CN117077377A - Full band gap regulation and control method of negative-stiffness super-structure beam and negative-stiffness super-structure beam - Google Patents
Full band gap regulation and control method of negative-stiffness super-structure beam and negative-stiffness super-structure beam Download PDFInfo
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Abstract
The application relates to the technical field of vibration reduction and noise reduction, and discloses a full band gap regulation and control method of a negative-stiffness super-structure beam and the negative-stiffness super-structure beam, wherein the method comprises the following steps: acquiring a first mass of a main body structure, a second mass of an inertia amplifying structure, a third mass of a local resonance structure, a first stiffness of a main spring, a second stiffness of a horizontal spring and a third stiffness of a vertical spring; constructing a dynamic equation related to displacement in the vibration reduction beam based on the first mass, the second mass, the third mass, the first stiffness, the second stiffness and the third stiffness; based on a dynamics equation, taking displacement as harmonic form motion to construct a dispersion relation equation, and obtaining an upper boundary, a lower boundary and a cut-off frequency of a band gap in the vibration reduction beam according to the dispersion relation equation; carrying out parameter analysis on the upper boundary, the lower boundary and the cut-off frequency to obtain the structural parameters of the vibration attenuation beam in the whole frequency domain; the application solves the problems that the existing band gap regulation mode has narrow action frequency band and can not adapt to changeable excitation in complex environment.
Description
Technical Field
The application relates to the technical field of vibration reduction and noise reduction, in particular to a full band gap regulation and control method of a negative-stiffness super-structure beam and the negative-stiffness super-structure beam.
Background
Unnecessary vibrations in engineering can cause harm to buildings, equipment, and even human health. Particularly, the low-frequency vibration has the characteristics of strong penetrability, large amplitude and difficult elimination. The control range of the isolator isolation frequency is affected by the system mass and stiffness. For conventional isolators, the system is effective in isolating vibration only when the excitation frequency is greater than 2 times the root number of the resonant frequency. Therefore, achieving low frequency vibration isolation requires a large mass or low stiffness, which is in contradiction to lightweight manufacturing and system stability. On this basis, it can be inferred that increasing the effective mass of the system or decreasing the effective height of the system is two major approaches to achieving low frequency vibration isolation. In recent studies, mechanical metamaterials can produce unnatural effective properties through artificial design and periodic alignment, thereby creating a band gap and preventing wave propagation. Particularly, the inertial amplification mechanism and the negative stiffness mechanism are introduced into the unit cell of the super structure, so that the effective mass can be respectively improved, the effective height can be reduced, the band gap can be reduced, and the attenuation of low-frequency vibration can be realized.
Generally, there are two bandgap formation mechanisms, bragg scattering and local resonance. The former can generate a wide band gap through unit design and optimization, but due to the limitation of size and quality, the regulation and control of low-frequency waves are difficult to realize; the latter can utilize the relative heavy or soft material connected local resonance body to realize the low frequency band gap, but along with the increase of quality or the reduction of rigidity, the lower the frequency is, the narrower the corresponding scope can't realize low frequency broadband vibration damping simultaneously, in sum, the super structure based on two mechanisms is better to the elastic wave regulation and control effect of each frequency channel respectively, but the effect frequency channel is single, makes it unable to adapt to the engineering application of changeable excitation under the complex environment. Therefore, it is needed to propose a novel structure and a corresponding band gap adjusting method, which can combine the adjusting and controlling characteristics of two mechanisms to realize the vibration attenuation of the full frequency band.
Disclosure of Invention
The application provides a full band gap regulation and control method of a negative-stiffness super-structure beam and the negative-stiffness super-structure beam, which are used for solving the problems that the existing band gap regulation and control mode has single action frequency band and cannot adapt to variable excitation in a complex environment.
In order to achieve the above object, the present application is realized by the following technical scheme:
in a first aspect, the present application provides a full band gap adjustment method for a negative stiffness superstructure beam, applied to a negative stiffness superstructure beam, the vibration reduction beam comprising: n unit cell structures, N is positive integer, connects each unit cell structure through main spring each other, unit cell structure includes: the main body structure, two inertial amplification structures that main body structure passes through the connecting rod to be connected, and set up between two vertical springs through the local resonance structure of horizontal spring connection, the method includes:
acquiring a first mass of a main body structure, a second mass of an inertia amplifying structure, a third mass of a local resonance structure, a first stiffness of a main spring, a second stiffness of a horizontal spring and a third stiffness of a vertical spring;
constructing a displacement-related kinetic equation in the vibration reduction beam based on the first mass, the second mass, the third mass, the first stiffness, the second stiffness, and the third stiffness;
based on the dynamics equation, taking displacement as harmonic form motion to construct a dispersion relation equation, and obtaining an upper boundary, a lower boundary and a cut-off frequency of a band gap in the vibration reduction beam according to the dispersion relation equation;
and carrying out parameter analysis on the upper boundary, the lower boundary and the cut-off frequency to obtain the structural parameters of the vibration damping of the whole frequency domain of the vibration damping beam, so as to design the negative-rigidity super-structural beam according to the structural parameters of the vibration damping of the whole frequency domain of the vibration damping beam.
Optionally, the constructing a dynamic equation related to displacement in the vibration reduction beam based on the first mass, the second mass, the third mass, the first stiffness, the second stiffness, and the third stiffness includes:
and constructing a dynamic equation related to displacement in the vibration reduction beam based on the first mass, the second mass, the third mass, the first rigidity, the second rigidity and the third rigidity through a centralized mass method and a Lagrangian equation, wherein the dynamic equation expression is as follows:
in M, m 1 And m 2 First, second and third masses, K, k, respectively 1 And k n Represents a first stiffness, a second stiffness and a third stiffness, respectively, u j Is the displacement of the jth main body structure, t is time, gamma is the tangent function of the horizontal included angle of the connecting rod mechanism, v j The displacement d for the jth local resonator represents the differential of the displacement.
Optionally, the constructing a dispersion relation equation based on the dynamics equation regarding displacement as harmonic form motion includes:
the dispersion relation equation is constructed by using the bloch theory to treat the displacement in the dynamics equation as the motion in harmonic form, wherein the dispersion relation equation expression is as follows:
in the method, in the process of the application,are dimensionless parameters. q is the wavenumber, l is the lattice constant, and ω is the vibration frequency.
Optionally, the obtaining the upper boundary, the lower boundary and the cut-off frequency of the band gap in the vibration reduction beam according to the dispersion relation equation includes:
based on the dispersion relation equation, the wave numbers are set to 0 and 1 respectively, and the upper boundary, the lower boundary and the cut-off frequency of the band gap in the vibration damping beam are obtained, wherein the expressions of the upper boundary, the lower boundary and the cut-off frequency are as follows:
in the method, in the process of the application,are all dimensionless parameters M, m 1 And m 2 First, second and third masses, K, k, respectively 1 And k n Respectively representing a first stiffness, a second stiffness and a third stiffness, omega U Representing the upper boundary, Ω L Representing the lower boundary, Ω C Represents the cut-off frequency +.>
Optionally, the performing parameter analysis on the upper boundary, the lower boundary and the cut-off frequency to obtain structural parameters of full frequency domain vibration damping of the vibration damping beam includes:
the negative stiffness ratio can be obtained by carrying out parameter analysis on the analytic expression of the upper and lower boundary frequencies of the band gap under certain conditionsThe lower boundary frequency of the proposed structure may tend to a value of 0;
the upper boundary frequency and the cut-off frequency of the band gap are equal, namely the band structure becomes two horizontal straight lines, and the expression of parameter coordination at the moment is as follows:
wherein,are all of no quantityThe class parameter, alpha, is the horizontal included angle of the four-bar mechanism;
when the structural parameters meet the two conditions, the energy band structure of the system is changed into two horizontal straight lines, and the quasi-full frequency domain vibration reduction can be realized.
In a second aspect, an embodiment of the present application provides a negative stiffness superstructure beam, where the vibration damping beam further includes an inertial amplifying mechanism and a negative stiffness mechanism, where the inertial amplifying mechanism and the negative stiffness mechanism are axially connected to the same main structure, and the main structure is connected to the main structure by a main spring.
Optionally, the negative stiffness mechanism is composed of a three-spring mechanism and a local resonance structure, the three-spring mechanism comprises two vertical springs and a horizontal spring, the two vertical springs are responsible for realizing the negative stiffness through precompression, and the horizontal spring is responsible for keeping the stability of the local resonance structure.
Optionally, the vibration reduction beam further comprises a relation amplifying mechanism, the inertia amplifying mechanism is composed of a four-bar mechanism and an inertia amplifying structure, the inertia amplifying structure is located at the upper top and the lower top of the four-bar mechanism, and the connecting mode between the connecting rods in the four-bar mechanism is hinged connection.
The beneficial effects are that:
according to the full band gap regulating and controlling method for the negative stiffness super-structure beam, provided by the application, the dynamic equation related to displacement in the vibration-damping beam is constructed, the displacement is regarded as harmonic motion based on the dynamic equation to construct the dispersion relation equation, the upper boundary, the lower boundary and the cutoff frequency of the band gap in the vibration-damping beam are obtained according to the dispersion relation equation, the upper boundary, the lower boundary and the cutoff frequency are subjected to parameter analysis, and the structural parameters of vibration damping of the vibration-damping beam in the full frequency domain are obtained, so that the effective regulation of the band gap and the frequency is achieved, the full frequency band vibration damping can be realized under the slight damping effect through the effective regulation of the static band gap and the cutoff frequency, and the method has a wider industrial application background.
Drawings
FIG. 1 is a flow chart of a method of full band gap modulation of a negative stiffness superstructure beam of a preferred embodiment of the present application;
FIG. 2 is a block diagram of a negative stiffness beam frame of a preferred embodiment of the present application;
FIG. 3 is a three-dimensional view of a negative stiffness beam frame of a preferred embodiment of the present application;
FIG. 4 is a schematic view of the components of a negative stiffness beam of a preferred embodiment of the present application, wherein a represents the main structure, b represents the connecting rod, c represents the inertial amplifying structure, and d represents the local resonant structure;
FIG. 5 is a schematic diagram showing the variation rule of band gap with negative stiffness when the negative stiffness mechanism of the preferred embodiment of the present application is singly applied;
FIG. 6 is a schematic diagram of a process for forming a quasi-full bandgap according to a preferred embodiment of the application;
FIG. 7 is a schematic diagram showing the formation of a full band gap after addition of damping in accordance with a preferred embodiment of the present application;
FIG. 8 is a schematic diagram showing the process of preparing and assembling the experimental sample of the application structure according to the preferred embodiment of the application;
fig. 9 is a schematic diagram for verifying experimental results of an embodiment example of the preferred embodiment of the present application.
Detailed Description
The following description of the present application will be made clearly and fully, and it is apparent that the embodiments described are only some, but not all, of the embodiments of the present application. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
Unless defined otherwise, technical or scientific terms used herein should be given the ordinary meaning as understood by one of ordinary skill in the art to which this application belongs. The terms "first," "second," and the like, as used herein, do not denote any order, quantity, or importance, but rather are used to distinguish one element from another. Likewise, the terms "a" or "an" and the like do not denote a limitation of quantity, but rather denote the presence of at least one. The terms "connected" or "connected," and the like, are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "upper", "lower", "left", "right", etc. are used merely to indicate a relative positional relationship, which changes accordingly when the absolute position of the object to be described changes.
Example 1
Referring to fig. 1, an embodiment of the present application provides a full band gap adjusting method for a negative stiffness superstructure beam, applied to a negative stiffness superstructure beam, where the vibration damping beam includes: n unit cell structures, N is positive integer, connects each unit cell structure through main spring each other, unit cell structure includes: the main body structure, two inertial amplification structures that main body structure passes through the connecting rod to be connected, and set up between two vertical springs through the local resonance structure of horizontal spring connection, the method includes:
acquiring a first mass of a main body structure, a second mass of an inertia amplifying structure, a third mass of a local resonance structure, a first stiffness of a main spring, a second stiffness of a horizontal spring and a third stiffness of a vertical spring;
constructing a displacement-related kinetic equation in the vibration reduction beam based on the first mass, the second mass, the third mass, the first stiffness, the second stiffness, and the third stiffness;
based on the dynamics equation, taking displacement as harmonic form motion to construct a dispersion relation equation, and obtaining an upper boundary, a lower boundary and a cut-off frequency of a band gap in the vibration reduction beam according to the dispersion relation equation;
and carrying out parameter analysis on the upper boundary, the lower boundary and the cut-off frequency to obtain the structural parameters of the vibration damping of the whole frequency domain of the vibration damping beam, so as to design the negative-rigidity super-structural beam according to the structural parameters of the vibration damping of the whole frequency domain of the vibration damping beam.
In the embodiment, the dynamic equation related to displacement in the vibration reduction beam is constructed, the displacement is regarded as harmonic motion based on the dynamic equation to construct a dispersion relation equation, the upper boundary, the lower boundary and the cutoff frequency of the band gap in the vibration reduction beam are obtained according to the dispersion relation equation, the upper boundary, the lower boundary and the cutoff frequency are subjected to parameter analysis, and the structural parameters of vibration reduction of the whole frequency domain of the vibration reduction beam are obtained, so that the effective adjustment of the band gap and the frequency is achieved, the whole-band vibration reduction can be realized under the slight damping effect by aligning the effective adjustment of the static band gap and the cutoff frequency, and the vibration reduction device has wider industrial application background.
Optionally, the constructing a dynamic equation related to displacement in the vibration reduction beam based on the first mass, the second mass, the third mass, the first stiffness, the second stiffness, and the third stiffness includes:
and constructing a dynamic equation related to displacement in the vibration reduction beam based on the first mass, the second mass, the third mass, the first rigidity, the second rigidity and the third rigidity through a centralized mass method and a Lagrangian equation, wherein the dynamic equation expression is as follows:
in M, m 1 And m 2 First, second and third masses, K, k, respectively 1 And k n Represents a first stiffness, a second stiffness and a third stiffness, respectively, u j Is the displacement of the jth main body structure, t is time, gamma is the tangent function of the horizontal included angle of the connecting rod mechanism, v j The displacement of the jth local resonator is represented by d, which represents the differential of the displacement.
Optionally, the constructing a dispersion relation equation based on the dynamics equation regarding displacement as harmonic form motion includes:
the dispersion relation equation is constructed by using the bloch theory to treat the displacement in the dynamics equation as the motion in harmonic form, wherein the dispersion relation equation expression is as follows:
in the method, in the process of the application,are dimensionless parameters. q is the wavenumber, l is the lattice constant, and ω is the vibration frequency.
Optionally, the obtaining the upper boundary, the lower boundary and the cut-off frequency of the band gap in the vibration reduction beam according to the dispersion relation equation includes:
based on the dispersion relation equation, the wave numbers are set to 0 and 1 respectively, and the upper boundary, the lower boundary and the cut-off frequency of the band gap in the vibration damping beam are obtained, wherein the expressions of the upper boundary, the lower boundary and the cut-off frequency are as follows:
in the method, in the process of the application,are all dimensionless parameters M, m 1 And m 2 First, second and third masses, K, k, respectively 1 And k n Respectively representing a first stiffness, a second stiffness and a third stiffness, omega U Representing the upper boundary, Ω L Representing the lower boundary, Ω C Represents the cut-off frequency +.>
Optionally, the performing parameter analysis on the upper boundary, the lower boundary and the cut-off frequency to obtain structural parameters of full frequency domain vibration damping of the vibration damping beam includes:
the negative stiffness ratio can be obtained by carrying out parameter analysis on the analytic expressions of the upper and lower boundaries of the band gap under certain conditionsThe lower boundary of the proposed structure may tend to be 0 value;
the upper boundary of the band gap is equal to the cut-off frequency, namely the band structure becomes two horizontal straight lines, and the expression of parameter coordination is:
wherein,are dimensionless parameters, and alpha is the horizontal included angle of the four-bar mechanism;
when the structural parameters meet the two conditions, the energy band structure of the system is changed into two horizontal straight lines, and the quasi-full frequency domain vibration reduction can be realized.
Example 2
Referring to fig. 2-9, a negative stiffness superstructure beam comprises: the main mass, the local resonance mass, the inertial amplification mass and the connecting rod are connected by a spring. The position of the spring is fixed by small round tables which are extended from each part. Wherein, two thin beams extending from the main mass are connected with the upper and lower ends of the local resonance mass, and the vertical springs are used for realizing negative rigidity through precompression. The other side of the local resonance mass is connected with the main mass side round table and is used for maintaining self stability; the middle round table of the main mass is connected with the main spring end to end and is responsible for the bearing capacity of the whole structure; four connecting rods in each unit cell are connected with the mass body through hinges, and inertial amplification masses are arranged at the upper end and the lower end of the connecting rods. The resulting schematic structure is shown in fig. 3. Fig. 2 is a view of the three-dimensional model of fig. 3 from various angles. The length of the structure can be adjusted in real time by using the connecting rod mechanism, and the structure is used for band gap regulation and control. In general, the length of the unit cell can be 8-12 cm, the width of the unit cell is 7cm, and the thickness of the unit cell is 4cm.
By varying the amount of precompression of the vertical springs in the structure, a variation in the magnitude of the negative stiffness can be achieved. As shown in FIG. 5, as the precompression amount increases, the band gap lower boundary of the structure gradually decreases, when satisfiedWhen the lower boundary of the band gap is 0, a quasi-static band gap appears, and the band gap can be used for vibration reduction of an ultralow frequency structure, but at the moment, the band gap of a medium-high frequency band still has a certain width.
To further reduce the bandgap, for inertial amplificationThe mechanism performs parameter adjustment. It has been found that when the system parameters are satisfiedThe upper boundary of the band gap becomes a straight line as shown in fig. 6. With the change of the negative rigidity, the upper boundary is not affected, the lower boundary is still reduced, and the lower boundary gradually becomes two horizontal straight lines, namely, the quasi-full band gap appears.
Next, considering the damping effect in practical engineering application, the transfer rate is calculated again by introducing a damping coefficient to the system, and the specific expression of the transfer function is 20×log10 (output acceleration/input acceleration). Theoretical calculation shows that the structure with the quasi-full band gap is more sensitive to damping, and the resonance peak value can be reduced to be below 0 under the condition of smaller damping coefficient, so that the full-band vibration reduction effect is finally realized, as shown in fig. 7.
In order to fully explain the vibration isolation performance and band gap characteristics of the super-structure beam, experimental samples are prepared, and sweep experiments are respectively carried out on different control groups by using vibration exciters. Fig. 8 shows a specific model of an experimental sample, the white part is a resin frame, the silver part is a metal mass block, and the frames are connected through a coil spring. In this experiment, in order to be convenient for observe the effect and reduce the damping, the main mass of structure is fixed on the slider of slide rail, and the slider only can follow a direction free movement.
When the field test is carried out on the experimental site, firstly, the signal generator sends out signals with different frequency bands and amplitudes, the signals are amplified by the power amplifier and then are transmitted to the left side of the super-structure beam in a vibration mode by the vibration exciter, and the first unit and the last unit of the super-structure beam are respectively provided with an acceleration sensor for detecting the vibration condition of each component and calculating the final transfer function.
Fig. 9 shows the final experimental results. It can be seen that the experimental results and the simulation calculation can show a substantially consistent change rule. In addition, by taking the single action of the inertia amplifying mechanism and the negative stiffness mechanism as a comparison group, the result shows that the quasi-static band gap cannot appear when the inertia amplifying mechanism acts, and the ultralow frequency vibration reduction is realized; when only the negative stiffness mechanism is in action, vibration at the middle and high frequency bands cannot be effectively attenuated. Therefore, when the two are combined, the cooperative attenuation of the low frequency band, the middle frequency band and the high frequency band can be simultaneously realized, and the vibration reduction effect of the full frequency band is realized.
The embodiment of the application also provides a negative-stiffness super-structure beam, the vibration reduction beam further comprises an inertia amplifying mechanism and a negative-stiffness mechanism, the inertia amplifying mechanism and the negative-stiffness mechanism are axially connected to the same main structure, and the main structure is connected with the main structure through a main spring.
Optionally, the negative stiffness mechanism is composed of a three-spring mechanism and a local resonance structure, the three-spring mechanism comprises two vertical springs and a horizontal spring, the two vertical springs are responsible for realizing the negative stiffness through precompression, and the horizontal spring is responsible for keeping the stability of the local resonance structure.
Optionally, the vibration reduction beam further comprises a relation amplifying mechanism, the inertia amplifying mechanism is composed of a four-bar mechanism and an inertia amplifying structure, the inertia amplifying structure is located at the upper top and the lower top of the four-bar mechanism, and the connecting mode between the connecting rods in the four-bar mechanism is hinged connection.
The foregoing describes in detail preferred embodiments of the present application. It should be understood that numerous modifications and variations can be made in accordance with the concepts of the application by one of ordinary skill in the art without undue burden. Therefore, all technical solutions which can be obtained by logic analysis, reasoning or limited experiments based on the prior art by the person skilled in the art according to the inventive concept shall be within the scope of protection defined by the claims.
Claims (8)
1. The full band gap regulation and control method of the negative-stiffness super-structure beam is applied to the negative-stiffness super-structure beam, and the vibration reduction beam comprises: n unit cell structures, N is positive integer, connects each unit cell structure through main spring each other, unit cell structure includes: the device comprises a main body structure, two inertial amplifying structures connected with the main body structure through connecting rods, and a local resonance structure arranged between two vertical springs and connected with each other through horizontal springs, and is characterized in that the device comprises:
acquiring a first mass of a main body structure, a second mass of an inertia amplifying structure, a third mass of a local resonance structure, a first stiffness of a main spring, a second stiffness of a horizontal spring and a third stiffness of a vertical spring;
constructing a displacement-related kinetic equation in the vibration reduction beam based on the first mass, the second mass, the third mass, the first stiffness, the second stiffness, and the third stiffness;
based on the dynamics equation, taking displacement as harmonic form motion to construct a dispersion relation equation, and obtaining an upper boundary, a lower boundary and a cut-off frequency of a band gap in the vibration reduction beam according to the dispersion relation equation;
and carrying out parameter analysis on the upper boundary, the lower boundary and the cut-off frequency to obtain the structural parameters of the vibration damping of the whole frequency domain of the vibration damping beam, so as to design the negative-rigidity super-structural beam according to the structural parameters of the vibration damping of the whole frequency domain of the vibration damping beam.
2. The method of full band gap modulation of a negative stiffness superstructure beam according to claim 1, wherein said constructing a displacement-related kinetic equation in a vibration damping beam based on said first mass, said second mass, said third mass, said first stiffness, said second stiffness, and said third stiffness comprises:
and constructing a dynamic equation related to displacement in the vibration reduction beam based on the first mass, the second mass, the third mass, the first rigidity, the second rigidity and the third rigidity through a centralized mass method and a Lagrangian equation, wherein the dynamic equation expression is as follows:
in M, m 1 And m 2 First, second and third masses, K, k, respectively 1 And k n Respectively represent the firstA first stiffness, a second stiffness and a third stiffness, u j Is the displacement of the jth main body structure, t is time, gamma is the tangent function of the horizontal included angle of the connecting rod mechanism, v j The displacement of the jth local resonator is represented by d, which represents the differential of the displacement.
3. The method of full band gap modulation of a negative stiffness superstructure beam according to claim 1, wherein said constructing a dispersion relation equation based on said kinetic equation regarding displacement as harmonic form motion comprises:
the dispersion relation equation is constructed by using the bloch theory to treat the displacement in the dynamics equation as the motion in harmonic form, wherein the dispersion relation equation expression is as follows:
wherein mu is 1 、μ 2 、λ 1 、λ n 、Ω、ω 0 Is a dimensionless parameterM、m 1 And m 2 First, second and third masses, K, k, respectively 1 And k n And respectively representing the first rigidity, the second rigidity and the third rigidity, wherein gamma is a tangent function of a horizontal included angle of the connecting rod mechanism, q is a wave number, l is a lattice constant, and omega is a vibration frequency.
4. The method for full band gap modulation of a negative stiffness superstructure beam according to claim 1, wherein said deriving upper and lower boundaries and cut-off frequencies of the band gap in the vibration damping beam from dispersion relation equations comprises:
based on the dispersion relation equation, the wave numbers are set to 0 and 1 respectively, and the upper boundary, the lower boundary and the cut-off frequency of the band gap in the vibration damping beam are obtained, wherein the expressions of the upper boundary, the lower boundary and the cut-off frequency are as follows:
wherein: mu (mu) 1 、μ 2 、λ 1 、λ n Are all dimensionless parametersM、m 1 And m 2 First, second and third masses, K, k, respectively 1 And k n Respectively representing a first stiffness, a second stiffness and a third stiffness, omega U Representing the upper boundary, Ω L Representing the lower boundary, Ω C Representing the cut-off frequency. a. b and c are coefficients of the above equation, and the specific expression is: />
5. The method for full band gap modulation of a negative stiffness superstructure beam according to claim 1, wherein said performing a parametric analysis on said upper boundary, said lower boundary, and said cutoff frequency, results in structural parameters of full frequency domain damping of the damping beam, comprising:
by parametric analysis of the analytical expressions of the upper and lower band gap boundaries, the negative stiffness ratio lambda c n Satisfy the following requirementsThe lower boundary of the proposed structure may tend to be 0 value;
the upper boundary of the band gap is equal to the cut-off frequency, namely the band structure becomes two horizontal straight lines, and the expression of parameter coordination is:
wherein,are dimensionless parameters, and alpha is the horizontal included angle of the four-bar mechanism;
when the structural parameters meet the two conditions, the energy band structure of the system is changed into two horizontal straight lines, and the quasi-full frequency domain vibration reduction can be realized.
6. The negative stiffness super-structure beam is characterized by further comprising an inertia amplifying mechanism and a negative stiffness mechanism, wherein the inertia amplifying mechanism and the negative stiffness mechanism are axially connected to the same main body structure, and the main body structure is connected with the main body structure through a main spring.
7. The negative stiffness superstructure beam according to claim 6, wherein the negative stiffness mechanism is comprised of a tri-spring mechanism comprising two vertical springs responsible for achieving negative stiffness by precompression and one horizontal spring responsible for maintaining stability of the local resonance structure.
8. The negative stiffness superstructure beam of claim 6, wherein the vibration reduction beam further comprises a relationship amplifying mechanism, the inertia amplifying mechanism is comprised of a four bar linkage, the inertia amplifying mechanism is located at the upper and lower vertices of the four bar linkage, and the connection between the links in the four bar linkage is a hinged connection.
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| US20210094799A1 (en) * | 2018-05-15 | 2021-04-01 | Mitsubishi Electric Corporation | Vibration damping device and elevator apparatus |
| CN110805348A (en) * | 2019-11-22 | 2020-02-18 | 河南理工大学 | Self-resetting rotary inertia capacity damper |
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