CN113153949B - Nonlinear coupling resonance unit and nonlinear acoustic metamaterial cellular structure - Google Patents
Nonlinear coupling resonance unit and nonlinear acoustic metamaterial cellular structure Download PDFInfo
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
- F16F7/00—Vibration-dampers; Shock-absorbers
- F16F7/10—Vibration-dampers; Shock-absorbers using inertia effect
- F16F7/104—Vibration-dampers; Shock-absorbers using inertia effect the inertia member being resiliently mounted
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
- F16F2224/00—Materials; Material properties
- F16F2224/02—Materials; Material properties solids
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
- F16F2228/00—Functional characteristics, e.g. variability, frequency-dependence
- F16F2228/06—Stiffness
- F16F2228/066—Variable stiffness
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Abstract
The invention relates to a nonlinear coupling resonance unit and a nonlinear acoustic metamaterial cellular structure, wherein the nonlinear coupling resonance unit comprises: the vibrator, the spring, the base, the sleeve and the supporting rod; the middle of the vibrator is provided with a central hole, and the support rod penetrates through the central hole of the vibrator; the vibrator and the supporting rod are coaxially arranged; the supporting rod takes the vibrator as a middle point, and two ends of the supporting rod are symmetrical and are sleeved in the sleeve; a base is arranged at one end of the sleeve, which is far away from the vibrator, and two ends of the vibrator are fixedly connected with the base through springs; gaps are arranged between the end face of the vibrator and the end face of the sleeve and between the center hole of the vibrator and the support rod. The unit has the characteristics of compact structure, adjustability and the like; by applying the unit, based on a typical plate-shell structure, a super-nonlinear material structure is designed, and a nonlinear local resonance band gap and a chaotic band can be generated, so that the unit can generate a vibration suppression effect of a low-frequency broadband under the condition of small additional mass.
Description
Technical Field
The invention relates to a nonlinear coupling resonance unit, a nonlinear acoustic metamaterial unit cell and a nonlinear acoustic metamaterial structure thereof, and belongs to the fields of aerospace, mechanical engineering, solid mechanics, vibration noise control and metamaterials.
Background
Structural vibration suppression is a significant impact on device/equipment/product performance. Particularly in the field of aerospace, the equipment service environment is severe, the structure is light and important, the plate shell structure on an airplane/rocket is more, the vibration generated under the excitation of an engine and pneumatic power not only influences the stability and safety of the structure of the airplane and the precision of precision instruments, but also vibrates and radiates noise, and the riding comfort is seriously influenced. Constrained by conditions such as weight, size, efficiency and environmental adaptability of engineering application, the realization of low-frequency, broadband and high-efficiency vibration suppression of a plate-shell structure under the condition of small additional mass is always a difficult problem which puzzles the design of equipment such as aerospace and the like, and a new vibration reduction and noise reduction technology is urgently required to be developed.
The acoustic metamaterial refers to an artificial metamaterial/structure with elastic wave sub-wavelength regulation characteristics. Different from the traditional material, the metamaterial regulates and controls low-frequency elastic waves based on a periodic microstructure which is artificially designed, and is based on the existing base material or composite material, the microstructure is reversely designed according to the technical requirements of products, and a novel material with new characteristics is obtained. Currently, a great deal of research is focused on linear acoustic metamaterials. However, the local resonance band gap bandwidth of the linear acoustic metamaterial is narrow, and the bandwidth is related to the additional mass of the local resonance unit, so that the vibration reduction performance of light weight, low frequency and wide band is difficult to realize at the same time. In addition, the passband of a linear metamaterial spectrum of finite size is made up of dense formants, and the greater the number of unit cells, the greater the number of formants within the passband. That is, the narrow band elastic band gap of the linear metamaterial can attenuate the structural vibration, but the response in the wider pass band is amplified by resonance.
Nonlinear acoustic metamaterials refer to acoustic metamaterials with significant nonlinear dynamic effects. Research shows that under the strong nonlinear condition, dense structural resonance becomes strong nonlinear coupling resonance and even chaotic response is generated. The effect has low-frequency, broadband and high-efficiency vibration suppression capability and is called as a chaotic band effect. According to the bridging coupling principle of the nonlinear local resonance band gaps, the frequency distance between the two nonlinear local resonance band gaps is increased, and the elastic wave suppression efficiency and the total attenuation bandwidth in the chaotic band can be improved. By utilizing the bridging coupling principle, the chaotic band of the nonlinear acoustic metamaterial is regulated, the limitation of the vibration suppression bandwidth of the traditional linear metamaterial can be broken through, and the ultra-low frequency, ultra-bandwidth and high-efficiency vibration suppression is realized. However, the design technology of the strong nonlinear unit cell needs to be innovated, and the design of the light adjustable nonlinear coupling resonance unit can promote the vibration and noise reduction application of the nonlinear acoustic metamaterial.
Disclosure of Invention
The technical problems to be solved by the invention are a design method of a strong nonlinear coupling resonance unit and a light low-frequency broadband vibration suppression problem of an engineering structure.
In order to achieve the purpose, the strong nonlinear coupling resonance unit designed by the invention is integrated by a Duffing resonator, a torsion resonator and a vibration-impact resonator, and generates strong nonlinear action through the collision of a segmented spring and a gap; the nonlinear stiffness coefficient is controlled by controlling the stiffness coefficient of the linear spring, the gap between the vibrator and the sleeve and the gap between the vibrator and the support rod; the vertical resonance frequency and the torsional resonance frequency of the resonance unit are controlled to adjust the position of the local resonance band gap, and further the vibration suppression bandwidth of the chaotic band is controlled. The cells are periodically arranged on a matrix beam slab shell structure to construct a nonlinear acoustic metamaterial structure, so that the vibration suppression of a low-frequency broadband is realized.
A non-linearly coupled resonant cell comprising: the vibrator, the spring, the base, the sleeve and the supporting rod;
the middle of the vibrator is provided with a central hole, and the support rod penetrates through the central hole of the vibrator; the vibrator and the supporting rod are coaxially arranged;
the supporting rod takes the vibrator as a middle point, and two ends of the supporting rod are symmetrical and are sleeved in the sleeve; a base is arranged at one end of the sleeve, which is far away from the vibrator, and two ends of the vibrator are fixedly connected with the base through springs;
a first gap delta is arranged between the end face of the vibrator and the end face of the sleeve1A second gap delta is arranged between the central hole of the vibrator and the support rod2。
Further, the vibrator includes a vertical vibration resonance frequency fAAnd torsional vibration resonance frequency fB，fAIs less than fBSaid vertical vibration resonance frequency fAAnd torsional vibration resonance frequency fBThe frequency distance between them forming a bridging coupling.
Furthermore, a boss is arranged at one end, close to the vibrator, of the base, one end of the spring is connected with the boss on the base, and the other end of the spring is connected with the surface of the vibrator through gluing.
Further, the sleeve and the base are connected in an interference fit or gluing mode.
Furthermore, both ends of the supporting rod are connected with the base through threads.
Furthermore, the sleeve, the base and the supporting rod are all made of composite materials.
Furthermore, a first gap delta exists between the sleeve and the surface of the vibrator1Controlled by the difference in height between the spring and the sleeve; a second gap delta between the vibrator and the support rod2The diameter of the vibrator and the diameter of the supporting rod are controlled.
Further, the spring and the sleeve have different stiffnesses and are displaced by less than delta1The vibration rigidity isThe spring rate; at displacements greater than delta1The vibration stiffness is a parallel value of the spring and the sleeve stiffness.
The invention also provides a nonlinear acoustic metamaterial unit cell, which comprises: the vibration damping device comprises a base structure to be damped and at least one nonlinear coupling resonance unit, wherein one end of a supporting rod in the nonlinear coupling resonance unit penetrates through a base and is connected with the base structure to be damped.
The invention also provides a nonlinear acoustic metamaterial structure which comprises a plurality of the nonlinear acoustic metamaterial unit cells which are arranged periodically.
The invention has the following beneficial effects:
the invention applies gap collision to generate strong nonlinear effect, adopts bridge-coupled torsional resonance to enhance nonlinearity in a low-frequency broadband, and provides a strong nonlinear coupling resonance unit which has the characteristics of compact structure, adjustability and the like; furthermore, by applying the unit, based on a typical plate-shell structure, the structural design of a super-nonlinear material is completed, and a nonlinear local resonance band gap and a chaotic band can be generated, so that the low-frequency, broadband and high-efficiency vibration suppression effect can be realized under the condition of small additional mass.
In addition to the objects, features and advantages described above, other objects, features and advantages of the present invention are also provided. The present invention will be described in further detail below with reference to the drawings.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the invention and, together with the description, serve to explain the invention and not to limit the invention. In the drawings:
FIG. 1 is a piecewise non-linear versus smooth cubic non-linear displacement versus force curve in a preferred embodiment of the invention.
Fig. 2 is a perspective view of a nonlinear coupling resonance unit in a preferred embodiment of the present invention.
FIG. 3 is a cross-sectional view and partial detail diagram of the nonlinear coupling resonant unit in the preferred embodiment of the invention.
Fig. 4 is a schematic structural diagram of a nonlinear acoustic metamaterial stiffened plate in a preferred embodiment of the invention. Wherein, the figure (a) is a unidirectional stiffened plate; (b) is a bidirectional stiffened plate.
FIG. 5 is a method for installing and testing the nonlinear coupling resonance unit and the nonlinear acoustic metamaterial stiffened plate according to the preferred embodiment of the invention. Wherein, in the figure, (a) a scheme for testing the vibration characteristic of the nonlinear metamaterial stiffened plate; (b) and (3) a natural frequency test scheme of the coupling resonance unit.
FIG. 6 shows the vibration test results of the unidirectional stiffened plate in the preferred embodiment of the present invention. In the figure, (a) a vibration transmissibility curve of a single vibrator model under different excitation amplitudes; (b) and (3) vibration transmissibility curves of the two vibrator models under different excitation amplitudes.
Fig. 7 shows the vibration test results of the bidirectional stiffened plate in the preferred embodiment of the invention. In the figure, (a) a vibration transmissibility curve of a single vibrator model under different excitation amplitudes; (b) and the vibration transmissibility curves of the two vibrator models under different excitation amplitudes.
The vibration damping device comprises a vibrator 1, a vibrator 2, a supporting rod 3, a base 4, a sleeve 5, a spring 6 and a matrix structure to be damped.
Detailed Description
The following description is only exemplary of the present invention and is not intended to limit the present invention in any way, and those skilled in the art can make various changes and modifications without departing from the scope of the present invention.
The strongly nonlinear coupling resonance unit and the nonlinear acoustic metamaterial related to the invention can be embodied by the following five steps.
The method comprises the following steps: determining coupling resonance unit real acting force and equivalent strong nonlinear stiffness coefficient
The vertical nonlinearity is realized by a piecewise nonlinear spring, and the change rule of the acting force F (x) applied to the vibrator along with the displacement x in the motion process is a piecewise function:
wherein k is1Is a linear spring rate; p is the sleeve stiffness; the stiffness of the sleeve is at least ten times higher than the spring stiffness, the acting force curve F (x) is a strong nonlinear function, and a smooth cubic nonlinear function F' (x) is used for simulating a piecewise function (1):
F′(x)＝kx+knx3 (2)
equivalent nonlinear stiffness coefficient knAnd the clearance value delta1And a segmental spring rate k1And P are related. The real acting force of the vibrator and the simulated three-time nonlinear force curve are shown in figure 1, and the two curves are well matched under the condition of small displacement (0-200 mu m). The vibration displacement of the coupled resonance unit vibrator is within hundreds of micrometers, so the segmented nonlinear spring can better realize the vertical nonlinear vibration of the vibrator.
Step two: determining the gap value delta1And delta2
δ1The vertical vibration amplitude of the vibrator is determined according to the vertical vibration amplitude of the vibrator under the actual use condition and a set nonlinear stiffness coefficient. Theoretically delta1Smaller is better, stronger non-linearity can be produced under very small vibration conditions, but due to machining/3D printing accuracy limitations, δ1It is not preferable to be too small, otherwise the gap nonlinearity of the vibrator will disappear. Thus delta1It should be as small as possible within the accuracy allowed and the maximum gap should not exceed the vertical vibration amplitude of the vibrator.
δ2Realized by the diameter difference between the inner hole of the vibrator and the supporting rod, and also considering the processing precision and the torsional vibration amplitude, delta, of the whole structure2The undersize can lead to the friction increase between oscillator and the bracing piece, influences the oscillator vibration, should guarantee simultaneously that the clearance is less than torsional vibration amplitude.
Step three: determining a vibration damping frequency range for a nonlinear acoustic metamaterial
Designing a metamaterial with two nonlinear local resonance band gaps according to the bridge coupling principle of the nonlinear acoustic metamaterial, and designing accordinglyThe coupled resonant unit has two resonant frequencies, i.e. vertical vibration resonant frequency fAAnd torsional vibration resonance frequency fB。
When the gap nonlinearity disappears, the linear metamaterial will cause two local resonance band gaps by the two resonances, and the band gaps are positioned near the resonance frequency.
In order to realize the vibration suppression effect of the nonlinear acoustic metamaterial low-frequency broadband, the resonant frequency f is adjustedADesigned at the starting frequency of the vibration damping range (low frequency), will fBDesigned at the end frequency of the damping range (high frequency). When gap nonlinearity appears, the two band gaps become nonlinear local resonance band gaps due to nonlinear coupling, vibration responses near and between the two nonlinear local resonance band gaps are changed into chaotic responses due to bridging coupling, and the chaotic band can efficiently inhibit resonance of the structure.
fAThe linear spring stiffness and the vibrator mass jointly determine, analysis shows that the vibrator mass has no significant influence on the vibration suppression effect of the nonlinear acoustic metamaterial, the vibrator mass can be selected to be smaller, and the low additional mass ratio is achieved when the low-frequency vibration suppression effect is achieved. But fAToo small results in fAThe nearby nonlinear effect is not obvious, and the nonlinear stiffness coefficient k should be increased at the same timen。fBDetermined by the torsional stiffness of the support rods and the additional mass of the structure, fBThe larger the damping bandwidth, the wider the damping bandwidth, but the structural design is difficult to realize the overlarge rigidity, and fBToo large results in a weaker nonlinear coupling and is not conducive to broadband vibration suppression.
Therefore, the vertical vibration resonance frequency f should be determined according to the requirements of specific vibration damping frequency range, structural design scheme, additional mass ratio and the likeAAnd torsional vibration resonance frequency fB。
Step four: nonlinear acoustic metamaterial unit cell combined by nonlinear coupling resonance unit
The strong nonlinear coupling resonance unit is combined with a base structure of a required vibration reduction design to construct a cell of the nonlinear acoustic metamaterial.
Step five: nonlinear acoustic metamaterial structure constructed by nonlinear metamaterial unit cells
The whole nonlinear acoustic metamaterial is composed of a periodic coupling resonance unit array. The one-dimensional nonlinear acoustic metamaterial beam is formed by an array of cells in a single direction; the two-dimensional nonlinear acoustic metamaterial plate is formed by an array of cells in two orthogonal directions; the three-dimensional nonlinear acoustic metamaterial structure is formed by a periodic array of unit cells in the circumferential direction or three orthogonal directions. Circumferentially arranged at periodic angles.
According to the design steps, the strong nonlinear coupling resonance unit and the nonlinear acoustic metamaterial with various specific structures can be designed and obtained. In order to explain the method for designing the nonlinear acoustic metamaterial based on the nonlinear coupling resonance unit and verify the vibration suppression effect of the nonlinear acoustic metamaterial, the invention specifically designs a sample of the nonlinear acoustic metamaterial based on a two-dimensional stiffened plate structure.
Referring to fig. 2 and 3, the invention relates to a coupling resonance unit, comprising: the device comprises a vibrator 1, a spring 5, a base 3, a sleeve 4 and a support rod 2;
the middle of the vibrator is provided with a central hole, and the support rod penetrates through the central hole of the vibrator; the vibrator and the supporting rod are coaxially arranged;
the supporting rod takes the vibrator as a middle point, and two ends of the supporting rod are symmetrical and are sleeved in the sleeve; a base is arranged at one end of the sleeve, which is far away from the vibrator, and two ends of the vibrator are fixedly connected with the base through springs;
a first gap delta is arranged between the end face of the vibrator and the end face of the sleeve1A second gap delta is arranged between the central hole of the vibrator and the support rod2。
The vibrator has a vertical vibration resonance frequency fAAnd torsional vibration resonance frequency fB，fAIs less than fBSaid vertical vibration resonance frequency fAAnd torsional vibration resonance frequency fBThe frequency distance between them forming a bridging coupling.
The base is close to the one end of oscillator and is equipped with the boss, the spring is in the oscillator longitudinal symmetry places, and one end is connected with the base boss, one end with oscillator surface connection, the connected mode can select through boss limit position, sticky etc..
The sleeve and the base are in rigid fixed connection, and interference fit or gluing and other modes can be selected.
The two ends of the supporting rod are connected with the upper base and the lower base through threads, and one end of the supporting rod is connected with the base body through threads.
The sleeve and the base are in rigid connection, and interference fit or gluing and other modes can be selected. Preferably, the sleeve and the base are made of low-density high-strength composite materials, such as aluminum alloy or high-molecular composite materials, and are connected in an interference fit manner; the support rod is made of aluminum material, and two ends of the support rod are respectively connected with the upper base, the lower base and the base body stiffened plate through threads. The supporting rod has a large Young modulus and drives the whole resonance unit to vibrate in a torsional mode.
A first gap delta existing between the sleeve and the surface of the vibrator1The initial clearance is controlled by designing the height difference between the spring and the sleeve; said gap delta1Can be changed by adjusting the length of the threaded connection between the support rod and the base. The vibrator and the support rod have a second gap delta2And controlling the diameters of the vibrator and the supporting rod by designing.
The spring and the sleeve have different stiffness and are displaced by less than delta1The vibration stiffness is the spring stiffness, the displacement is greater than delta1The vibration stiffness is a parallel value of the spring and the sleeve stiffness.
Through the gap delta between the vibrator and the sleeve1Realizing the nonlinear effect of transverse vertical vibration by utilizing the clearance delta between the support rod and the vibrator2Producing a vibration-shock effect.
In one embodiment, the distance between the sleeve and the vibrator is adjusted by screwing to control the gap delta10.1 mm; the clearance delta is controlled by selecting the inner hole radius of the vibrator20.15 mm. At the moment, the two small gaps can enable the coupled resonance unit to generate strong force under smaller excitationNon-linear.
Determining the nonlinear local resonance frequency f from the natural frequencies of the vertical and torsional vibrations of the coupled resonance unitAAnd fBAnd f isA＜fB. Using vibration exciter to induce vertical vibration and torsional vibration of coupled resonance unit, respectively testing velocity signals of excitation point and response point by laser vibration meter (as shown in (b) of FIG. 5), and analyzing vibration transmissibility thereof, wherein the natural frequency of vertical vibration corresponds to fAThe natural frequency of torsional vibration corresponds to fB. In this case fA＝70Hz，fB＝350Hz。
The structure comprises a base structure 6 to be damped and at least one nonlinear coupling resonance unit, wherein one end of a support rod in the nonlinear coupling resonance unit penetrates through a base to be connected with the base structure 6 to be damped, so that a nonlinear acoustic metamaterial unit cell is formed.
Furthermore, a nonlinear acoustic metamaterial structure is constructed by periodically arranging nonlinear acoustic metamaterial cells formed by the coupling resonance units, taking the base structure to be damped as a two-dimensional unidirectional and bidirectional reinforced plate structure as an example, 8 × 8 coupling resonance units are added on the reinforced plate base to form the nonlinear acoustic metamaterial reinforced plate structure, as shown in fig. 4. The thickness h of the metamaterial reinforced plate is 1mm, the lattice constant a is 93.75mm, and the plate edge length L is 850 mm. Additional oscillator individual mean mass mr＝4.844g。
The nonlinear acoustic metamaterial reinforced plate structure has the natural frequency fAWith a natural frequency fBNear a nonlinear local resonance band gap at fAAnd fBThe frequency band between them has a chaotic band with a damping effect. By using bridge coupling principle to change natural frequency fAAnd fBThe vibration suppression bandwidth of the nonlinear acoustic metamaterial reinforced plate structure can be adjusted.
Furthermore, a vibration test is carried out to test the dynamic response characteristics under different excitation conditions (namely different nonlinear strengths), and the effectiveness of the design method of the light, low-frequency and broadband strong nonlinear coupling resonance unit is verified.
In the experimental test, the metamaterial stiffened plate is hung on the bracket to simulate the free boundary. Excitation is performed at a position which is deviated from the left of the center of the nonlinear metamaterial stiffened plate, as shown in (a) in fig. 5. And scanning and testing the vibration response of each node of the reinforced plate structure by using a laser vibration meter according to the grid division, and further analyzing the average vibration response of the whole plate. The excitation signal is white noise signal, and different excitation amplitudes are realized by adjusting the voltage of the signal generator, wherein the excitation level L1: the excitation voltage of the signal generator is 0.4V (the input amplitude is 1.3 mm/s); excitation level L2: the signal generator exciting voltage is 1V (input amplitude is 3 mm/s); excitation level L3: the signal generator excites the voltage 3V (input amplitude 9.7 mm/s). Different excitation amplitudes represent different non-linear intensities.
The vibration response of the stiffened plate without the additional coupling resonance unit is tested as a reference value, and the unidirectional stiffened plate is selected from 1 vibrator (m)r4.844g), the structure additional mass ratio is 9.06%. The vibration transmission rate of the metamaterial unidirectional stiffened plate under different excitation levels is shown in (a) in fig. 6. Compared with the stiffened plate without the additional coupling resonance unit, the nonlinear metamaterial unidirectional stiffened plate has the advantages that the dense resonance peak average attenuation of 10.5dB in the range of 65-1000Hz (chaotic band) is obvious, and the vibration reduction effect is obvious. Along with the increase of the excitation amplitude, namely the increase of the nonlinear strength, the attenuation amplitude of the high-frequency vibration amplitude is slightly enhanced, which shows that the stronger nonlinear effect can be realized under the level of smaller excitation amplitude, and the broadband and high-efficiency vibration reduction performance is realized.
Then, the mass of the oscillator is increased, and two oscillators (m) are selectedr9.688g), the vibration transmissibility of the metamaterial unidirectional stiffened plate model at different excitation levels is shown as (b) in fig. 6. Compared with a single oscillator model, the two oscillator models have stronger vibration suppression effect in the whole frequency band, and particularly, the resonance peaks in the low frequency ranges of 80-240Hz and 470-600Hz are further attenuated. The chaotic band is slightly widened towards low frequency, the resonance peak in the range of 60-1000Hz is averagely attenuated by 13dB, the low frequency peak value is obviously attenuated, and the vibration suppression of low frequency and broadband is realized under the same small excitation level.
And testing the vibration characteristic of the bidirectional stiffened plate model by using the same idea. The vibration transfer rate of the metamaterial bidirectional stiffened plate (the additional mass ratio is 6.25%) formed by the mass of a single oscillator under different excitation levels is shown in (a) in fig. 7, the equivalent Young modulus of the bidirectional stiffened plate is larger, and the resonance peak is sparse. The metamaterial bidirectional stiffened plate has strong nonlinear effect within the range of 80-700Hz, has obvious inhibition effect on a resonance peak, and averagely reduces the vibration transfer rate by about 8 dB. As the excitation amplitude increases, the damping effect is better in the low frequency 125-220Hz range, but the high frequency damping performance is reduced. After the mass of the oscillator is doubled, the vibration transfer rate of the metamaterial stiffened plate model under different excitation levels is shown in (b) in fig. 7. Compared with a single vibrator model, the vibration attenuation amplitude of the two vibrator models in the range of 160-400Hz is more obvious, and the low-frequency vibration attenuation performance is greatly improved.
The experiment results show that the nonlinear acoustic metamaterial stiffened plate constructed by the strong nonlinear coupling resonance unit designed by the invention can realize the vibration reduction effect with low frequency, wide band and high efficiency under the condition of light additional mass.
Although the present invention has been described with reference to a preferred embodiment, it should be understood that various changes and modifications can be made without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (9)
1. A nonlinear coupled resonant cell, comprising: the vibrator, the spring, the base, the sleeve and the supporting rod;
the middle of the vibrator is provided with a central hole, and the support rod penetrates through the central hole of the vibrator; the vibrator and the supporting rod are coaxially arranged;
the supporting rod takes the vibrator as a middle point, and two ends of the supporting rod are symmetrical and are sleeved in the sleeve; a base is arranged at one end of the sleeve, which is far away from the vibrator, and two ends of the vibrator are fixedly connected with the base through springs;
an end face of the vibrator anda first gap delta is arranged between the end surfaces of the sleeves1A second gap delta is arranged between the central hole of the vibrator and the support rod2；
The vibrator having a vertical vibration resonance frequency fAAnd torsional vibration resonance frequency fB，fAIs less than fBSaid vertical vibration resonance frequency fAAnd torsional vibration resonance frequency fBThe frequency distance between them forming a bridging coupling.
2. The nonlinear coupling resonance unit according to claim 1, wherein a boss is provided at one end of the base close to the vibrator, one end of the spring is connected with the boss on the base, and the other end of the spring is connected with the surface of the vibrator by gluing.
3. The nonlinear-coupled resonance unit of claim 1, wherein the sleeve and the base are connected by interference fit or gluing.
4. The nonlinear-coupled resonance unit according to claim 1, wherein both ends of the support rod are connected to the base by screws.
5. The nonlinear coupled resonance unit according to claim 1, wherein the sleeve, the base and the support rod are made of composite materials.
6. The nonlinear coupled resonance unit according to claim 1, wherein a first gap δ between the vibrator end surface and the sleeve end surface1Controlled by the difference in height between the spring and the sleeve; a second gap delta between the vibrator and the support rod2The diameter of the vibrator and the diameter of the supporting rod are controlled.
7. The nonlinear-coupled resonance unit of claim 1, wherein the stiffness of the spring and the sleeveIn contrast, the displacement at the vibrator is less than delta1The vibration stiffness is the spring stiffness; displacement at vibrator greater than delta1The vibration stiffness is a parallel value of the spring and the sleeve stiffness.
8. A nonlinear acoustic metamaterial unit cell, comprising: a base structure to be damped and at least one nonlinear coupling resonance unit as set forth in any one of claims 1 to 7, wherein one end of a support rod in the nonlinear coupling resonance unit is connected with the base structure to be damped through a base.
9. A nonlinear acoustic metamaterial structure comprising a plurality of periodically arranged nonlinear acoustic metamaterial cells as defined in claim 8.
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