Low-frequency elastic wave bandgap regulation method based on viscoelastic damping material

Abstract

This invention relates to the field of low-frequency elastic wave bandgap technology, and more particularly to a method for controlling the low-frequency elastic wave bandgap based on viscoelastic damping materials. The invention includes the following steps: converting the Young's modulus of the viscoelastic damping material into a function varying with frequency, introducing a first control factor; analyzing the control law of the first control factor on the negative property material parameters, and analyzing the elastic wave transmission characteristics in the viscoelastic damping material when the material parameters within the bandgap are negative; introducing a second control factor to adjust the viscoelastic damping material parameters to a complex form, and analyzing the control law of the second control factor on the complex property material parameters; determining the dispersion curve when the viscoelastic damping material parameters are complex, and analyzing the influence of the complex property tensile modulus on the elastic wave transmission characteristics based on the real and imaginary parts of the dispersion curve; and analyzing the control law of the elastic wave dispersion characteristics when the tensile modulus of the viscoelastic damping material is complex. This invention can solve the problem of high difficulty in low-frequency vibration reduction and noise reduction.

Description

Technical Field

[0001] This invention relates to the field of low-frequency elastic wave bandgap technology, and in particular to a method for controlling the low-frequency elastic wave bandgap based on viscoelastic damping materials. Background Technology

[0002] Vibration causes deformation in solid materials, and the deformation is transmitted in the form of elastic waves. The mechanical properties of the material determine the propagation mode of the elastic waves. Changing the equivalent mechanical parameters of the material can cause different phenomena such as free and lossless propagation, complete blockage, and dissipative propagation of elastic waves within the material.

[0003] Traditional viscoelastic materials have fixed parameters such as loss factor, Young's modulus, density, and Poisson's ratio, making their mechanical properties unchangeable. Acoustic metamaterials, on the other hand, are a class of acoustic materials with subwavelength artificial microstructures. Through acoustic structural design, their macroscopic equivalent properties can exhibit characteristics rarely found in traditional materials, such as negative density, negative modulus, and negative Poisson's ratio, overcoming the limitation of unchangeable mechanical properties in traditional materials. Furthermore, localized resonant mechanical metamaterials possess the ability to control large-wavelength low-frequency fluctuations, generating bandgap barriers to block the propagation of low-frequency elastic waves, providing a new approach to low-frequency vibration reduction and noise reduction. The low-frequency bandgap refers to the effect that elastic waves within a specific frequency band cannot propagate outward in viscoelastic damping materials. To generate a low-frequency bandgap in a structure, its equivalent material parameters should exhibit metamaterial characteristics such as negative modulus and negative density, which can theoretically be achieved by setting the viscoelastic damping material parameters as dynamic mechanical parameters.

[0004] Therefore, in order to address the above problems, the industry urgently needs a method for controlling the bandgap of low-frequency elastic waves based on viscoelastic damping materials. Summary of the Invention

[0005] (a) Technical problems to be solved

[0006] The technical problem to be solved by this invention is to provide a low-frequency elastic wave bandgap control method based on viscoelastic damping materials, thereby solving the technical problem of high difficulty in low-frequency vibration reduction and noise reduction.

[0007] (II) Technical Solution

[0008] To address the aforementioned technical problems, this invention provides a method for controlling the bandgap of low-frequency elastic waves based on viscoelastic damping materials, comprising the following steps:

[0009] The Young's modulus of the viscoelastic damping material is converted into a function that varies with frequency, and a first control factor is introduced to give it an extraordinary negative parameter region.

[0010] Adjust the first control factor and analyze the first control law of the first control factor on the negative property material parameters;

[0011] The first control factor is selected to generate a bandgap at the first resonant frequency, and the elastic wave transmission characteristics in the viscoelastic damping material are analyzed when the material parameters within the bandgap are negative.

[0012] Adjust the first control factor and analyze the first influence law of the first control factor on the elastic wave dispersion characteristics when the tensile modulus of the viscoelastic damping material is negative.

[0013] Based on the first control law, the elastic wave transmission characteristics, and the first influence law, a second adjustment factor is introduced to adjust the viscoelastic damping material parameters into a complex form;

[0014] Adjust the second control factor and analyze the second control law of the second control factor on the parameters of complex property materials;

[0015] Select a preset first control factor and a preset second control factor to determine the dispersion curve when the parameters of the viscoelastic damping material are complex. Analyze the second influence law of the complex tensile modulus on the elastic wave transmission characteristics based on the real and imaginary parts of the dispersion curve.

[0016] By adjusting the preset first control factor and the preset second control factor respectively, the control law of elastic wave dispersion characteristics when the tensile modulus of the viscoelastic damping material is complex is analyzed.

[0017] Furthermore, by converting the tensile modulus of the viscoelastic damping material into a function of frequency, the material parameters that produce negative properties can be expressed as:

[0018]

[0019] In the formula, E p E0 and E0 represent the negative material parameter and the original parameter, respectively, ω p ω z These are the poles and zeros, respectively, and they satisfy the relationship: ω z <ω p ;f p It is the first control factor of the material parameters, and its physical meaning represents the frequency point.

[0020] Furthermore, the first control law is that the tensile modulus produces a resonance effect at the frequency corresponding to the first control factor and exhibits a negative region within the set frequency range.

[0021] Furthermore, by adjusting the first control factor, the resonance effect of the real part of the tensile modulus and the negative property region both appear at the corresponding frequency positions.

[0022] Furthermore, the selection of the first control factor generates a bandgap at the first resonant frequency, and the analysis of the elastic wave transmission characteristics in the viscoelastic damping material when the material parameters within the bandgap are negative specifically includes the following steps:

[0023] Select the frequency point at the first mode and determine the dispersion curve of the structure within a specific frequency band;

[0024] Based on the real and imaginary parts of the dispersion curve, the elastic wave propagation characteristics in the structure are analyzed when the material parameters within the band gap are negative.

[0025] Furthermore, the first influence law is that by adjusting the set first control factor to shift the bandgap towards the set frequency, the resonance effect is not affected, and the peak values ​​of the real and imaginary parts of the wavenumber within the bandgap do not show a weakening trend.

[0026] Furthermore, the complex form of the viscoelastic damping material parameters is as follows:

[0027]

[0028] In the formula, E p E0 and E0 represent the negative material parameter and the original parameter, respectively, ω p ω z These are the poles and zeros, respectively, and they satisfy the relationship: ω z <ω p β is the second control factor of the material parameters, and its physical meaning represents the loss factor.

[0029] Furthermore, the second control law is that as the second regulation factor increases, the resonance effect in the real part of the tensile modulus gradually weakens, while the peak value of the imaginary part of the tensile modulus gradually decreases and its non-zero range gradually widens.

[0030] Furthermore, the second influence law is that after introducing the second regulation factor, the peak value of the imaginary wavenumber decreases, and the resonance effect is gradually weakened by adjusting the second regulation factor.

[0031] Furthermore, the regulatory principle is as follows:

[0032] Adjusting the preset first control factor to change the position of the band gap and control the propagation of elastic waves at a specific frequency;

[0033] Adjust the preset second control factor to enhance the attenuation intensity.

[0034] (III) Beneficial Effects

[0035] The above-described technical solution of the present invention has the following advantages:

[0036] The present invention relates to a low-frequency elastic wave bandgap control method based on viscoelastic damping materials. By changing the material modulus to a negative or complex number, it enables the material to possess extraordinary properties, thereby generating a bandgap in the structure. Elastic waves cannot propagate outward within the bandgap region. By changing the control factor, the elastic waves can be blocked and consumed. Attached Figure Description

[0037] Figure 1 This is a schematic flowchart of the low-frequency elastic wave bandgap modulation method based on viscoelastic damping materials of the present invention.

[0038] Figure 2 Elastic wave change cloud diagrams before and after setting the negative property material parameters of the present invention;

[0039] Figure 3 This is a graph showing the change of the real part of the tensile modulus of the present invention with the first control factor.

[0040] Figure 4(a) is a real part diagram of the dispersion curve when the material parameters of the present invention are negative;

[0041] Figure 4(b) is the imaginary part of the dispersion curve when the material parameters of the present invention are negative;

[0042] Figure 5(a) is the real part of the dispersion curve of the first control factor when the material parameter of the present invention is negative;

[0043] Figure 5(b) is the imaginary part of the dispersion curve of the first control factor when the material parameters of the present invention are negative.

[0044] Figure 6 Elastic wave change cloud diagram before and after setting the complex property material parameters of the present invention;

[0045] Figure 7(a) shows the change of the real part of the tensile modulus of the present invention as adjusted by the second control factor;

[0046] Figure 7(b) shows the change of the imaginary part of the tensile modulus of the present invention as adjusted by the second control factor;

[0047] Figure 8(a) is a real part diagram of the dispersion curve when the material parameters of the present invention are complex numbers;

[0048] Figure 8(b) is a diagram of the imaginary part of the dispersion curve when the material parameters of the present invention are complex numbers;

[0049] Figure 9(a) is a graph showing the real part of the dispersion curve of the first control factor when the material parameters of the present invention are complex.

[0050] Figure 9(b) is a graph showing the change of the imaginary part of the dispersion curve when the material parameters of the present invention are complex numbers and the first control factor is adjusted.

[0051] Figure 10(a) is a graph showing the real part of the dispersion curve of the second control factor when the material parameters of the present invention are complex.

[0052] Figure 10(b) is a graph showing the change of the imaginary part of the dispersion curve when the material parameters of the present invention are complex numbers and the second control factor is adjusted. Detailed Implementation

[0053] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0054] In the description of this invention, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0055] See Figure 1 This invention provides a method for controlling the bandgap of low-frequency elastic waves based on viscoelastic damping materials, which may include the following steps:

[0056] S100: The Young's modulus of the viscoelastic damping material is converted into a function that varies with frequency, and a first control factor is introduced to give it an extraordinary negative parameter region.

[0057] Specifically, by combining the concept of acoustic metamaterials, the Young's modulus of viscoelastic damping materials is written as a function of frequency, which can make the equivalent macroscopic mechanical parameters of the material exhibit extraordinary properties. This allows us to study the influence of the equivalent tensile modulus on the propagation characteristics of elastic waves and reveal the generation mechanism of low-frequency bandgap by controlling the equivalent material parameters.

[0058] Furthermore, by converting the tensile modulus of the viscoelastic damping material into a function of frequency, the material parameters that produce negative properties can be expressed as:

[0059]

[0060] In the formula, E p E0 and E0 represent the negative material parameter and the original parameter, respectively, ω p ω z These are the poles and zeros, respectively, and they satisfy the relationship: ω z <ω p ;f p It is the first control factor of the material parameters, and its physical meaning represents the frequency point.

[0061] By introducing the first regulatory factor f p This gives it an exceptionally high negative parameter range, resulting in a low-frequency elastic wave bandgap. By setting the material parameters to negative properties, it is possible to transform the lossless propagation of elastic waves in traditional viscoelastic damping materials into complete blockage, such as... Figure 2 As shown.

[0062] S200. Adjust the first control factor and analyze the first control law of the first control factor on the negative property material parameters.

[0063] Specifically, changing the first regulatory factor f p This study investigates the control effect of changes in the regulating factor on the parameters of negatively performing materials, demonstrating that band gaps can be generated at arbitrary frequency bands by adjusting the regulating factor. Changing the first regulating factor f... p The effects of the control factor on the negative material parameter E were studied at 40Hz, 42Hz, and 44Hz respectively. p The influence pattern, such as Figure 3 As shown, it can be observed that the tensile modulus, under the first control factor f... p A resonance effect is generated at the corresponding frequency, and a negative region appears within a certain frequency range. By changing the first regulation factor f... p The resonance effect of the real part of the tensile modulus and the negative property region both appeared at the corresponding frequency positions.

[0064] S300. Select the first control factor to generate a bandgap at the first resonant frequency, and analyze the elastic wave transmission characteristics in the viscoelastic damping material when the material parameters within the bandgap are negative.

[0065] Specifically, the regulatory factor is selected as f. p =42Hz, which means introducing the negative material parameter E p The real and imaginary parts of the dispersion curve were plotted, and the influence on the elastic wave transmission characteristics of the viscoelastic damping material was analyzed, as shown in Figures 4(a) and (b). In Figures 4(a) and (b), the solid line represents the dispersion curve calculated using the original parameter E0, and the dashed line represents the dispersion curve with the introduction of the negative material parameter E0. p The resulting wavenumber curve. From the imaginary part of the wavenumber in Figures 4(a) and (b), it can be seen that at the set frequency point f... p Around 42Hz, the wavenumber has a large imaginary part, indicating that elastic waves cannot propagate outward within this frequency range, thus creating a bandgap. The shaded areas in Figures 4(a) and (b) represent the bandgap regions.

[0066] S400. Adjust the set first control factor and analyze the first influence law of the first control factor on the elastic wave dispersion characteristics when the tensile modulus of the viscoelastic damping material is negative.

[0067] Specifically, changing the first regulatory factor f p The variation pattern of the band gap is analyzed, as shown in Figures 5(a) and (b). From Figures 5(a) and (b), it can be seen that changing f... p The position of the bandgap changed systematically; as the control factor changed, the bandgap shifted towards the set frequency. Simultaneously, it could be observed that adjusting f... pThe magnitude of the wavenumber does not affect the resonance effect, and the peak values ​​of the real and imaginary parts of the wavenumber within the band gap do not show a weakening trend.

[0068] S500. Based on the first control law, elastic wave transmission characteristics and the first influence law, a second adjustment factor is introduced to adjust the parameters of the viscoelastic damping material into a complex form.

[0069] Specifically, further, the complex form of the viscoelastic damping material parameters is:

[0070]

[0071] In the formula, E p E0 and E0 represent the negative material parameter and the original parameter, respectively, ω p ω z These are the poles and zeros, respectively, and they satisfy the relationship: ω z <ω p β is the second control factor of the material parameters, and its physical meaning represents the loss factor.

[0072] Introducing a new second control factor β, whose physical meaning represents the loss factor, is equivalent to adding a damping effect to the structure, enabling the adjustment of the resonance peak. By setting complex property material parameters, the elastic wave in traditional viscoelastic damping materials can be transformed from lossless propagation to dissipative propagation, such as... Figure 6 As shown.

[0073] S600. Adjust the second control factor and analyze the second control law of the second control factor on the parameters of complex property materials.

[0074] Specifically, the study investigates the effect of changes in the second regulatory factor β on the composite material parameter E. p The control law was investigated, and the curves of the tensile modulus of the viscoelastic damping material as a function of the second control factor β were plotted, as shown in Figures 7(a) and (b). From Figures 7(a) and (b), it can be observed that as the second control factor β increases, the resonance effect in the real part of the tensile modulus gradually weakens, manifested in the resonance peak changing from sharp to gentle. Simultaneously, the peak value of the imaginary part of the tensile modulus also gradually decreases, and its non-zero range gradually widens.

[0075] S700. Select the preset first control factor and the preset second control factor to determine the dispersion curve when the parameters of the viscoelastic damping material are complex. Analyze the second influence law of the complex tensile modulus on the elastic wave transmission characteristics based on the real and imaginary parts of the dispersion curve.

[0076] Specifically, select the regulatory factor f p =42Hz, β=0.001, construct the material parameters as complex numbers E pThe dispersion curves are obtained, and the transmission characteristics of elastic waves are analyzed based on the real and imaginary parts of the dispersion curves, as shown in Figures 8(a) and (b). In Figures 8(a) and (b), the solid lines represent the dispersion curves calculated using the original parameter E0, and the dashed lines represent the material parameter E0. p The real and negative wavenumbers were obtained at that time. From the imaginary part of the wavenumbers in Figures 8(a) and (b), it can be seen that at the set frequency point f... p A bandgap appeared around 42Hz. Compared with the dispersion curve when the material parameters were negative, the peak value of the imaginary wavenumber was significantly reduced after introducing the new second control factor β, indicating that the resonance effect could be gradually weakened by adjusting β.

[0077] S800, adjust the preset first control factor and the preset second control factor respectively, and analyze the control law of elastic wave dispersion characteristics when the tensile modulus of the viscoelastic damping material is complex.

[0078] Specifically, change f respectively p The variation law of the dispersion curve was studied with β, as shown in Figures 9(a), (b), and 10(a), (b). From Figures 9(a) and (b), it can be seen that changing f... p The post-bandgap position shifted, as shown in Figures 10(a) and (b). Changing the control factor β significantly reduced the wavenumber peak, and the curve gradually smoothed out as β increased. This indicates that adjusting f... p The position of the band gap can be changed to control the propagation of elastic waves at a specific frequency. Adjusting β can enhance the attenuation intensity. The sharper the peak value, the more obvious the attenuation effect will be, thereby achieving the blocking and consumption of elastic waves.

[0079] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for controlling the bandgap of low-frequency elastic waves based on viscoelastic damping materials, characterized in that, The method includes the following steps: The Young's modulus of the viscoelastic damping material is converted into a function that varies with frequency, and a first control factor is introduced to give it an extraordinary negative parameter region. Adjust the first control factor and analyze the first control law of the first control factor on the negative property material parameters; The first control factor is selected to generate a bandgap at the first resonant frequency, and the elastic wave transmission characteristics in the viscoelastic damping material are analyzed when the material parameters within the bandgap are negative. Adjust the first control factor and analyze the first influence law of the first control factor on the elastic wave dispersion characteristics when the tensile modulus of the viscoelastic damping material is negative. Based on the first control law, the elastic wave transmission characteristics, and the first influence law, a second adjustment factor is introduced to adjust the viscoelastic damping material parameters into a complex form; Adjust the second control factor and analyze the second control law of the second control factor on the parameters of complex property materials; Select a preset first control factor and a preset second control factor to determine the dispersion curve when the parameters of the viscoelastic damping material are complex. Analyze the second influence law of the complex tensile modulus on the elastic wave transmission characteristics based on the real and imaginary parts of the dispersion curve. By adjusting the preset first control factor and the preset second control factor respectively, the control law of elastic wave dispersion characteristics when the tensile modulus of the viscoelastic damping material is complex is analyzed.

2. The low-frequency elastic wave bandgap modulation method based on viscoelastic damping material according to claim 1, characterized in that, Converting the tensile modulus of a viscoelastic damping material into a function of frequency, the material parameters that produce negative properties can be expressed as: In the formula, E p , E0 respectively represent negative material parameters and original parameters, ω p , ω z are respectively poles and zeros, and the two satisfy the relationship: ω z < ω p ; f p is a first regulation factor of the material parameter, and the physical meaning thereof represents a frequency point.

3. The low-frequency elastic wave bandgap modulation method based on viscoelastic damping material according to claim 1, characterized in that, The first control law is that the tensile modulus produces a resonance effect at the frequency corresponding to the first control factor and appears in a negative region within the set frequency range.

4. The low-frequency elastic wave bandgap modulation method based on viscoelastic damping material according to claim 1 or 3, characterized in that, By adjusting the first control factor, the resonance effect of the real part of the tensile modulus and the negative property region both appear at the corresponding frequency positions.

5. The low-frequency elastic wave bandgap modulation method based on viscoelastic damping material according to claim 1, characterized in that, The selection of a first control factor to generate a bandgap at the first resonant frequency, and the analysis of the elastic wave transmission characteristics in the viscoelastic damping material when the material parameters within the bandgap are negative, specifically includes the following steps: Select the frequency point at the first mode and determine the dispersion curve of the structure within a specific frequency band; Based on the real and imaginary parts of the dispersion curve, the elastic wave propagation characteristics in the structure are analyzed when the material parameters within the band gap are negative.

6. The low-frequency elastic wave bandgap modulation method based on viscoelastic damping material according to claim 1, characterized in that, The first influence law is that by adjusting the set first control factor to shift the bandgap to a set frequency, the resonance effect is not affected, and the peak values ​​of the real and imaginary parts of the wavenumber within the bandgap do not show a weakening trend.

7. The method for controlling the bandgap of low-frequency elastic waves based on viscoelastic damping materials according to claim 1, characterized in that, The complex form of the parameters of the viscoelastic damping material is: In the formula, E p , E0 respectively represent negative material parameters and original parameters, ω p , ω z are respectively poles and zeros, and the relationship ω z < ω p is satisfied between the two; β is a second regulating factor of the material parameters, and its physical meaning represents a loss factor; f p It is the first control factor of the material parameters, and its physical meaning represents the frequency point.

8. The method for controlling the bandgap of low-frequency elastic waves based on viscoelastic damping materials according to claim 1, characterized in that, The second control law is that as the second regulation factor increases, the resonance effect in the real part of the tensile modulus gradually weakens, while the peak value of the imaginary part of the tensile modulus gradually decreases and its non-zero range gradually widens.

9. The method for controlling the bandgap of low-frequency elastic waves based on viscoelastic damping materials according to claim 1, characterized in that, The second influence law is that after the second regulation factor is introduced, the peak value of the imaginary wavenumber decreases, and the resonance effect is gradually weakened by adjusting the second regulation factor.

10. The method for controlling the bandgap of low-frequency elastic waves based on viscoelastic damping materials according to claim 1, characterized in that, The regulation principle is as follows: Adjusting the preset first control factor to change the position of the band gap and control the propagation of elastic waves at a specific frequency; Adjust the preset second control factor to enhance the attenuation intensity.

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