A symmetrical power-index prism phononic crystal structure and its parameter optimization method

Abstract

The present invention belongs to the technical field of vibration reduction and noise reduction, and in particular, relates to a power-exponential pyramid phononic crystal structure and a parameter optimization method thereof. A power-exponential pyramid phononic crystal structure comprises two power-exponential pyramids symmetrically arranged on the upper and lower end faces of a target plate; the power-exponential pyramid is composed of a frustum with a square cross-section and a base formed by extending outward from the large end face of the frustum; a circular groove is arranged at the center of the small end face of the frustum; the bases of the two power-exponential pyramids are attached to the upper and lower end faces of the target plate; the present invention draws on the power-exponential inclined plane configuration of an acoustic black hole and proposes a power-exponential pyramid phononic crystal configuration. It can use the unique band gap characteristics of phononic crystals to block the propagation of bending waves, and can also use the energy focusing effect generated by the power-exponential cross-section to suppress the bending vibration of the structure; compared with the traditional acoustic black hole configuration, the present invention has a good expansion path and a variety of design and application solutions, and has good physical properties and broad application prospects.

Description

Technical Field

[0001] The invention belongs to the technical field of vibration reduction and noise reduction, and relates to a power exponential pyramid phononic crystal structure and a parameter optimization method thereof. Background Art

[0002] During the voyage of a ship, the hull structure will inevitably vibrate. Hull vibration not only affects the acoustic stealth performance of the ship, but also poses a serious threat to the use and life of the equipment. Traditional vibration and noise reduction technologies often have limitations such as poor broadband effects, and high weight and volume costs. The lightweighting of vibration reduction structures and the high efficiency of vibration reduction effects have become hot issues that urgently need to be addressed in research. Acoustic metamaterials represent a new concept in composite structure design. Based on the understanding and use of traditional materials, new composite structures can be designed according to the needs of designers to achieve special functions. Their application value has attracted great attention from governments, academia, and the military. Among them, the acoustic black hole ABH converts the structural thickness into a power exponential function h(x)=ε|x| m The form of m≥2 is reduced, and an energy gathering area can be generated at the tip of the structure, thereby achieving vibration reduction, noise reduction and energy regulation. Phononic crystals can effectively suppress vibrations in specific frequency bands by utilizing their unique band gap characteristics. The present invention draws on the acoustic black hole configuration and proposes a power exponential prism phononic crystal, which can effectively suppress the bending vibration of thin plates by combining the energy focusing effect and band gap characteristics of acoustic black holes. Summary of the invention

[0003] The purpose of the invention is to design a light-weight, easily adjustable vibration reduction frequency range, and a power-exponential pyramid phononic crystal structure that can effectively block the propagation of bending waves in a thin plate structure within the band gap frequency band without weakening the structural strength, and to provide a parameter optimization method for facilitating structural design applications.

[0004] The power-index pyramid phononic crystal and parameter optimization method of the present invention mainly calculate the dispersion curve to clarify the bending wave band gap existing in the phononic crystal plate structure, so as to suppress the bending vibration of the phononic crystal plate.

[0005] To achieve the aforementioned objectives, the present invention adopts the following technical solutions.

[0006] A symmetrical power-index pyramid phononic crystal structure comprises two power-index pyramids 1 symmetrically arranged on the upper and lower end surfaces of a target plate 2; the power-index pyramid 1 is composed of a frustum 10 with a square cross section and a base 11 formed by extending outward from the large end surface of the frustum 10; a circular groove 12 is arranged at the center of the small end surface of the frustum 10; the bases 11 of the two power-index pyramids 1 are attached to the upper and lower end surfaces of the target plate 2;

[0007] The side length of the base 11 is a and the total height is h A, and 30mm < a < 70mm; the contraction dimension of the frustum 10 from the bottom to the top is 2*r A , 0.12a < r A < 0.4a, the top side length of the frustum 10 is a - 2r A , the total height of the frustum 10 is H A ; the radius of the circular groove 12 is r A1 , 0 < r A1 < a / 2 - r A , the depth is H A1 , 0 < H A1 < 0.8H A ;

[0008] The power - exponential curve function corresponding to the side face of the power - exponential frustum 1 is: H(x) = ε|x| m +h A , where ε is the power - exponential function m is the power of the power - exponential function.

[0009] For a further improvement or preferred implementation of the above - mentioned symmetric power - exponential frustum phononic crystal structure, it includes multiple power - exponential frustums 1 arranged in a rectangular array on the upper and lower end faces of the target plate 2; the array direction of the rectangular array is consistent with the direction of the side of the square cross - section of the frustum 10.

[0010] For a further improvement or preferred implementation of the above - mentioned symmetric power - exponential frustum phononic crystal structure, the power - exponential frustum matrix 1 is made of polycarbonate material; the thin - plate structure is made of steel plate.

[0011] For a further improvement or preferred implementation of the above - mentioned symmetric power - exponential frustum phononic crystal structure, it includes periodically arranging the power - exponential frustum structure 1 on both sides of the target steel plate.

[0012] The present invention also provides a method for optimizing the parameters of a symmetric power - exponential frustum phononic crystal structure, including the following steps:

[0013] Step 1. Obtain the vibration - damping target parameters, including:

[0014] Measure or specify the material parameters, geometric parameters of the flat plate structure to be vibration - damped, and the load frequency acting on the flat plate structure; the material parameters include the Young's modulus, Poisson's ratio and density of the thin - plate structure, and the geometric parameters include the length, width and thickness of the thin - plate structure, where the thickness h of the thin - plate B should satisfy: 0.1mm < h B < 2mm, and the load frequency refers to the harmonic load frequency vertically applied to the thin - plate structure.

[0015] Step 2. Calculate the dispersion curve of the symmetric power - exponential frustum phononic crystal structure to determine whether it contains the load frequency; including:

[0016] The dispersion curve characterizes the propagation mode of elastic waves in the phononic crystal configuration. A geometric model is established based on the power-exponential pyramid phononic crystal configuration, and the material parameters of the configuration are defined. According to the irreducible Brillouin zone of the structure, the function of the wave vector k is defined using the function definition function of the software. At the same time, periodic boundary conditions are used around the structure, and the eigenmodes of the phononic crystal under different wave vectors are calculated through parametric scanning and eigenfrequency solver. The dispersion curve of the symmetrical power-exponential pyramid phononic crystal structure can be obtained by solving the eigenvalues ​​with finite element software.

[0017] Step 3. Analyze the dispersion curve, identify the bending wave band gap frequency band, and determine whether it contains the loading frequency; including:

[0018] In the dispersion curve, each set of wave vectors and frequencies corresponds to a plane wave, and the single cell vibration mode corresponding to the wave vector and frequency is called an eigenmode. For waves that cannot propagate, there is no wave vector corresponding to the frequency, which results in a bandgap in the dispersion curve. The bandgap characteristics of phononic crystals can be used to effectively suppress the propagation of waves in phononic crystal structures with a finite period. In structures with finite thickness, there are generally three basic wave modes: bending waves, longitudinal waves, and horizontal shear waves. Thin plate structures mainly produce large vibrations and noise due to displacement in the Z direction perpendicular to the plate. Bending waves in thin plate structures are the main reason for the vertical bending vibration of the structure. The bending wave modes in the dispersion curve need to be identified to clarify the bending wave band gap. According to the dispersion curve calculated in step 2, analyze the displacement components of the eigenmodes at any point of each dispersion curve in each direction, clarify the bending wave modes, and then clarify the bending wave band gap.

[0019] Step 4: If the band gap range does not include the loading frequency, return to step 2, adjust the geometric parameters of the symmetrical power exponential pyramid phononic crystal structure, and then calculate its dispersion curve until the loading frequency is within the band gap range. A Should meet: 0.1h b <h A <2h b , the power m of the power exponential function should satisfy: m ≥ 2, the power exponential prism height H A Should meet: 8h b <H A <20h b ;

[0020] Step 5: Arrange the designed phononic crystals periodically at the steel plate to be damped to suppress the bending vibration within the band gap frequency band of the structure.

[0021] A further improvement or specific implementation scheme for the parameter optimization method of the aforementioned symmetrical power-exponential pyramid phononic crystal structure, wherein step 2 is implemented in Comsol software, and the model dimension is set to three dimensions, the physical field is set to solid mechanics physical field, and the research module is set to characteristic frequency.

[0022] Its beneficial effects are:

[0023] The present invention draws on the power exponential slope configuration of acoustic black holes and proposes a symmetrical power exponential pyramid phononic crystal structure. It can use the unique band gap characteristics of phononic crystals to block the propagation of bending waves, and can also use the energy focusing effect generated by the power exponential cross section to suppress the bending vibration of the structure; compared with the traditional acoustic black hole configuration, the present invention has a good expansion path and a variety of design and application schemes, and has good physical properties and broad application prospects. The traditional acoustic black hole configuration is an elastic thin plate structure that is reduced to zero in the cross-sectional direction according to a certain power exponential law, which will concentrate the vibration wave energy flow propagating along this direction at the tip of the structure, and then absorb the vibration energy through additional damping materials to achieve a vibration reduction effect. This acoustic black hole configuration has a fatal flaw when applied to practice, that is, the reduction of the cross-sectional thickness will greatly reduce the structural strength. The present invention can use a bonding method to periodically arrange the power exponential pyramid made of lightweight materials on the plate structure, which can suppress the bending vibration of the plate without destroying the structural strength. Based on the structural form of the symmetrical power-index pyramid phononic crystal structure of the present invention, the band gap range can be quickly and effectively adjusted by directly using the power function of the pyramid side surface. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 It is a periodic structure of the symmetrical power-index pyramid phononic crystal structure in the embodiment;

[0025] Figure 2 is an assembly diagram of a symmetrical power-index pyramid phononic crystal structure in an embodiment;

[0026] Figure 3 is the irreducible Brillouin zone of the symmetrical power-index pyramidal phononic crystal structure in the embodiment;

[0027] Figure 4 is a finite element mesh division diagram of a symmetrical power-exponential pyramid phononic crystal structure in an embodiment;

[0028] Figure 5 is a dispersion curve diagram of a symmetrical power-index pyramidal phononic crystal structure in an embodiment;

[0029] Figure 6 is the eigenmode diagram of point A in the dispersion curve in the embodiment;

[0030] Figure 7 is the eigenmode diagram of point B in the dispersion curve in the embodiment;

[0031] Figure 8 is the eigenmode diagram of the midpoint C of the dispersion curve in the embodiment;

[0032] Fig. 9 is the eigenmode diagram of the midpoint D of the dispersion curve in the embodiment;

[0033] Fig.10 is the eigenmode diagram of the midpoint E of the dispersion curve in the embodiment;

[0034] Fig.11 is the eigenmode diagram of the midpoint F of the dispersion curve in the embodiment;

[0035] Fig.12 is the eigenmode diagram of the midpoint G of the dispersion curve in the embodiment;

[0036] Fig.13 is a stereogram of a power-index pyramid phononic crystal plate in an embodiment;

[0037] Fig.14 is a transmission loss curve of a power-index pyramidal phononic crystal plate and a flat plate under a simple harmonic load in an embodiment;

[0038] Fig.15 This is the displacement cloud diagram of the power exponential pyramid phononic crystal plate under the simple harmonic load of 4000Hz;

[0039] Fig.16 It is the displacement cloud diagram of the flat plate structure under the simple harmonic load with a frequency of 4000Hz;

[0040] Fig.17 This is a schematic diagram of the effect of the total height change of the prism on the band gap range;

[0041] Fig.18 This is a schematic diagram of the effect of the change in the thickness of the prism boundary on the band gap range;

[0042] Fig.19 This is a schematic diagram of the effect of the power change of the prism side on the band gap range. DETAILED DESCRIPTION

[0043] The present invention is described in detail below in conjunction with specific embodiments.

[0044] like Figure 1 As shown, the power-index prism phononic crystal of the present invention comprises a power-index prism substrate 1 and a thin plate 2; the power-index prism 1 means: the power-index prism 1 means: the upper end face and the lower end face are square, the size of the upper end face is smaller than the size of the lower end face, the side of the prism is bent inward in the form of a power-index curve, and a prism structure with a circular groove processed in the center of the upper end face is provided;

[0045] like Figure 2 As shown, the power exponential curve function corresponding to the side of the power exponential prism 1 is: H(x)=ε|x| m +h A , the cube of the power pyramid base has a side length of a and an edge thickness of h A , the total height of the prism is H A , the width of the depression is r A The radius of the cylindrical hole in the middle of the prism is r A1 , the depth of the cavity is H A1 The length and width of the thin plate are consistent with the lower end of the prism, and the thickness is h B In the specific implementation, when determining the edge thickness h A , the total height of the prism is H A , the width of the depression is r A , the specific value of the power m of the power function can determine the coefficient ε of the power function.

[0046] The following is a detailed description of its structural features, parameter design method and working mode in combination with a specific structural design. In this embodiment, the side length a of the power exponential pyramid is 50 mm, the edge thickness h is 0.3 mm, the power m of the power function is 5, and the width of the fan-shaped concave is r. A The total height of the power exponential prism is 10mm, and there is a cylindrical cavity with a radius of 11mm and a depth of 10mm. It is attached to a flat plate structure with a length of 50mm, a width of 50mm and a thickness of 0.5mm.

[0047] To facilitate comparison, the physical property data of the material of the power-exponential pyramid phononic crystal structure of the present invention are obtained at the same time, and the power-exponential pyramid phononic crystal structure of the present invention is analyzed and calculated using Comsol software. The specific contents include the calculation of the dispersion curve of the power-exponential pyramid phononic crystal, the analysis of the dispersion curve, and the calculation of the transfer function of the plate structure attached with the symmetrical power-exponential pyramid phononic crystal structure under the action of simple harmonic load, and comparison with the flat plate structure without the phononic crystal of the present invention attached to determine its actual performance, and the influence of geometric structure parameters on the band gap range is given.

[0048] The steps for calculating the energy band curve of phononic crystal using finite element method are as follows:

[0049] Step 1. Obtaining vibration reduction target parameters, including: measuring or specifying material parameters, geometric parameters, and load frequency acting on the vibration reduction steel plate;

[0050] Step 2. Calculate the dispersion curve of the symmetric power-exponential pyramid phononic crystal structure; including:

[0051] The dispersion curve characterizes the propagation mode of elastic waves in the phononic crystal configuration. Select the solid mechanics module for the physical field, and select the characteristic frequency in the study options. Establish a geometric model based on the power exponential pyramid phononic crystal configuration and define the material parameters of the configuration. Select periodic boundary conditions around the model and set the piecewise function of the wave vector k to scan along the irreducible Brillouin zone, such as Figure 3 In the meshing of the structure, the power pyramid structures on both sides of the thin plate structure use free tetrahedral meshes, and the thin plate structure uses sweeping, and ensures that the bending wave wavelength corresponding to each frequency in the calculated dispersion curve contains at least 5 to 6 mesh units, as shown in Figure 4 By studying the parametric scanning to solve the eigenmode of the power-exponential pyramid phononic crystal structure under a specific wave vector, the dispersion curve of the symmetrical power-exponential pyramid phononic crystal structure can be obtained, as shown in Figure 5 shown.

[0052] Step 3. Analyze the dispersion curve, identify the bending wave band gap frequency band, and determine whether the band gap frequency band contains the loading frequency; including:

[0053] In the dispersion curve, each set of wave vectors and frequencies corresponds to a plane wave, and the single-cell vibration mode corresponding to the wave vector and frequency is called an eigenmode. For waves that cannot propagate, there is no wave vector corresponding to the frequency, which results in a bandgap in the dispersion curve. In a plate structure of finite thickness, there are generally three basic wave modes: bending waves, longitudinal waves, and horizontal shear waves. Analyze the eigenmodes at any point in each curve. Select any point in each curve of the dispersion curve, and read the displacement components of the eigenmodes of the selected point in the x, y, and z directions through the results in the software - 3D drawing group - parameter solution. When the displacement component of the eigenmode in the z direction is much larger than the displacement components in the x and y directions, it can be considered that the dispersion curve at this point corresponds to a bending wave mode. Figure 6 The dispersion curves are listed ( Figure 5 ) The displacement components of the eigenmode of point AG in the x, y and z directions. The vibration amplitude of the eigenmode at points A, B, C, D, and E in the z direction is much greater than that in the other two directions, while the eigenmodes at points F and G produce large displacements in the x and y directions respectively, which indicates that the black dot in the dispersion curve of point AE corresponds to the bending wave mode, and the curves at points E and F correspond to the bending wave mode. Figure 5 The red dots correspond to other wave modes. Because the thin plate structure has a large vibration in the vertical direction due to the existence of bending waves, the present invention focuses on the bending wave mode in the dispersion curve, but does not pay attention to the wave modes of horizontal shear waves and longitudinal waves. When the wave modes of horizontal shear waves and longitudinal waves in the dispersion curve are hidden, the band gap range of bending waves can be clearly defined. Figure 5 It can be seen that the phononic crystal structure of the embodiment has three bending wave band gaps, and the band gap frequency bands are shown in Table 1.

[0054] Table 1 Flexural wave band gap frequency band

[0055] Band Gap Name Starting frequency / Hz Stop frequency / Hz The first band gap 2910 4366 Band Gap 2 6016 7656 Band Gap 3 9528 10660

[0056] Step 4. If the band gap range does not include the loading frequency, return to step 2, adjust the prism slope of the symmetrical power exponential prism phononic crystal structure and then calculate its dispersion curve until the loading frequency is within the band gap range;

[0057] Step 5. Periodically attach the designed phononic crystals to both sides of the steel plate to be damped to block the propagation of bending waves with frequencies within the band gap range.

[0058] like Figure 1 As shown, the power exponential pyramid phononic crystal unit cell is composed of a power exponential pyramid 1 and a thin plate 2, wherein the power exponential pyramid matrix is ​​made of polycarbonate PC; the specific material parameters are shown in Table 2:

[0059] Table 2 Material parameters

[0060] Material Name <![CDATA[Density ρ / kg·m -3 > Elastic modulus E / Gpa Poisson's ratio μ steel 7800 210 0.3 Polycarbonate 1200 2.048 0.3

[0061] In actual application, the power-exponential pyramid phononic crystal structure is a periodic structure composed of a phononic crystal structure attached to a flat plate structure for use. Based on the above calculation results, the periodic structure composed of the power-exponential pyramid phononic crystal structure array is attached to the target flat plate structure to be vibrated.

[0062] In order to facilitate the analysis and calculation, Figure 7 As shown, in this embodiment, 4×4 power-exponential pyramidal phononic crystal configurations are arranged in the middle of a target flat plate structure with a length of 300 mm, a width of 200 mm, and a thickness of 0.5 mm. At the same time, a simple harmonic load with a frequency of 1000-12000 Hz, a force of 10 N, and a direction perpendicular to the plate is set at point P1 (-125, 0) of the phononic crystal plate. The dispersion curve can predict the vibration reduction frequency band of the phononic crystal, but the transfer function is still needed to verify the vibration reduction effect of the phononic crystal. In vibration research, the transfer loss function is usually defined as Where X1 is the acceleration amplitude at point P2, and X0 is the acceleration amplitude at point P1.

[0063] Import the test model into Comsol software, select the corresponding materials for each part of the structure, select Physical Field-Solid Mechanics-Point Load when adding periodic loads, and select the convenient selection options according to Figure 7Set the corresponding excitation point in the test model, select the total force option in the force-load type, and enter -10[N] in the Z direction, that is, the load size is 10N, and the direction is the negative direction of the Z axis, and set the boundaries around the model to fixed constraints, that is, the rotation angle and displacement around the structure are 0. In the test model, the power exponential pyramid structure selects free tetrahedral mesh for mesh division, and the thin plate structure selects sweeping. The test model has 27,400 mesh vertices, 84,356 tetrahedral mesh units, and 50,200 triangular mesh units.

[0064] Select the "Frequency Domain" option in the study module. The "Frequency Domain" study is used to calculate the response of a linear or linearized model when it is excited by one or more harmonic frequencies. Enter range(1000,3,12000) in the Frequency Domain-Settings-Study Settings-Frequency option to calculate the response of the phononic crystal plate structure under the frequency load every time the frequency is increased by 3Hz until the effect of the periodic load of 12000Hz on the plate structure is calculated.

[0065] At the same time, in order to prove the effectiveness of the symmetrical power-exponential pyramid phononic crystal structure, the transfer function of the flat plate structure with the same size as the test model under the same load was compared without the power-exponential pyramid phononic crystal structure attached, such as Figure 8 As shown in the figure, the acceleration amplitude at the same point of the flat plate structure is also collected to calculate the transfer function. The flat plate structure is meshed by sweeping, with 1250 mesh vertices and 576 hexahedral elements.

[0066] pass Figure 7 It can be seen that compared with the flat plate structure, the phononic crystal plate has an obvious energy attenuation section in the bandgap frequency band, and also has a certain vibration reduction effect in the non-bandgap frequency band. Fig. 9 and Fig.10 The displacement cloud diagrams of the phononic crystal plate with a power exponential pyramid structure and the flat plate structure under a simple harmonic load of 4000 Hz are shown respectively. By comparison, it can be seen that the band gap characteristics of the bending wave in the phononic crystal and its own energy focusing effect inhibit the propagation of the bending wave of the plate structure and the bending vibration of the plate.

[0067] In order to more intuitively demonstrate the vibration reduction effect of the power-indexed pyramid phononic crystal plate, the displacement sizes of the phononic crystal plate and the flat plate structure under different simple harmonic load excitations at the excitation point P1 and the response point P2 are listed, as shown in Table 3.

[0068] Table 3 Displacement values ​​at the P2 response point measured by the phononic crystal plate and the flat plate structure

[0069]

[0070] When a simple harmonic load outside the 1243Hz band gap acts vertically on the structure, the total displacement of the phononic crystal plate at the response point P2 increases by 6.25% compared to the flat plate structure.

[0071] When the simple harmonic load within the first band gap of 3752 Hz acts vertically on the structure, the total displacement of the phononic crystal plate at the response point P2 is reduced by 73.6% compared with the flat plate structure.

[0072] When a simple harmonic load outside the 5188Hz band gap acts vertically on the structure, the total displacement of the phononic crystal plate at the response point P2 increases by 4.41% compared to the flat plate structure.

[0073] When the simple harmonic load within the second band gap of 6670 Hz acts vertically on the structure, the total displacement of the phononic crystal plate at the response point P2 is reduced by 99.9% compared with the flat plate structure.

[0074] When a simple harmonic load outside the 8836Hz band gap acts vertically on the structure, the total displacement of the phononic crystal plate at the response point P2 is reduced by 54.1% compared to the flat plate structure.

[0075] When the simple harmonic load within the third band gap of 10072 Hz acts vertically on the structure, the total displacement of the phononic crystal plate at the response point P2 is reduced by 99.9% compared with the flat plate structure.

[0076] In summary, the power-exponential pyramid phononic crystal structure of the present invention can efficiently suppress the propagation of bending waves in the structure in the band gap frequency band, and has a certain effect in suppressing the bending vibration of the plate structure. To facilitate the readers' use of the present invention, the influence of geometric parameters on the band gap range of the symmetrical power-exponential pyramid phononic crystal structure is analyzed.

[0077] (1) Effect of prism height change on band gap range

[0078] like Fig.11 As shown, as the total height of the prism increases, the end frequencies of the three band gaps will increase, the starting frequency of the first band gap will begin to decrease, and the range of its band gap will expand.

[0079] (2) Effect of boundary thickness variation on band gap range

[0080] like Fig.12 As shown, with the increase of the thickness of the pyramid structure boundary, the starting frequency and the ending frequency of the three band gaps will increase simultaneously, and the band gap frequency will gradually decrease.

[0081] (3) Effect of the power change of the prism side on the band gap range

[0082] like Fig.13As shown in the figure, as the pyramid power m increases, the bandwidths of the first and third band gaps gradually expand, while the starting frequency of the second band gap gradually decreases. The phononic crystal only produces a band gap when the pyramid power m is greater than or equal to 2. This is because the energy focusing effect will only occur when the power of the pyramid side meets the relationship m≥2, and the local resonance effect caused by the energy focusing effect will be stimulated to produce a band gap.

[0083] The above embodiments are only used to illustrate the technical solution of the present application, rather than to limit the scope of protection of the present application. Although the present application has been described in detail with reference to the preferred embodiments, a person skilled in the art should understand that the technical solution of the present application can be modified or replaced by equivalents without departing from the essence and scope of the technical solution of the present application.

Claims

1. A symmetrical power-index pyramidal phononic crystal structure, characterized in that: It comprises two power exponential prisms (1) symmetrically arranged on the upper and lower end surfaces of a target plate (2); The power exponential pyramid (1) is composed of a frustum (10) with a square cross section and a base (11) formed by extending the large end surface of the frustum (10) outward; a circular groove (12) is arranged at the center of the small end surface of the frustum (10); the bases (11) of the two power exponential pyramids (1) are attached to the upper and lower end surfaces of the target plate (2); The side length of the base (11) is a, and the total height is h A , and 30mm < a < 70mm; the shrinkage dimension of the frustum (10) from the bottom to the top is 2*r A , 0.12a < r A < 0.4a, the top side length of the frustum (10) is a - 2r A , the total height of the frustum (10) is H A ; the radius of the circular groove (12) is r A1 , 0 < r A1 < a / 2 - r A , the depth is H A1 , 0 < H A1 < 0.8H A ; The power exponential curve function corresponding to the side of the power exponential prism (1) is: H(x)=ε|x| m +h A , where ε is a power exponential function m is the power of the exponential function; The parameters of the power exponential pyramid phononic crystal structure are determined based on the following steps: Step 1. The step of obtaining the vibration reduction target parameters specifically refers to: determining the material parameters, geometric parameters of the target plate (2) and the load frequency acting on the plate structure; The material parameters include Young's modulus, Poisson's ratio and density of the thin plate structure, and the geometric parameters include the length, width and thickness of the thin plate structure, wherein the thickness h of the thin plate is B Should meet: 0.1mm <h B <2mm, the load frequency refers to the frequency of the simple harmonic load applied vertically to the thin plate structure; Step 2. Calculate the dispersion curve of the symmetric power-exponential pyramid phononic crystal structure; specifically, establish a geometric model based on the power-exponential pyramid phononic crystal configuration, define the material parameters of the configuration, define the function of the wave vector k using the function definition function of the software according to the irreducible Brillouin zone of the structure, and use periodic boundary conditions around the structure. Calculate the eigenmodes of the phononic crystal under different wave vectors through parametric scanning and eigenfrequency solver, solve the eigenvalues ​​through finite element software, and obtain the dispersion curve of the symmetric power-exponential pyramid phononic crystal structure; Step 3. Analyze the dispersion curve, identify the bending wave band gap frequency band, and determine whether it contains the load frequency, including: confirming the bending wave band structure according to the eigenmode of the dispersion curve, and then identifying the bending wave band gap; Step 4. Analyze the band gap range of the energy band curve to determine whether it contains the load frequency; if the band gap range does not contain the load frequency, return to step 2, adjust the geometric parameters of the symmetrical power exponential pyramid phononic crystal structure and then calculate its dispersion curve until the load frequency is within the band gap range; the power exponential pyramid boundary thickness h A Should meet: 0.1h B <h A <2h B , the power m of the power exponential function should satisfy: m32, the power exponential prism height H A Should meet: 8h B <H A <20h B ; Step 5. Arrange the designed phononic crystals periodically at the steel plate to be damped to suppress the bending vibration within the band gap frequency band of the structure.

2. A symmetrical power-index pyramidal phononic crystal structure according to claim 1, characterized in that: It comprises a plurality of pairs of power-exponential pyramids (1) arranged in a rectangular array on the upper and lower end surfaces of a target plate (2); the array direction of the rectangular array is consistent with the direction of the side of the square cross section of the pyramid (10).

3. A symmetrical power-index pyramidal phononic crystal structure according to claim 1, characterized in that: The power exponential pyramid (1) is made of polycarbonate material; the target plate (2) is made of steel plate.

4. The symmetrical power-index pyramid phononic crystal structure according to claim 1, characterized in that: The step 2 specifically includes: establishing a geometric model based on the power-exponential pyramid phononic crystal configuration, defining the material parameters of the configuration, determining the periodic boundary conditions around the model, setting the wave vector k, scanning along the irreducible Brillouin zone, meshing the power-exponential pyramid structure based on a tetrahedral grid, forming a thin plate structure based on sweeping, adjusting the above parameters to ensure that the wavelength corresponding to each frequency in the dispersion curve contains at least 5 to 6 power-exponential pyramid phononic crystals, and solving the characteristic value to obtain the dispersion curve of the symmetrical power-exponential pyramid phononic crystal structure.

5. The symmetrical power-exponential pyramidal phononic crystal structure according to claim 1, characterized in that: The step 3 specifically includes: analyzing the three basic wave modes of the plate structure, namely, bending wave, longitudinal wave, and horizontal shear wave; selecting any point in each dispersion curve, and reading the displacement components of the eigenmode of the selected point in the x, y, and z directions. When the displacement component of the eigenmode in the z direction is much larger than the displacement components in the x and y directions, the dispersion curve at the point corresponds to the bending wave mode, and the eigenmode of any point in the curve is obtained.

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