Cantilever beam type phononic crystal and parameter optimization method

Abstract

The present application belongs to the technical field of ship vibration control structure or method, and particularly relates to a cantilever beam type phononic crystal for vibration isolation and a parameter optimization method. The phononic crystal comprises a power-law prism base, a cross-shaped cantilever beam and a mass block. The power-law prism base comprises a power-law prism part and a base part. The cross-shaped cantilever beam is a cross-shaped flat plate structure, and the mass block is located at the end of the cross-shaped cantilever beam. The cantilever beam type phononic crystal based on the present application can be used for vibration control of different materials and different thicknesses. In actual application, only the material parameters and thickness of the flat plate need to be substituted, and the other part sizes and materials of the cantilever beam type phononic crystal are designed according to the flat plate size and vibration source frequency, so that the band gap frequency range covers the load frequency, and the vibration of the target frequency can be blocked. The structure of the cantilever beam type phononic crystal based on the present application can use materials with different elastic moduli to prepare the cross-shaped cantilever beam and materials with different densities to prepare the mass block, so that the band gap frequency range can be adjusted conveniently and quickly.

Description

Technical Field

[0001] This invention belongs to the technical field of ship vibration control structures or methods, and particularly relates to a cantilever beam phonon crystal for vibration isolation and a parameter optimization method. Background Technology

[0002] Ship vibration not only affects the service life of machinery and equipment but also endangers the health of crew members. The hazards of vibration are even more pronounced for submarines, affecting not only the service life of machinery and equipment and the health of crew members but also weakening the submarine's acoustic stealth capabilities and worsening its survivability. Ship vibrations include hull vibrations caused by the interaction of high-speed incoming currents with the hull plating, propeller vibrations caused by unevenly cut incoming currents by propeller blades, and hull vibrations caused by force imbalances in large equipment such as power plants. Hull vibrations caused by large mechanical devices are a significant component of ship vibration. Current control methods for this type of vibration mainly include active control by generating anti-phase vibrations mechanically and vibration isolation using elastic bases at the connection between the vibration source and the hull. These methods have limitations such as requiring energy input and poor low-frequency isolation effectiveness. Summary of the Invention

[0003] The purpose of this invention is to provide a phonon crystal configuration with good vibration isolation effect within a designed frequency band. This configuration generates a coupling bandgap through the combined effects of local resonance and energy focusing, thereby passively and effectively blocking low-frequency vibrations within the bandgap. Simultaneously, a method is provided for rapidly calculating this phonon crystal configuration, adjusting and designing the vibration isolation frequency band, and optimizing parameters.

[0004] To achieve the above objectives, the present invention adopts the following technical solution.

[0005] A cantilever beam phononic crystal for vibration reduction of a flat plate structure is disposed on the large end face of the flat plate structure and includes a power-law frustum substrate 1, a cross-shaped cantilever beam 2, and a mass block 3.

[0006] The power-law frustum base 1 includes a power-law frustum portion 10 and a base portion 11;

[0007] The power-law frustum 10 is a vertically arranged quadrangular prism structure with square upper and lower faces. The side length of the upper face of the power-law frustum base 1 is smaller than the side length of the lower face. The edges of the power-law frustum 10 are in the shape of a power-law curve.

[0008] The base portion 11 is formed by extending vertically downward from the bottom of the power-law frustum portion 10; the bottom of the base portion 11 is connected to the vibration reduction target;

[0009] The cross-shaped cantilever beam 2 is a cross-shaped flat plate structure, and the cross-shaped cantilever beam 2 is fixed to the top of the power law truncated pyramid 1; the two arms of the cross-shaped cantilever beam 2 are of equal length and are respectively set parallel to the top edge of the power law truncated pyramid 1; the beam width of the cross-shaped cantilever beam 2 is consistent with the side length of the square at the top of the power law truncated pyramid 1.

[0010] The mass block 3 is located at the end of the cross-shaped cantilever beam 2.

[0011] Further improvements or optimizations to the aforementioned cantilever beam phonon crystal result in the following power-law curve function corresponding to the edges of the power-law frustum 10:

[0012]

[0013] The coordinate system of the curve function takes the bottom corner of the power-law frustum base 1 as the origin and the direction of the side length passing through the corner as the x-axis; where 'a' refers to the bottom side length of the power-law frustum 10, 'b' refers to the top side length of the power-law frustum 10, and H... B h refers to the total height of the power-law frustum base 1. A It is the height of the base part 11, and p is a power function greater than 2.

[0014] Further improvements or optimizations to the aforementioned cantilever phononic crystals include the use of polycarbonate for the power-law frustum substrate 1 and 304 stainless steel for the cross-shaped cantilever beam 2 and the mass block 3.

[0015] This application also provides a parameter optimization method for cantilever beam phononic crystals, comprising the following steps:

[0016] Step 1. Obtain the basic parameters of the vibration reduction target;

[0017] The basic parameters include at least the elastic modulus, Poisson's ratio, density, geometric parameters, and load frequency acting on the steel plate of the vibration reduction target.

[0018] Step 2. Determine the number of periods of the cantilever beam phononic crystal based on the dimensions of the flat plate structure, and determine the material parameters and geometric dimensions of the cantilever beam phononic crystal;

[0019] The number of cycles refers to the number of cantilever beam phononic crystals set on the vibration-isolated plate, which is determined by the size of the plate to be isolated, and indirectly determines the cell side length of the cantilever beam phononic crystal; the geometric dimensions of the cantilever phononic crystal are first scaled down proportionally to the cell side length determined above in the embodiment.

[0020] Step 3. Calculate the band structure of the cantilever beam phonon crystal; including:

[0021] Establish a geometric model in a three-dimensional multiphysics modeling environment: draw the cantilever beam phononic crystal unit cell structure in the geometry and determine the material parameters; use the wave vector covering the irreducible Brillouin zone to perform separate analysis on the periodic unit cell; set the piecewise function of the wave vector k in the irreducible Brillouin zone, and set the piecewise function with m as the independent variable that the wave vector k needs to use when sweeping the boundary of the irreducible Brillouin zone according to the range of the irreducible Brillouin zone;

[0022] The side length 'a' of the phononic crystal is set as the lattice constant. To ensure that the wave vector takes values ​​along the irreducible Brillouin zone X→M→Γ→X, the wave vector coordinates are (π / l,0)→(π / l,π / l)→(0,0)→(π / l,0). A piecewise function is set. Where kx is the component of wave vector k in the x-direction, and ky is the component of wave vector k in the y-direction;

[0023] Select the required material parameters and set periodic conditions; perform finite element mesh generation on the model, and perform parametric scanning of the independent variable m from 0 to 3 to achieve wave vector scanning of the first irreducible Brillouin zone boundary of the cantilever beam phononic crystal, and obtain the dispersion curve of the cantilever beam phononic crystal.

[0024] Step 4. Analyze the bandgap frequency band of the bandgap curve to determine whether the load frequency is within the bandgap frequency band;

[0025] Step 5. If the load frequency is within the bandgap frequency, proceed directly to step 6; if the load frequency is not within the bandgap frequency band, return to step 2 and adjust the material and geometry of the cantilever beam phononic crystal.

[0026] Step 6. Arrange the designed cantilever beam phonon crystal on the flat plate structure according to the number of periods determined in Step 2 to block the vibration of the target load frequency.

[0027] A further improvement or preferred implementation of the parameter optimization method for the aforementioned cantilever beam phononic crystal, in step 3, is to select a periodic condition in the solid mechanics module, set the periodicity type to Floquet period in the periodic condition settings, input the kx and ky piecewise functions that were previously defined in the x and y directions, and add a parametric scan in the study, with the scan parameter being m and the scan range being 0 to 3.

[0028] A further improvement or preferred embodiment of the parameter optimization method for the aforementioned cantilever beam phononic crystal, in step 3, during mesh generation, the cantilever beam and mass block are first divided into structured hexahedral meshes, then the frustum is divided into free tetrahedral meshes, and finally the connecting plate is divided into triangular prism meshes. During mesh generation, it must be ensured that each wavelength of the elastic wave contains at least 5 to 6 elements.

[0029] Its beneficial effects are as follows:

[0030] The cantilever beam phononic crystal based on the present invention can be used for vibration control of plates of different materials and thicknesses. In practical applications, it is only necessary to substitute the material parameters and thickness of the plate and design the dimensions and materials of other parts of the cantilever beam phononic crystal according to the plate size and vibration source frequency, so that the bandgap frequency band covers the load frequency, thereby achieving the isolation of vibration at the target frequency.

[0031] Based on the cantilever beam phononic crystal structure of this invention, cross-shaped cantilever beams can be fabricated using materials with different elastic moduli, and mass blocks can be fabricated using materials with different densities, allowing for convenient and rapid adjustment of the bandgap frequency band. Furthermore, based on the cantilever beam phononic crystal structure of this invention, the bandgap frequency band can be quickly and effectively adjusted by changing the thickness and extension length of the cross-shaped cantilever beam and the length and height of the mass block. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of the structure of a cantilever beam phononic crystal monomer;

[0033] Figure 2 This is a schematic diagram showing the range of the irreducible Brillouin zone of a cantilevered phononic crystal monomer.

[0034] Figure 3 This is a schematic diagram of the finite element mesh generation for a cantilever beam phononic crystal model.

[0035] Figure 4 It is the calculated dispersion curve of the cantilever beam phonon crystal;

[0036] Figure 5 It is a finite element model of a multiphonon crystal model plate;

[0037] Figure 6 It is a vibration transmission curve calculated from response displacement and excitation displacement in the range of 10Hz to 3000Hz;

[0038] Figure 7 The displacement response of the cantilever beam phonon crystal plate under an excitation load of 1220 Hz;

[0039] Figure 8 The displacement response of the flat plate under an excitation load of 1220Hz;

[0040] Figure 9 This is a schematic diagram illustrating the effect of the thickness of the cross-shaped cantilever beam 2 on the bandgap frequency band.

[0041] Figure 10 This is a schematic diagram showing the effect of the height of mass block 4 on the bandgap frequency band. Detailed Implementation

[0042] The phonon crystal in this application refers to a periodic composite structure with periodically distributed elastic constants and mass density, and possessing both elastic wave band structure and elastic wave bandgap. Periodically arranged phonon crystals can block the propagation of elastic waves within the bandgap frequency band. Furthermore, the low-frequency bandgap of locally resonant phonon crystals, which can achieve "small size control of large wavelength," plays a significant role in ship vibration control, as it can block the propagation of elastic waves within the bandgap.

[0043] The present invention will be described in detail below with reference to specific embodiments.

[0044] like Figure 1 As shown, the cantilever beam phonon crystal of the present invention includes a power-law truncated pyramid substrate 1, a cross-shaped cantilever beam 2, a mass block 3, and a vibration reduction target 4. The power-law truncated pyramid substrate 1 includes a power-law truncated pyramid portion 10 and a base portion 11. The power-law truncated pyramid portion 10 is a vertically arranged quadrangular prism structure with square upper and lower end faces. The side length of the upper end face of the power-law truncated pyramid substrate 1 is smaller than the side length of the lower end face. The edges of the power-law truncated pyramid portion 10 are power-law curved. The base portion 11 is formed by extending vertically downward from the bottom of the power-law truncated pyramid portion 10. The bottom of the base portion 11 is connected to the vibration reduction target 4. The cross-shaped cantilever beam 2 is located directly above the power-law truncated pyramid 1. The cross-shaped cantilever beam 2 refers to a sheet-like structure with a certain thickness and a cross shape. The mass block 3 refers to a cuboid connected to the end of the cross-shaped cantilever beam. The vibration reduction target 4 refers to a cuboid plate connected to the lower end face of the power-law truncated pyramid 1.

[0045] Design a cantilever phonon crystal with a lattice size of 50 mm, as required. The connecting plate has a side length of 50 mm and a thickness of 0.5 mm. The lower end face of the power-law frustum has a side length 'a' of 30 mm, the upper end face has a side length 'b' of 10 mm, and the edge thickness is 'h'. A Given a height of 0.6 mm, a power of m of the power function, and a total height of 15 mm for the power-law frustum, the equation of the upper edge arc of the power-law frustum can be determined as follows: Where x∈[[0,(30-10) / 2]]; the extension length of the cross-shaped cantilever beam is 19mm, the beam width is 10mm, and the thickness is 0.45mm; the mass block is 10mm long, 2mm wide, and 6.5mm high.

[0046] The cantilever beam phononic crystal of the present invention was analyzed and calculated using Comsol software. The specific contents include calculating the dispersion curve of the cantilever beam phononic crystal, determining the bandgap frequency band of the cantilever beam phononic crystal, calculating the displacement of the plate with the cantilever beam phononic crystal of the present invention under load in the bandgap frequency band, and comparing it with the plate structure to determine its actual performance. At the same time, the influence of geometric structural parameters on the bandgap frequency band is given.

[0047] The steps for calculating the band structure of a phononic crystal using the finite element method are as follows:

[0048] Step 1. Obtain the target parameters for vibration isolation, including:

[0049] Measure or specify the material parameters, geometric parameters, and load frequency acting on the steel plate to be isolated;

[0050] The required vibration-damping flat plate structure is 250mm long, 250mm wide, and 0.5mm high. It is made of 304 stainless steel with a Poisson's ratio of 0.3 and a density of 7930 kg / m³. 3 The elastic modulus is 194 GPa. It is now necessary to isolate the vibration with an excitation frequency of 1220 Hz near one edge of the plate.

[0051] Step 2. Determine the number of periods of the cantilever beam phononic crystal based on the dimensions of the flat plate structure, determine the material parameters and geometric dimensions of the cantilever beam phononic crystal, and draw the geometric model, including:

[0052] The geometric dimensions and material mechanical parameters of the power-law frustum matrix 1, the cross-shaped cantilever beam 2, and the mass block 3 are determined, and a geometric model is established in a three-dimensional multiphysics modeling environment based on these parameters. In practice, the graph of the cantilever beam phononic crystal unit cell is drawn in the geometry, a new empty material is created in the material, the corresponding material parameters are input, and the set material parameters are assigned to the corresponding geometric structure.

[0053] A cantilever beam phonon crystal with a lattice size of 50 mm is designed and attached in a 3*5 array in the middle of a flat plate. The connecting plate in the phonon crystal has a side length of 50 mm and a thickness of 0.5 mm. The lower end face of the power-law frustum has a side length 'a' of 30 mm, the upper end face has a side length 'b' of 10 mm, and the edge thickness 'hA' is 0.6 mm. The power of the power function is m = 5, and the total height of the power-law frustum is 15 mm. The equation of the upper edge arc of the power-law frustum can be determined as follows: Where x∈[[0,(30-10) / 2]]; the extended length of the cross-shaped cantilever beam is 19mm, the beam width is 10mm, and the thickness is 0.45mm; the mass block is 10mm long, 2mm wide, and 6.5mm high. The cross-shaped cantilever beam 2, mass block 3, and connecting plate 4 are made of 304 stainless steel with a Poisson's ratio of 0.3, a density of 7930Kg / m3, and an elastic modulus of 194Gpa. The power-law frustum is made of polycarbonate with a Poisson's ratio of 0.3, a density of 1200Kg / m3, and an elastic modulus of 2.048Gpa. A geometric model is constructed in Comsol, and material parameters are assigned to each geometric structure.

[0054] Step 3. Calculate the band structure of the cantilever beam phonon crystal; including:

[0055] A periodic unit cell is analyzed separately using the wave vector covering the irreducible Brillouin zone; a piecewise function of the wave vector k in the irreducible Brillouin zone is set, based on... Figure 2The irreducible Brillouin zone is defined by setting the wave vector k, which is a piecewise function with m as the independent variable needed when sweeping the boundary of the irreducible Brillouin zone. The side length a of the phonon crystal is set as the lattice constant. To ensure the wave vector takes values ​​along the irreducible Brillouin zone X→M→Γ→X, the wave vector coordinates are (π / l,0)→(π / l,π / l)→(0,0)→(π / l,0). A piecewise function is then set. Where kx is the component of wave vector k in the x-direction, and ky is the component of wave vector k in the y-direction.

[0056] Select the required material parameters and set periodic conditions; such as... Figure 3 As shown, based on the model obtained in step 2 above, a finite element mesh is generated, and the independent variable m is parametrically scanned from 0 to 3 to achieve wave vector scanning of the first irreducible Brillouin zone boundary of the cantilever beam phononic crystal, thereby obtaining the dispersion curve of the cantilever beam phononic crystal.

[0057] In practice, select the periodicity condition in the solid mechanics module, set the periodicity type to Floquet period in the periodicity condition settings, and input the piecewise function of the wave vector k set in the definition in the x and y directions in the x and y directions. Add a parametric scan in the study, with the scan parameter being m and the scan range being 0 to 3.

[0058] See the schematic diagram of the cantilever beam phonon crystal mesh generation. Figure 3 During mesh generation, the cantilever beam ends and mass blocks are first meshed into structured hexahedral meshes. Then, the middle part of the cantilever beam is meshed into triangular prism meshes, the frustums are meshed into free tetrahedral meshes, and finally, the connecting plate is meshed into triangular prism meshes. When meshing, it is essential to ensure that each wavelength of the elastic wave contains at least 5 to 6 elements.

[0059] Step 4. Analyze the bandgap frequency band of the bandgap curve to determine whether the load frequency is within the bandgap frequency band;

[0060] Figure 4 To calculate the dispersion curve of the cantilever beam phonon crystal, the "deep V"-shaped band near Γ in the dispersion curve is a non-pure bending wave and is ignored when searching for band gaps. Outside the "deep V"-shaped band, three band gaps can be found below 3 kHz, with frequency bands of 341 Hz to 431 Hz, 924 Hz to 1546 Hz, and 2024 Hz to 2555 Hz. The load frequency of 1220 Hz falls within the band gap frequency band.

[0061] Step 5. If the load frequency is within the bandgap frequency, proceed directly to step 6; if the load frequency is not within the bandgap frequency band, return to step 2 and adjust the material and geometry of the cantilever beam phononic crystal.

[0062] Analysis revealed that the load frequency of 1220Hz is within the bandgap band. Therefore, there is no need to return to step 2 to adjust the phonon crystal material and geometric parameters; proceed directly to step 6.

[0063] Step 6. Arrange the designed cantilever beam phonon crystal in a 3*5 pattern on the flat plate structure as determined in Step 2 to block the vibration of the target load frequency.

[0064] To verify the effectiveness of the vibration isolation of the cantilever beam phonon crystal plate involved, such as Figure 5 As shown, a finite element model of the phonon crystal plate is established.

[0065] The appropriate materials were selected for each part of the phonon crystal plate. Fixed constraint boundary conditions were applied around the phonon crystal plate, and a simple harmonic load of 10N was applied at the vibration source. Frequency domain analysis was performed in the range of 10Hz to 3000Hz. The range of the vibration emitted from the source after being blocked by the phonon crystal was defined as the response domain. The average displacement of the response domain was taken as the response displacement, and the displacement at the vibration source was taken as the excitation displacement. The vibration transfer function was calculated in the range of 10Hz to 3000Hz using the response displacement and the excitation displacement. The calculated vibration transfer curve is shown below. Figure 6 As shown. The vibration transmission curve is defined as... Where Z0 is the displacement at the excitation point P1, and Z1 is the displacement at the response point P2.

[0066] To demonstrate the vibration reduction characteristics of the cantilever beam phononic crystal bandgap of this invention, a comparison plate was used. The plate dimensions remained 250*250*0.5 mm. The same fixed constraints and vibration source as the phononic crystal plate were applied to the plate. The same response displacement and excitation displacement were used to calculate the transfer function. The vibration transfer curves within the range of 10 Hz to 3000 Hz are shown below. Figure 6 As shown. In Figure 6 It is evident that the phononic crystal plate exhibits excellent vibration isolation within the bandgap frequency band, reducing vibration displacement by up to 90 dB, and by 58 dB at the excitation frequency of 1220 Hz. Table 1 lists the displacements of the cantilever beam phononic crystal plate at point P1 at the excitation source and point P2 after isolation by the cantilever beam phononic crystal at different excitation frequencies. Table 1 clearly demonstrates the excellent vibration isolation effect of the phononic crystal plate within the bandgap frequency band, reducing the displacement at point P1 to less than one percent of that at point P0, showing a significant vibration control effect compared to a flat plate.

[0067] Table 1 Displacement Transfer of Cantilever Beam Phononic Crystal Plate

[0068] Location Frequency / Hz Z0 / m (displacement at point P1) Z1 / m (displacement at point P2) Z1 / Z0 Within the first band gap 400 3.00e-4 5.49e-7 0.18％ Between the first and second band gaps 660 3.25e-4 4.42e-4 136.15％ Second band gap 1220 3.52e-5 1.50e-7 0.43％ Between the second and third band gaps 1830 8.90e-6 8.42e-6 142.06％ Within the third band gap 2210 2.12e-4 2.17e-4 0.33％

[0069] Table 2 Displacement Transfer Table for Flat Plates

[0070] Frequency / Hz Z0 / m (displacement at point P1) Z1 / m (displacement at point P2) Z1 / Z0 400 1.02e-3 7.56e-4 73.66％ 660 5.34e-5 8.89e-5 166.61％ 1220 1.02e-4 4.55e-5 44.53％ 1830 1.27e-5 1.93e-5 151.19％ 2210 4.97e-5 1.66e-7 102.53％

[0071] Figure 7 The displacement response of the flat plate under an excitation load of 1220Hz is given. Figure 8 The displacement response of the cantilever beam phonon crystal plate under an excitation load of 1220 Hz is given. Figure 7 and Figure 8 The comparison shows that under a 1220Hz excitation load, the cantilever beam phonon crystal plate has a good vibration isolation effect. The first row of phonon crystals near the excitation source can effectively block vibration.

[0072] In summary, the cantilever beam phononic crystal of the present invention can significantly reduce the vibration of the plate within the bandgap frequency band. To facilitate the reader's adjustment of the bandgap of the cantilever beam phononic crystal of the present invention, the influence of geometric parameters on the bandgap frequency band of the local resonant phononic crystal is analyzed below.

[0073] (1) The effect of the thickness of the cross-shaped cantilever beam on the bandgap frequency band

[0074] like Figure 9 As shown, as the thickness of the cross-shaped cantilever beam increases, the frequency of the first bandgap gradually increases and the first bandgap widens continuously; the starting frequency of the second bandgap remains almost unchanged, while the ending frequency continuously increases.

[0075] (2) The effect of mass block 4 height on bandgap frequency band

[0076] like Figure 10 As shown, as the height of the mass block increases, the frequency of the first bandgap decreases and the width narrows slightly; the termination frequency of the second bandgap remains unchanged, the starting frequency decreases and the bandgap gradually widens; the frequency of the third bandgap decreases and the width narrows.

[0077] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit the scope of protection of the present invention. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the essence and scope of the technical solutions of the present invention.

Claims

1. A cantilever beam phonon crystal for vibration damping of a flat plate structure, disposed on the large end face of the flat plate structure, characterized in that, Includes a power-law frustum base (1), a cross-shaped cantilever beam (2), and a mass block (3); The power-law frustum base (1) includes a power-law frustum portion (10) and a base portion (11). The power-law frustum (10) is a quadrangular prism structure with a vertical arrangement and a square upper and lower end face. The side length of the upper end face of the power-law frustum base (1) is smaller than the side length of the lower end face. The edges of the power-law frustum (10) are in the shape of a power-law curve. The base part (11) is formed by extending vertically downward from the bottom of the power-law frustum part (10); the bottom of the base part (11) is connected to the vibration reduction target; The cross-shaped cantilever beam (2) is a cross-shaped flat plate structure. The cross-shaped cantilever beam (2) is fixed on the top of the power law frustum base (1). The two arms of the cross-shaped cantilever beam (2) are of equal length and are set parallel to the top edge of the power law frustum base (1). The beam width of the cross-shaped cantilever beam (2) is consistent with the side length of the square at the top of the power law frustum base (1). The mass block (3) is located at the end of the cross-shaped cantilever beam 2; The power-law curve function corresponding to the edge of the power-law frustum (10) is: ； The coordinates of the curve function are based on the bottom corner of the power-law frustum base (1) as the origin, and the x-axis is the direction of the side length passing through the corner; where a refers to the bottom side length of the power-law frustum (10), b refers to the top side length of the power-law frustum (10), and H... B The total height of the power-law frustum matrix (1), h A It is the height of the base part (11), and p is a power function greater than 2.

2. The cantilever beam phonon crystal according to claim 1, characterized in that, In the cantilevered phononic crystal, the power-law frustum matrix (1) is made of polycarbonate, and the cross-shaped cantilever beam (2) and the mass block (3) are made of 304 stainless steel.

3. A parameter optimization method for the cantilever beam phonon crystal of claim 1, characterized in that, Includes the following steps: Step 1. Obtain the basic parameters of the vibration reduction target; The basic parameters include at least the elastic modulus, Poisson's ratio, density, geometric parameters, and load frequency acting on the steel plate of the vibration reduction target. Step 2. Determine the number of periods of the cantilever beam phononic crystal based on the dimensions of the flat plate structure, and preliminarily determine the material and geometric dimensions of the cantilever beam phononic crystal; The number of cycles refers to the number of cantilever phononic crystals set on the vibration-isolated plate, which is determined by the size of the plate to be isolated, and indirectly determines the cell side length of the cantilever phononic crystal; the geometric size of the cantilever phononic crystal is first scaled down proportionally to the cell side length determined above by a preset geometric size. Set the material type according to preset parameters; Step 3. Calculate the band structure of the cantilever beam phonon crystal; including: Establish a geometric model in a three-dimensional multiphysics modeling environment: draw the cantilever beam phononic crystal unit cell structure in the geometry and determine the material parameters; The periodic unit cell is analyzed separately using the wave vector covering the irreducible Brillouin region; a piecewise function of the wave vector k in the irreducible Brillouin region is set, and the piecewise function with m as the independent variable is set according to the range of the irreducible Brillouin region when the wave vector k sweeps the boundary of the irreducible Brillouin region. The side length 'a' of the phononic crystal is set as the lattice constant. To ensure that the wave vector takes values ​​along the irreducible Brillouin zone X→M→Γ→X, the wave vector coordinates are (π / l,0)→(π / l,π / l)→(0,0)→(π / l,0). A piecewise function is set. , Where kx is the component of wave vector k in the x-direction, and ky is the component of wave vector k in the y-direction; Select the required material parameters and set periodic conditions; perform finite element mesh generation on the model, and perform parametric scanning of the independent variable m from 0 to 3 to achieve wave vector scanning of the first irreducible Brillouin zone boundary of the cantilever beam phononic crystal, and obtain the dispersion curve of the cantilever beam phononic crystal. Step 4. Analyze the bandgap frequency band of the bandgap curve to determine whether the load frequency is within the bandgap frequency band; Step 5. If the load frequency is within the bandgap frequency, proceed directly to step 6; if the load frequency is not within the bandgap frequency band, return to step 2 and adjust the material and geometry of the cantilever beam phononic crystal. Step 6. Arrange the designed cantilever beam phonon crystal on the flat plate structure according to the number of periods determined in Step 2 to block the vibration of the target load frequency.

4. The parameter optimization method for cantilever beam phonon crystal according to claim 3, characterized in that, In step 3, a periodicity condition is selected in the solid mechanics module, and the periodicity type is set to Floquet period in the periodicity condition settings. The piecewise kx and ky functions that were previously defined are input in the x and y directions, and a parametric scan is added to the study. The scan parameter is m, and the scan range is 0 to 3.

5. The parameter optimization method for cantilever beam phonon crystal according to claim 3, characterized in that, In step 3, when meshing, the cantilever beam and mass block are first divided into structured regular hexahedral meshes, then the frustum is divided into free tetrahedral meshes, and finally the connecting plate is divided into triangular prism meshes. When meshing, it is necessary to ensure that each wavelength of the elastic wave contains at least 5 to 6 elements.

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