore, various aspects of the disclosure can be with specific implementation is as follows, it may be assumed that complete hardware embodiment, complete
The embodiment combined in terms of full Software Implementation (including firmware, microcode etc.) or hardware and software, can unite here
Referred to as circuit, " module " or " system ".
The electronic equipment 1200 of this embodiment according to the disclosure is described referring to Figure 12.The electricity that Figure 12 is shown
Sub- equipment 1200 is only an example, should not function to the embodiment of the present disclosure and use scope bring any restrictions.
As shown in figure 12, electronic equipment 1200 is showed in the form of universal computing device.The component of electronic equipment 1200 can
To include but is not limited to: at least one above-mentioned processing unit 1210, connects not homologous ray at least one above-mentioned storage unit 1220
The bus 1230 of component (including storage unit 1220 and processing unit 1210).
Wherein, the storage unit is stored with program code, and said program code can be held by the processing unit 1210
Row, so that various according to the disclosure described in the execution of the processing unit 1210 above-mentioned " illustrative methods " part of this specification
The step of illustrative embodiments.For example, the processing unit 1210 can execute as shown in Figure 1: step S110, from week
A single cell model is obtained in phase structure, and obtains the corresponding stiffness matrix of the single cell model and mass matrix；Step S120, root
According to the stiffness matrix and mass matrix, the frequency and wave vector equation of the single cell model are obtained；Step S130, according to the list
The frequency and wave vector equation of born of the same parents' model, obtain the band gap properties of the elastic wave.
Storage unit 1220 may include the readable medium of volatile memory cell form, such as Random Access Storage Unit
(RAM) 12201 and/or cache memory unit 12202, it can further include read-only memory unit (ROM) 12203.
Storage unit 1220 can also include program/utility with one group of (at least one) program module 12205
12204, such program module 12205 includes but is not limited to: operating system, one or more application program, other programs
It may include the realization of network environment in module and program data, each of these examples or certain combination.
Bus 1230 can be to indicate one of a few class bus structures or a variety of, including storage unit bus or storage
Cell controller, peripheral bus, graphics acceleration port, processing unit use any bus structures in a variety of bus structures
Local bus.
Electronic equipment 1200 can also be with one or more external equipments 1300 (such as keyboard, sensing equipment, bluetooth equipment
Deng) communication, can also be enabled a user to one or more equipment interact with the electronic equipment 1200 communicate, and/or with make
The electronic equipment 1200 can with it is one or more of the other calculating equipment be communicated any equipment (such as router, modulation
Demodulator etc.) communication.This communication can be carried out by input/output (I/O) interface 1250.Also, electronic equipment 1200
Network adapter 1260 and one or more network (such as local area network (LAN), wide area network (WAN) and/or public affairs can also be passed through
Common network network, such as internet) communication.As shown, network adapter 1260 passes through its of bus 1230 and electronic equipment 1200
The communication of its module.It should be understood that although not shown in the drawings, other hardware and/or software can be used in conjunction with electronic equipment 1200
Module, including but not limited to: microcode, device driver, redundant processing unit, external disk drive array, RAID system, magnetic
Tape drive and data backup storage system etc..
Through the above description of the embodiments, those skilled in the art is it can be readily appreciated that example described herein is implemented
Mode can also be realized by software realization in such a way that software is in conjunction with necessary hardware.Therefore, according to the disclosure
The technical solution of embodiment can be embodied in the form of software products, which can store non-volatile at one
Property storage medium (can be CD-ROM, USB flash disk, mobile hard disk etc.) in or network on, including some instructions are so that a calculating
Equipment (can be personal computer, server, terminal installation or network equipment etc.) is executed according to disclosure embodiment
Method.
In addition, above-mentioned attached drawing is only the schematic theory of the processing according to included by the method for disclosure exemplary embodiment
It is bright, rather than limit purpose.It can be readily appreciated that the time that above-mentioned processing shown in the drawings did not indicated or limited these processing is suitable
Sequence.In addition, be also easy to understand, these processing, which can be, for example either synchronously or asynchronously to be executed in multiple modules.
Those skilled in the art after considering the specification and implementing the invention disclosed here, will readily occur to its of the disclosure
His embodiment.This application is intended to cover any variations, uses, or adaptations of the disclosure, these modifications, purposes or
Adaptive change follow the general principles of this disclosure and including the undocumented common knowledge in the art of the disclosure or
Conventional techniques.The description and examples are only to be considered as illustrative, and the true scope and spirit of the disclosure are by claim
It points out.
Claims (10)
1. a kind of control method of periodic structure Propagation of Elastic Wave characteristic, which is characterized in that by applying Temperature Field Control institute
State propagation characteristic of the elastic wave in the periodic structure, which comprises
A single cell model is obtained from periodic structure, and obtains the corresponding stiffness matrix of the single cell model and mass matrix；
According to the stiffness matrix and mass matrix, the frequency and wave vector equation of the single cell model are obtained；
According to the frequency of the single cell model and wave vector equation, the band gap properties of the elastic wave are obtained.
2. the method according to claim 1, wherein it is described obtain the corresponding stiffness matrix of the single cell model with
Mass matrix, comprising:
The single cell model is divided into multiple identical beam elements according to dynamic model；
The axial direction generated under the temperature field action according to the motion control equation of the beam element and the single cell model
Power obtains the corresponding mass matrix of the beam element and stiffness matrix；
Mass matrix and stiffness matrix to the beam element carry out unit assembling, to obtain the corresponding quality of the single cell model
Matrix and stiffness matrix.
3. according to the method described in claim 2, it is characterized in that, the motion control equation according to the beam element and
The axial force that the single cell model generates under the temperature field action obtains the corresponding mass matrix of the beam element and rigidity
Matrix, comprising:
The axial direction generated under the temperature field action according to the motion control equation of the beam element and the single cell model
Power obtains the parameter value of the beam element correspondingly-shaped function；
The corresponding matter of the beam element is obtained based on the golden method of gal the Liao Dynasty according to the parameter value of the beam element correspondingly-shaped function
Moment matrix and stiffness matrix.
4. according to the method described in claim 3, it is characterized in that, the single cell model is divided according to dynamic model described
Before multiple identical beam elements, the method also includes:
The dynamic model is established according to timoshenko beam theory.
5. the method according to claim 1, wherein described according to the stiffness matrix and mass matrix, acquisition
The frequency and wave vector equation of the single cell model, comprising:
According to the stiffness matrix and mass matrix, the equation of motion of the single cell model is established；
According to Bloch theorem, the relation equation of displacement vector Yu freedom degree condensation matrix is obtained；
According to the equation of motion and the relation equation, the frequency and wave vector equation of the single cell model are obtained.
6. according to the method described in claim 5, it is characterized in that, the frequency according to the single cell model and wave vector side
Journey obtains the band gap properties of the elastic wave, comprising:
According to the frequency of the single cell model and wave vector equation, the natural frequency of vibration of elastic wave described in the single cell model is obtained；
According to the natural frequency of vibration, the band gap properties of the elastic wave are obtained.
7. the method according to claim 1, wherein the method also includes:
Regulate and control the propagation of elastic wave described in the periodic structure according to the band gap properties of the elastic wave.
8. a kind of control device of periodic structure Propagation of Elastic Wave characteristic, which is characterized in that by applying Temperature Field Control institute
State propagation characteristic of the elastic wave in the periodic structure, comprising:
First obtains module, and for obtaining a single cell model from the periodic structure, and it is corresponding to obtain the single cell model
Stiffness matrix and mass matrix；
Second obtains module, for obtaining the frequency and wave vector of the single cell model according to the stiffness matrix and mass matrix
Equation；
Third obtains module, and for the frequency and wave vector equation according to the single cell model, the band gap for obtaining the elastic wave is special
Property.
9. a kind of computer storage medium, is stored thereon with computer program, which is characterized in that the computer program is processed
The control method of periodic structure Propagation of Elastic Wave characteristic described in any one of claim 1~7 is realized when device executes.
10. a kind of electronic equipment characterized by comprising
Processor；And
Memory, for storing the executable instruction of the processor；
Wherein, the processor is configured to come any one of perform claim requirement 1~7 institute via the execution executable instruction
The control method for the periodic structure Propagation of Elastic Wave characteristic stated.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111563294A (en) * | 2020-04-23 | 2020-08-21 | 西北工业大学 | Optimization design method of bent rod periodic structure based on band gap |
| CN111563316A (en) * | 2020-04-09 | 2020-08-21 | 西北工业大学 | Method for regulating and controlling elastic wave propagation characteristics in chiral periodic structure |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106777771A (en) * | 2017-01-09 | 2017-05-31 | 温州大学 | Two-dimension phonon crystal slab structure band gap method for designing based on wavelet finite element model |
| CN109519494A (en) * | 2018-12-04 | 2019-03-26 | 中国航空工业集团公司西安飞机设计研究所 | A kind of vibration and noise reducing spring of double helix periodic structure |
-
2019
- 2019-07-16 CN CN201910641165.XA patent/CN110472287A/en active Pending
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106777771A (en) * | 2017-01-09 | 2017-05-31 | 温州大学 | Two-dimension phonon crystal slab structure band gap method for designing based on wavelet finite element model |
| CN109519494A (en) * | 2018-12-04 | 2019-03-26 | 中国航空工业集团公司西安飞机设计研究所 | A kind of vibration and noise reducing spring of double helix periodic structure |
Non-Patent Citations (2)
| Title |
|---|
| KAI ZHANG 等: "Effect of pre-load on wave propagation characteristics of hexagonal lattices", 《COMPOSITE STRUCTURES》, vol. 203, 1 November 2018 (2018-11-01), pages 361 - 372 * |
| YING WU 等: "Effect of thermal stresses on frequency band structures of elastic metamaterial plates", 《JOURNAL OF SOUND AND VIBRATION》, no. 413, 20 January 2018 (2018-01-20), pages 101 - 119 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111563316A (en) * | 2020-04-09 | 2020-08-21 | 西北工业大学 | Method for regulating and controlling elastic wave propagation characteristics in chiral periodic structure |
| CN111563294A (en) * | 2020-04-23 | 2020-08-21 | 西北工业大学 | Optimization design method of bent rod periodic structure based on band gap |
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