Method for analyzing influence of low-frequency elastic wave transmission characteristics based on dynamic mechanical parameters

Abstract

The present application relates to the technical field of elastic wave propagation, and particularly relates to a low-frequency elastic wave transmission characteristic influence analysis method based on dynamic mechanical parameters. The low-frequency elastic wave transmission characteristic influence analysis method based on dynamic mechanical parameters comprises the following steps: obtaining a motion differential equation of a cylindrical shell based on a viscoelastic damping material according to a selected annular viscoelastic damping layer microcell; establishing an elastic wave dispersion relation characteristic equation of the cylindrical shell based on a plane wave assumption and the motion differential equation, and obtaining a dispersion curve of the cylindrical shell; obtaining a wave pattern of the cylindrical shell according to the dispersion curve, and analyzing the propagation type of the wave under different circumferential orders in a low-frequency band; and selecting a set circumferential order to determine the influence of negative property material parameters on the elastic wave transmission of the cylindrical shell according to the analysis result, and determining a first influence law of the negative property material parameters on the elastic wave transmission characteristic in the low-frequency band. The method can solve the problem of how to realize adjustable elastic wave.

Description

Technical Field

[0001] This invention relates to the field of elastic wave propagation technology, and in particular to a method for analyzing the influence of dynamic mechanical parameters on the transmission characteristics of low-frequency elastic waves. Background Technology

[0002] When any structure is excited, stress is generated, causing the structural elements to vibrate. This vibration is transmitted to adjacent elements through the elastic interaction between the elements, thus forming elastic waves in the structure. A continuous stress difference between the elements is a prerequisite for the forward propagation of elastic waves. Abrupt changes in the stress difference between the elements will cause changes in the propagation characteristics of elastic waves. If the stress difference is zero or reversed (which can be achieved by artificially introducing external stress), the elastic waves will be unable to propagate forward, resulting in a band gap.

[0003] The constitutive relationship of material stress and strain is usually described by the material's dynamic mechanical parameters (such as tensile modulus and shear modulus). If a dynamic stress field is artificially introduced into the material, it will change the material's stress-strain relationship, which will be macroscopically manifested as a change in the equivalent dynamic mechanical parameters.

[0004] Therefore, in order to address the above issues, the industry urgently needs a method for analyzing the impact of dynamic mechanical parameters on the transmission characteristics of low-frequency elastic waves. 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 method for analyzing the influence of low-frequency elastic wave transmission characteristics based on dynamic mechanical parameters, and to solve the technical problem of how to achieve adjustable elastic waves.

[0007] (II) Technical Solution

[0008] To address the aforementioned technical problems, this invention provides a method for analyzing the influence of dynamic mechanical parameters on the transmission characteristics of low-frequency elastic waves, comprising the following steps:

[0009] Based on the selected annular viscoelastic damping layer micro-cell, the motion differential equation of the cylindrical shell based on the viscoelastic damping material is obtained;

[0010] Based on the plane wave assumption and in conjunction with the aforementioned differential equation of motion, the characteristic equation of the elastic wave dispersion relationship of the cylindrical shell is established, and the dispersion curve of the cylindrical shell is obtained.

[0011] Based on the dispersion curve, the waveform diagram of the cylindrical shell is obtained, and the propagation type of the waveform at different circumferential orders in the low frequency band is analyzed.

[0012] Based on the analysis results, the set circumferential order is selected to determine the effect of negative property material parameters on the elastic wave transmission of the cylindrical shell, and the first influence law of the negative property material parameters on the elastic wave transmission characteristics in the low frequency band is determined.

[0013] Furthermore, based on the selected annular viscoelastic damping layer micro-cell, the motion differential equation of the cylindrical shell based on the viscoelastic damping material is obtained, specifically as follows:

[0014] Select a segment of annular viscoelastic damping layer microcell, determine the forces and moments on the cylindrical shell microcell, and obtain the motion differential equation based on the balance relationship between forces and bending moments in different directions.

[0015] Furthermore, the characteristic equation for the elastic wave dispersion relationship of the cylindrical shell is established based on the plane wave assumption and in conjunction with the motion differential equation, and the dispersion curve of the cylindrical shell is obtained, specifically as follows:

[0016] Based on the plane wave assumption and the aforementioned motion differential equation, the wave equation of the viscoelastic damping layer is established. Based on the wave equation, the characteristic equations of elastic wave dispersion relationship corresponding to different circumferential modes are obtained. The dispersion curves are calculated using analytical and numerical methods, respectively.

[0017] Furthermore, the dispersion curves obtained by analytical and numerical methods completely overlap.

[0018] Furthermore, the step of obtaining the waveform diagram of the cylindrical shell based on the dispersion curve specifically involves:

[0019] Select a frequency point of the dispersion curve and plot its waveform.

[0020] Furthermore, the analysis of the propagation types of waveforms at different circumferential orders in the low-frequency band specifically includes:

[0021] When the circumferential order n = 0, it has longitudinal and torsional waves. As the circumferential order increases, the start and end frequencies of the propagating wave gradually shift to higher frequencies.

[0022] When the circumferential order n = 1, the entire frequency band is a propagating wave;

[0023] When the circumferential order n>15, only non-propagating near-field waves exist within the 1~300Hz range.

[0024] Furthermore, based on the analysis results, a set circumferential order is selected to determine the effect of negative property material parameters on the elastic wave transmission of the cylindrical shell, and the first influence law of the negative property material parameters on the elastic wave transmission characteristics in the low-frequency band is determined, specifically as follows:

[0025] By selecting a circumferential order n=1, different tensile moduli E of the viscoelastic damping layer are obtained. 22 E33 By adjusting the material parameters to negative values ​​to create an extraordinary negative parameter range, the primary influence of negative tensile modulus on the elastic wave propagation characteristics of different materials was determined.

[0026] Furthermore, when setting E 22 E 33 To generate an exceptionally negative tensile modulus, the imaginary part of the wavenumber produces a negative region.

[0027] Furthermore, after determining the first influence law of the negative property material parameters on the elastic wave transmission characteristics in the low-frequency band, the method further includes:

[0028] Based on the first influence law, the dynamic mechanical parameters are changed, and the material modulus in the cylindrical shell is adjusted to be a complex number. The second influence law of complex property material parameters on elastic wave transmission characteristics is analyzed.

[0029] Furthermore, the second influence law of the analysis of complex property material parameters on elastic wave propagation characteristics is as follows:

[0030] When the tensile modulus is designed to be complex, damping is added to the material to smooth the peak value within the resonant frequency range.

[0031] (III) Beneficial Effects

[0032] The above-described technical solution of the present invention has the following advantages:

[0033] The present invention provides a method for analyzing the influence of low-frequency elastic wave transmission characteristics based on dynamic mechanical parameters. By changing the modulus of the viscoelastic damping layer material to a negative or complex number, it enables the material to possess extraordinary properties, thereby generating an adjustable bandgap in the structure. Elastic waves cannot propagate outward within the bandgap region, while elastic waves propagate freely outside the bandgap region. Furthermore, the method achieves the blocking and dissipation of elastic waves by changing the tensile modulus. Attached Figure Description

[0034] Figure 1 This is a flowchart illustrating the method for analyzing the influence of dynamic mechanical parameters on the transmission characteristics of low-frequency elastic waves according to the present invention.

[0035] Figure 2 This is a schematic diagram of the force distribution of a single microcell of the annular viscoelastic damping layer of the present invention.

[0036] Figure 3 Elastic wave change cloud diagrams before and after setting the negative property material parameters of the present invention;

[0037] Figure 4(a) is a graph showing the changes of the real and imaginary parts of the tensile modulus with frequency when the circumferential order n = 0 in this invention.

[0038] Figure 4(b) is a graph showing the changes in the real and imaginary parts of the tensile modulus with frequency when the circumferential order n=1 in this invention.

[0039] Figure 4(c) is a graph showing the changes of the real and imaginary parts of the tensile modulus with frequency when the circumferential order n=5 of the present invention.

[0040] Figure 4(d) is a graph showing the changes in the real and imaginary parts of the tensile modulus with frequency when the circumferential order n = 8 in this invention.

[0041] Figure 4(e) is a graph showing the changes of the real and imaginary parts of the tensile modulus with frequency when the circumferential order n = 15 in this invention.

[0042] Figure 4(f) is a graph showing the changes in the real and imaginary parts of the tensile modulus with frequency when the circumferential order n = 16 of the present invention.

[0043] Figure 5(a) shows the circumferential order n=1 and tensile modulus E of the present invention. 22 Dispersion curve of the real part when the material parameter is negative;

[0044] Figure 5(b) shows the circumferential order n=1 and tensile modulus E of the present invention. 22 Dispersion curve of the imaginary part when the material parameters are negative;

[0045] Figure 6(a) shows the circumferential order n=1 and tensile modulus E of the present invention. 33 Dispersion curve of the real part when the material parameter is negative;

[0046] Figure 6(b) shows the circumferential order n=1 and tensile modulus E of the present invention. 33 Dispersion curve of the imaginary part when the material parameters are negative;

[0047] Figure 7(a) shows the circumferential order n=1 and tensile modulus E of the present invention. 22 Dispersion curves when the material parameters are complex numbers with real parts;

[0048] Figure 7(b) shows the circumferential order n=1 and tensile modulus E of the present invention. 22 Dispersion curves when the material parameters are complex numbers with the imaginary part;

[0049] Figure 8(a) shows the circumferential order n=1 and tensile modulus E of the present invention. 33 Dispersion curves of material parameters when the material parameters are complex numbers and have real parts;

[0050] Figure 8(b) shows the circumferential order n=1 and tensile modulus E of the present invention. 33 Dispersion curves of material parameters with the imaginary part of complex numbers. Detailed Implementation

[0051] 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.

[0052] 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.

[0053] See Figure 1 This invention provides a method for analyzing the influence of dynamic mechanical parameters on the transmission characteristics of low-frequency elastic waves, which may include the following steps:

[0054] S100. Based on the selected annular viscoelastic damping layer microcell, the motion differential equation of the cylindrical shell based on the viscoelastic damping material is obtained.

[0055] Specifically, a segment of a ring-shaped viscoelastic damping layer microcell is selected, such as... Figure 2 As shown, the axial and circumferential coordinates of the cylindrical shell based on the viscoelastic damping material are represented by z, Indicates that u, v, and w represent the axial, circumferential, and radial displacements of the inner surface of the shell, respectively; N z , Q represents the internal forces in the shell along the axial, circumferential, and tangential directions, respectively. z , Let u and v represent the shear forces in the axial and circumferential directions of the shell, respectively. The infinitesimal unit cell is in equilibrium in the three directions of u, v, and w. The forces and moments on the cylindrical shell element are determined, and the differential equations of motion are obtained based on the equilibrium relationships of forces and moments in different directions.

[0056] S200. Based on the plane wave assumption and the combined motion differential equation, establish the characteristic equation of elastic wave dispersion relationship of the cylindrical shell, and obtain the dispersion curve of the cylindrical shell.

[0057] Specifically, based on the plane wave assumption and combined with the differential equations of motion, the wave equation of the viscoelastic damping layer is established. Based on the wave equation, the characteristic equations of elastic wave dispersion relations corresponding to different circumferential modes are obtained, and the dispersion curves are calculated using analytical and numerical methods, respectively. For example... Figure 3 As shown, Figure 3 The solid line represents the analytical solution of the elastic wave dispersion curve in the viscoelastic damping layer, and the annulus represents the finite element analysis results. Figure 3 As can be seen, the curves obtained by the two methods completely overlap, proving the accuracy of the elastic wave propagation model established based on the plane wave assumption, and providing a theoretical basis for analyzing the propagation characteristics of elastic waves in viscoelastic damping layers.

[0058] S300. Based on the dispersion curve, obtain the waveform diagram of the cylindrical shell and analyze the propagation type of the waveform at different circumferential orders in the low-frequency band.

[0059] Specifically, circumferential orders of 0, 1, 5, 8, 15, and 16 were selected to analyze the start and end frequencies and wave types of propagation waves corresponding to different circumferential orders in the low-frequency band of the viscoelastic damping layer. The real and imaginary parts of the wavenumber were plotted, with an imaginary part of 0 indicating that the wave can propagate. A waveform diagram was plotted at a specific frequency point on the oscilloscope dispersion curve to analyze the wave propagation type, such as... Figures 4(a) to 4(f) As shown in the figure, the results indicate that the toroidal viscoelastic damping layer produces helical bending waves with different circumferential orders. When n = 0, it exhibits both longitudinal and torsional waves. As the circumferential order increases, the start and end frequencies of the propagation waves gradually shift towards higher frequencies. When n > 15, only non-propagating near-field waves exist within the range of 1–300 Hz. When the circumferential order n = 1, the entire frequency band is a propagation wave. When n > 1, elastic wave control can be achieved by selecting an appropriate frequency position based on the starting frequency of the propagation wave.

[0060] S400. Based on the analysis results, select the set circumferential order to determine the elastic wave transmission of the cylindrical shell by the negative property material parameters, and determine the first influence law of the negative property material parameters on the elastic wave transmission characteristics in the low frequency band.

[0061] Specifically, by selecting a circumferential modal order n=1, different tensile moduli E of the viscoelastic damping layer are obtained. 22 E 33 By adjusting the material parameters to negative values ​​to achieve an exceptionally high negative parameter range, the influence of negative tensile modulus on the elastic wave propagation characteristics of different materials was investigated. The results are as follows: Figure 5(a) , 5(b) and Figure 6(a) , 6(b) As shown. Figure 5(a) , 5(b) and Figure 6(a) , 6(b) These represent the selected tensile modulus E. 22 E 33 The generated dispersion curve shows that setting E... 22 E 33 To generate an exceptionally negative tensile modulus, a significant negative region is produced in the imaginary part of the wavenumber, where the shaded area represents the band gap, within which elastic waves cannot propagate outwards. (Compare with E...) 22 E 33 The dispersion curve can be obtained compared to E. 33 In other words, E 22 The effect is more obvious.

[0062] As an optional implementation, after determining the first influence law of negative property material parameters on elastic wave transmission characteristics in the low-frequency band, step S400 further includes:

[0063] S500. Based on the first influence law, change the dynamic mechanical parameters and adjust the material modulus in the cylindrical shell to a complex number to analyze the second influence law of complex property material parameters on elastic wave transmission characteristics.

[0064] Specifically, by adjusting the material parameters of the viscoelastic damping layer to be complex numbers, different complex tensile moduli E are studied. 22 E 33 The influence of elastic wave propagation characteristics, such as Figure 7(a) , 7(b) and Figure 8(a) , 8(b) As shown in the figure, when the tensile modulus is designed to be complex, the peak of the frequency response curve becomes gentler, which is equivalent to adding damping to the material, dissipating the elastic waves in the structure, making the peak value within the resonant frequency smoother, and E 22 The effect is significantly better than E 33 Its effects.

[0065] 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 analyzing the influence of dynamic mechanical parameters on the transmission characteristics of low-frequency elastic waves, characterized in that, The method includes the following steps: Based on the selected annular viscoelastic damping layer micro-cell, the motion differential equation of the cylindrical shell based on the viscoelastic damping material is obtained; Based on the plane wave assumption and in conjunction with the aforementioned differential equation of motion, the characteristic equation of the elastic wave dispersion relationship of the cylindrical shell is established, and the dispersion curve of the cylindrical shell is obtained. Based on the dispersion curve, the waveform diagram of the cylindrical shell is obtained, and the propagation type of the waveform at different circumferential orders in the low frequency band is analyzed. Based on the analysis results, the set circumferential order is selected to determine the effect of negative property material parameters on the elastic wave transmission of the cylindrical shell, and the first influence law of the negative property material parameters on the elastic wave transmission characteristics in the low frequency band is determined.

2. The method for analyzing the influence of dynamic mechanical parameters on the transmission characteristics of low-frequency elastic waves according to claim 1, characterized in that, Based on the selected annular viscoelastic damping layer micro-cell, the motion differential equations of the cylindrical shell based on the viscoelastic damping material are obtained as follows: Select a segment of annular viscoelastic damping layer microcell, determine the forces and moments on the cylindrical shell microcell, and obtain the motion differential equation based on the balance relationship between forces and bending moments in different directions.

3. The method for analyzing the influence of dynamic mechanical parameters on the transmission characteristics of low-frequency elastic waves according to claim 1, characterized in that, The characteristic equation for the elastic wave dispersion relationship of the cylindrical shell is established based on the plane wave assumption and in conjunction with the motion differential equation, and the dispersion curve of the cylindrical shell is obtained, specifically as follows: Based on the plane wave assumption and the aforementioned motion differential equation, the wave equation of the viscoelastic damping layer is established. Based on the wave equation, the characteristic equations of elastic wave dispersion relationship corresponding to different circumferential modes are obtained. The dispersion curves are calculated using analytical and numerical methods, respectively.

4. The method for analyzing the influence of dynamic mechanical parameters on the transmission characteristics of low-frequency elastic waves according to claim 3, characterized in that, The dispersion curves obtained by analytical and numerical methods completely overlap.

5. The method for analyzing the influence of dynamic mechanical parameters on the transmission characteristics of low-frequency elastic waves according to claim 1, characterized in that, The waveform diagram of the cylindrical shell is obtained based on the dispersion curve, specifically as follows: Select a frequency point of the dispersion curve and plot its waveform.

6. The method for analyzing the influence of dynamic mechanical parameters on the transmission characteristics of low-frequency elastic waves according to claim 1, characterized in that, The analysis of the propagation types of waveforms at different circumferential orders in the low-frequency band specifically includes: When the circumferential order n = 0, it has longitudinal and torsional waves. As the circumferential order increases, the start and end frequencies of the propagating wave gradually shift to higher frequencies. When the circumferential order n = 1, the entire frequency band is a propagating wave; When the circumferential order n>15, only non-propagating near-field waves exist within the 1~300Hz range.

7. The method for analyzing the influence of dynamic mechanical parameters on the transmission characteristics of low-frequency elastic waves according to claim 1, characterized in that, Based on the analysis results, a set circumferential order is selected to determine the effect of negative property material parameters on the elastic wave transmission of the cylindrical shell, and the first influence law of the negative property material parameters on the elastic wave transmission characteristics in the low-frequency band is determined, specifically as follows: By selecting a circumferential order n=1, different tensile moduli E of the viscoelastic damping layer are obtained. 22 E 33 By adjusting the material parameters to negative values ​​to create an extraordinary negative parameter range, the primary influence of negative tensile modulus on the elastic wave propagation characteristics of different materials was determined.

8. The method for analyzing the influence of dynamic mechanical parameters on the transmission characteristics of low-frequency elastic waves according to claim 7, characterized in that, When setting E 22 E 33 To generate an exceptionally negative tensile modulus, the imaginary part of the wavenumber produces a negative region.

9. The method for analyzing the influence of dynamic mechanical parameters on the transmission characteristics of low-frequency elastic waves according to claim 1, characterized in that, After determining the first influence law of the negative property material parameters on the elastic wave transmission characteristics in the low-frequency band, the method further includes: Based on the first influence law, the dynamic mechanical parameters are changed, and the material modulus in the cylindrical shell is adjusted to be a complex number. The second influence law of complex property material parameters on elastic wave transmission characteristics is analyzed.

10. The method for analyzing the influence of dynamic mechanical parameters on the transmission characteristics of low-frequency elastic waves according to claim 9, characterized in that, The second influence law of the analysis of complex property material parameters on elastic wave propagation characteristics is as follows: When the tensile modulus is designed to be complex, damping is added to the material to smooth the peak value within the resonant frequency range.

Images