A particle-damped phononic crystal structure and a method for constructing its equivalent theoretical model

Abstract

The present invention provides a particle damping phononic crystal structure and a method for constructing an equivalent theoretical model thereof, and relates to the field of vibration and noise reduction processing technology for aerospace and construction. Among them, this structure includes at least one damping structure, and the damping structure includes a base layer and a damper; a plurality of dampers are fixedly arranged on the base layer and arranged in an orderly manner; the damper includes an outer shell and damping particles filled in the inner cavity of the outer shell; a side of the base layer in one damping structure away from the damper is connected to a side of the damper in another damping structure that is not fixed to the base layer, and the structure has a good vibration reduction effect. The present invention also provides a method for constructing an equivalent theoretical model based on the above-mentioned particle damping phononic crystal structure, which can provide a new research paradigm for the study of the use of particle damping technology in the field of vibration.

Description

Technical Field

[0001] The present invention relates to the technical field of vibration and noise reduction processing in aerospace and architecture, and in particular to a particle damping phononic crystal structure and a method for constructing an equivalent theoretical model thereof. Background Art

[0002] Particle damping technology is a technology that provides damping by particles filled in the cavity (or additional cavity) of the vibrating structure. When the structure vibrates, due to the motion coupling and energy transfer between the vibrating particle container and the internal particles, collisions, friction, radiation noise, etc. are generated between the particle units and between the particle units and the vibrating container, thereby dissipating the energy of the vibrating main structure. This particle damping technology can be used in the vibration and noise reduction of aerospace equipment and construction equipment.

[0003] Although the mechanism of particle damping vibration reduction has not yet been determined, using the energy consumption principle between particle units to reduce the vibration of elastic bodies has become a hot topic in vibration and noise reduction research. Many scholars have carried out a lot of research, such as gear vibration reduction and particle damping double-layer float valve vibration reduction for heavy compressor units. At present, the vibration reduction and energy consumption characteristics of particle damping are mainly obtained through experimental verification and theoretical analysis. In terms of theoretical analysis, there are mainly equivalent restitution coefficient analysis method, equivalent viscous damping analysis method, theoretical energy consumption analysis method based on discrete element, discrete element-finite element coupling analysis method, etc. However, general structural vibration is the propagation of vibration energy of elastic waves in the medium over time, which is essentially the propagation of stress waves. The above theoretical methods mainly analyze the collision energy consumption, friction energy consumption, particle unit body motion law, random and average collision force of particles on the damper wall of particle aggregates during forced vibration. Although the feasibility of theoretical analysis has been verified by experiments, the propagation characteristics, wave conversion, force chain characteristics of elastic waves in particle assemblies when objects vibrate have not been analyzed to improve the fatigue strength of forced vibration of actual engineering structures such as ships, rail transit vehicles, building bridges, aerospace equipment, high-end equipment, etc., which are periodic structures arranged in geometric space. Improve the structural dynamic characteristics. In order to study the transmission characteristics and regulation mechanism of elastic waves and realize the vibration control of periodic structures, many scholars have proposed to design specific artificial periodic structures based on the phononic crystal band gap theory, such as phononic crystal vehicle sound insulation board structure, local resonance double matrix plate structure, two-dimensional gradient phononic crystal plate structure, phononic crystal plate hollow cylinder-rod structure, double-sided phononic crystal plate, local resonance periodic plate-beam structure, etc. However, the actual designed structures are difficult to apply in engineering. Summary of the invention

[0004] One of the purposes of the present invention is to provide a particle damping phononic crystal structure, which can improve the vibration problem generated during the operation of the equipment.

[0005] Another object of the present invention is to provide a method for constructing an equivalent theoretical model based on a particle damped phononic crystal structure, which is used to provide a discrete-continuum equivalent theoretical analysis method for the designed particle damped phononic crystal structure, and has extremely high engineering and theoretical application value.

[0006] In order to solve the above technical problems, the present invention provides a particle damping phononic crystal structure, which includes at least one damping structure, wherein the damping structure includes a substrate layer and a damper; a plurality of the dampers are fixedly arranged on the substrate layer and arranged in an orderly manner; the damper includes an outer shell and damping particles filled in the inner cavity of the outer shell; a side of the substrate layer in one damping structure away from the damper is connected to a side of the damper in another damping structure that is not fixed to the substrate layer.

[0007] As a further optimization, the damping particle filling rate of the damper is 10%-100%.

[0008] As a further optimization, the density of the damping particles is 1.2 g / cm 3 ~18.3g / cm 3 , the longest diameter is 0.1mm~12mm, the surface friction factor is 0.02~0.99, and the surface recovery coefficient is 0.1~1.

[0009] As a further optimization, the damper is cylindrical.

[0010] As a further optimization, the ratio of the contact area between the damper and the base layer to the connection surface area between the base layer and the damper satisfies the following relationship:

[0011]

[0012] Wherein, D is the outer diameter of the damper, a is the distance between the centers of two adjacent dampers, and f is the ratio of the contact area to the connection surface area.

[0013] As a further optimization, the material of the damping particles is steel, glass or ceramic.

[0014] As a further optimization, the material of the base layer is steel, aluminum, carbon fiber material or glass.

[0015] As a further optimization, the shell is made of steel or aluminum.

[0016] The present invention also provides a method for constructing an equivalent theoretical model based on the above-mentioned particle damped phononic crystal structure, which is used to obtain the equivalent physical characteristic parameters of the particle damped phononic crystal structure, comprising the following steps:

[0017] Obtaining physical characteristics of the particle damping phononic crystal structure; wherein the physical characteristics at least include the overall mass of the damping particles, the volume of the shell, the Young's modulus of the damping particle material, the Poisson's ratio of the damping particle material, the spherical radius of the damping particles, the mass of the damping particles, and the overlap between the damping particles;

[0018] Based on the physical characteristics and vibration frequency, construct equivalent physical characteristic parameters of the particle damping phononic crystal structure; wherein the equivalent physical characteristic parameters at least include equivalent elastic modulus, equivalent dynamic density, equivalent dynamic Poisson's ratio and dynamic Rayleigh damping;

[0019] Based on the equivalent physical characteristic parameters, the theoretical transmission loss value of the particle damping phononic crystal structure is obtained by Fourier transform calculation.

[0020] As a further optimization, based on the physical characteristics and vibration frequency, constructing equivalent physical characteristic parameters of the particle damped phononic crystal structure includes the following steps:

[0021] The equivalent dynamic elastic modulus E d (f) satisfies the relationship with the vibration frequency f as follows:

[0022]

[0023] In formula (1), are the polynomial coefficients, is a constant;

[0024] The equivalent dynamic density satisfies the following relationship:

[0025]

[0026] In formula (2), ρ d is the equivalent dynamic density, ρ sta is the static mass density, m to is the overall mass of the damping particles, and V is the volume of the shell;

[0027] The relationship between the dynamic Rayleigh damping C(f) and the vibration frequency satisfies the following relationship:

[0028] C d (f) = α(f)[M] + β(f)[K] (3)

[0029] In formula (3), α, β are functions related to vibration frequency, stiffness matrix [K], and mass matrix [M];

[0030] in,

[0031] α(f)=ξ1f 6 +ξ2f 5+ξ3f 4 +ξ4f 3 +ξ5f 2 +ξ6f+ξ (4)

[0032]

[0033] In formula (4) and formula (5), ξ1, ξ2, ξ3, ξ4, ξ5, ξ6 are polynomial coefficients; ξ, ζ are constants;

[0034] The equivalent dynamic Poisson's ratio ν satisfies the following relationship under a certain external pressure static equilibrium state:

[0035]

[0036] In formula (6), λ = k c-t / k n-e , k c-t is the tangential stiffness of the damping particle unit, k n-e is the normal stiffness of the damping particle element;

[0037] in,

[0038]

[0039] In formula (7), E is the Young's modulus of the damping particle material, νp is the Poisson's ratio of the damping particle material, R is the sphere radius of the damping particle, and m is the mass of the damping particle;

[0040]

[0041] In formula (8), δ is the overlap between the damping particles, and A is the dissipation coefficient, which is approximately 0.7071.

[0042] By adopting the above technical solution, the present invention can achieve the following technical effects:

[0043] The present invention provides a particle damping phononic crystal structure, in which the damper is arranged in an orderly manner on a substrate layer, so that the particle damping phononic crystal structure has periodic and array characteristics. When the equipment vibrates, the energy can be more effectively transferred to the damping particles in the damper, so that motion coupling and energy transfer occur between the damping particles and the outer shell and the damping particles, thereby achieving a vibration reduction effect.

[0044] The present invention also provides a method for constructing an equivalent theoretical model based on a particle damping phononic crystal structure, which obtains equivalent physical characteristic parameters such as equivalent elastic modulus, equivalent dynamic damping ratio coefficient, equivalent dynamic density, equivalent dynamic Poisson's ratio, etc. of the particle damping phononic crystal structure, and then finally calculates the theoretical transmission loss value through these equivalent physical characteristic parameters. After measurement, the theoretical transmission loss value obtained by the present invention has a high consistency with the actual measured transmission loss value, which proves that the equivalent theoretical model construction method provided by the present invention can provide a new research paradigm for the research on the application of particle damping technology in the field of vibration. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying creative work.

[0046] Figure 1 It is a structural schematic diagram of the particle damping phononic crystal structure provided by the present invention;

[0047] Figure 2 yes Figure 1 The cross-section of the damper;

[0048] Figure 3 It is the equivalent physical characteristic parameters and frequency response function diagram obtained by the equivalent theoretical model construction method provided by the present invention; wherein, a is the relationship curve between the equivalent elastic modulus and the frequency; b is the approximate relationship curve between the equivalent Rayleigh damping α coefficient and the frequency; c is the relationship curve between the equivalent Rayleigh damping β coefficient and the frequency; d is the finite structure transmission frequency response function curve.

[0049] Markings in the figure: 1-damping structure; 10-base layer; 20-damper; 21-housing; 22-damping particles. DETAILED DESCRIPTION

[0050] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the invention claimed for protection, but merely represents the selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0051] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", "clockwise", "counterclockwise" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the referred device or element must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present invention.

[0052] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.

[0053] In the present invention, unless otherwise clearly specified and limited, the terms "installed", "connected", "connected", "fixed" and the like should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, it can be the internal connection of two elements or the interaction relationship between two elements. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0054] In the present invention, unless otherwise clearly specified and limited, a first feature being "above" or "below" a second feature may include that the first and second features are in direct contact, or may include that the first and second features are not in direct contact but are in contact through another feature between them. Moreover, a first feature being "above", "above" and "above" a second feature includes that the first feature is directly above and obliquely above the second feature, or simply indicates that the first feature is higher in level than the second feature. A first feature being "below", "below" and "below" a second feature includes that the first feature is directly below and obliquely below the second feature, or simply indicates that the first feature is lower in level than the second feature.

[0055] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments:

[0056] Depend on Figure 1 As shown, the present invention provides a particle damping phononic crystal structure, comprising at least one damping structure 1, wherein the damping structure 1 comprises a base layer 10 and a damper 20. A plurality of the dampers 20 are fixedly disposed on the base layer 10 and arranged in an orderly manner. Figure 2 As shown, the damper 20 includes a shell 21 and damping particles 22 filled in the inner cavity of the shell 21. The side of the substrate layer 10 in one layer of the damping structure 1 away from the damper 20 is connected to the side of the damper 20 in another layer of the damping structure 1 that is not fixed to the substrate layer 10. When the particle damping phononic crystal structure is used, the damper 20 is affected by the vibration of the equipment, so that the damper 20 generates interaction forces between the outer shell 21 of the damper 20 and the filled damping particles 22, and between the damping particles 22 and the damping particles 22. The energy is consumed by the collision and friction between the outer shell 21 of the damper 20 and the damping particles 22, and between the damping particles 22 and the damping particles 22, and the impact energy is quickly dissipated, thereby achieving a good vibration reduction and noise reduction effect. In addition, the particle damping phononic crystal structure has a simple structure and can effectively reduce the vibration caused by the equipment. In addition, the band gap characteristics of particle damping periodic structures with different arrangement types can be obtained by changing the arrangement and quantity of the dampers 20, the filling rate of the damping particles 22 and the number of layers of the damping structure 1, so as to better adapt to the vibration reduction effect to be achieved by different devices.

[0057] It should be noted that the damper 20 can be connected to the base layer 10 by glue or by welding, but is not limited thereto. The damper 20 and the inner cavity of the damper 20 can be cylindrical, rectangular or other shapes, but are not limited thereto. More preferably, as Figure 1 or Figure 2As shown, the damper 20 and the inner cavity of the damper 20 are cylindrical, so that the contact area between the damper 20 and the damping particles 22 is maximized, thereby improving the vibration reduction effect. The base layer 10 may be in the shape of a long plate, a circular plate, or an irregular plate, but is not limited thereto.

[0058] As a further optimization, the dampers 20 are arranged periodically or in an array on the base layer 10. More preferably, Figure 1 As shown, the damper 20 is fixed on the base layer 10 in an array with a fixed spacing, which makes it easier to obtain the band gap characteristics of the particle damping periodic structure and facilitates the subsequent research on the equivalent theoretical model construction method.

[0059] As a further optimization, the material of the base layer 10 is steel, aluminum, carbon fiber or glass. By changing the stiffness of the material of the base layer 10, the low-frequency band gap characteristics of different types of particle damping periodic structures can be obtained to achieve structural ultra-low frequency vibration reduction and noise reduction. More preferably, the material of the base layer 10 is aluminum alloy, which has high strength and is not easily corroded, and can provide good support for the damper 20 and extend its service life.

[0060] As a further optimization, the material of the shell 21 is steel or aluminum. When vibration occurs, the energy consumed by the collision between the shell 21 and the damping particles 22 made of different materials is different, and can be selected according to actual conditions. More preferably, in a preferred embodiment of the present invention, the material of the shell 21 is aluminum alloy, which has high strength and is not easily corroded, thereby extending the service life.

[0061] As a further optimization, the damping particles 22 are made of steel, glass or ceramic. Damping particles 22 made of different materials have different vibration reduction and noise reduction effects, and the damping particles 22 can be selected according to actual equipment requirements.

[0062] As a further optimization, the filling rate of the damping particles 22 of the damper 20 is 10%-100%. The damper 20 with different vibration reduction effects can be obtained by changing the filling rate of the damping particles 22. Preferably, the filling rate is 45-100%. More preferably, the damping effect is best when the filling rate of the damping particles 22 is between 75% and 100%.

[0063] As a further optimization, the density of the damping particles 22 is 1.2 g / cm 3 ~18.3g / cm 3, the longest diameter is 0.1 mm to 12 mm, the surface friction factor is 0.02 to 0.99, and the surface recovery coefficient is 0.1 to 1. Different physical parameters of the damping particles 22 can enable the particle damping phononic crystal structure to obtain different types of particle damping periodic structure band gap characteristics.

[0064] As a further optimization, the damping particles 22 are one or more of a sphere with a diameter of 0.1-12 mm, an ellipsoid with a major and minor axis length between 0.1-12 mm, and a regular or irregular polyhedron with a side length of 0.1-12 mm. Preferably, the damping particles 22 are spheres with a diameter of 0.1-12 mm. The spherical structure has a greater degree of freedom of movement, and the collision probability between the damping particles 22 is high, thereby increasing damping and having better anti-vibration ability.

[0065] As a further optimization, based on the above embodiment, the ratio of the contact area between the damper 20 and the base layer 10 and the connection surface area between the base layer 10 and the damper 20 satisfies the following relationship:

[0066]

[0067] Wherein, D is the outer diameter of the damper 20, a is the distance between the centers of two adjacent dampers 20; and f is the ratio of the contact area to the connection surface area.

[0068] In this embodiment, the best vibration reduction and noise reduction effect can be achieved by reasonably configuring a certain number of dampers 20 on the base layer 10 .

[0069] The present invention also provides a method for constructing an equivalent theoretical model based on the above-mentioned particle damped phononic crystal structure, which is used to obtain the equivalent physical characteristic parameters of the particle damped phononic crystal structure, comprising the following steps:

[0070] S101, obtaining physical characteristics of the particle damping phononic crystal structure; wherein the physical characteristics at least include the overall mass of the damping particles 22, the volume of the shell 21, the Young's modulus of the damping particles 22 material, the Poisson's ratio of the damping particles 22 material, the spherical radius of the damping particles 22, the mass of the damping particles 22, and the overlap between the damping particles 22;

[0071] S102, constructing equivalent physical characteristic parameters of the particle damped phononic crystal structure based on the physical characteristics and the vibration frequency; wherein the equivalent physical characteristic parameters at least include an equivalent elastic modulus, an equivalent dynamic density, an equivalent dynamic Poisson's ratio, and a dynamic Rayleigh damping;

[0072] S103, based on the equivalent physical characteristic parameters, obtain a theoretical transmission loss value of the particle damping phononic crystal structure through Fourier transformation calculation.

[0073] The present invention provides a method for constructing an equivalent theoretical model based on a particle damping phononic crystal structure, which obtains equivalent physical characteristic parameters such as an equivalent elastic modulus, an equivalent dynamic damping ratio coefficient, an equivalent dynamic density, and an equivalent dynamic Poisson's ratio of the particle damping phononic crystal structure. Among them, the equivalent elastic modulus can be equivalent to the elastic modulus of the particle damping phononic crystal structure, the equivalent dynamic density can be equivalent to the dynamic density of the particle damping phononic crystal structure, the equivalent dynamic Poisson's ratio can be equivalent to the dynamic Poisson's ratio of the particle damping phononic crystal structure, and the dynamic Rayleigh damping can be equivalent to the energy consumption generated by the collision of the damping particles 22. Then, the theoretical transmission loss value is finally calculated through these equivalent physical characteristic parameters. After measurement, the theoretical transmission loss value obtained by the present invention has a high consistency with the actual measured transmission loss value, which proves that the equivalent theoretical model construction method provided by the present invention can provide a new research paradigm for the research on the use of particle damping technology in the field of vibration.

[0074] As a further optimization, based on the physical characteristics and vibration frequency, constructing equivalent physical characteristic parameters of the particle damped phononic crystal structure includes the following steps:

[0075] The equivalent dynamic elastic modulus E d (f) satisfies the relationship with the vibration frequency f as follows:

[0076]

[0077] In formula (1), are the polynomial coefficients, is a constant; wherein the polynomial coefficients and constants are fitted based on experimental comparison data.

[0078] The equivalent dynamic density satisfies the following relationship:

[0079]

[0080] In formula (2), ρ d is the equivalent dynamic density, ρ sta is the static mass density, m to is the overall mass of the damping particles 22, and V is the volume of the housing 21;

[0081] The relationship between the dynamic Rayleigh damping C(f) and the vibration frequency satisfies the following relationship:

[0082] C d (f) = α(f)[M] + β(f)[K] (3)

[0083] In formula (3), α, β are functions related to vibration frequency, stiffness matrix [K], and mass matrix [M];

[0084] in,

[0085] α(f)=ξ1f 6 +ξ2f 5 +ξ3f 4 +ξ4f 3 +ξ5f 2 +ξ6f+ξ (4)

[0086]

[0087] In formula (4) and formula (5), ξ1, ξ2, ξ3, ξ4, ξ5, ξ6 are polynomial coefficients; ξ, ζ are constants, wherein the polynomial coefficients and constants are obtained by fitting based on experimental comparison data.

[0088] The equivalent dynamic Poisson's ratio ν satisfies the following relationship under a certain external pressure static equilibrium state:

[0089]

[0090] In formula (6), λ = k c-t / k n-e , k c-t is the tangential stiffness of the damping particle 22 unit, k n-e is the normal stiffness of the damping particle 22 unit;

[0091] in,

[0092]

[0093] In formula (7), E is the Young's modulus of the material of the damping particles 22, νp is the Poisson's ratio of the material of the damping particle 22, R is the spherical radius of the damping particle 22, and m is the mass of the damping particle 22;

[0094]

[0095] In formula (8), δ is the overlap between the damping particles 22, and A is the dissipation coefficient, which is approximately 0.7071.

[0096] As a further optimization, based on the equivalent physical characteristic parameters, the theoretical transmission loss value of the particle damping phononic crystal structure is obtained by Fourier transform calculation, specifically including:

[0097] In an infinite periodic structure, the undamped equation satisfies the following relationship:

[0098] ([K]-ω2 [M]){U}=0 (9)

[0099] In formula (9), [K] is the stiffness matrix, [M] is the mass matrix, and ω is the natural frequency of the particle damped crystal structure;

[0100] in,

[0101]

[0102]

[0103] In formulas (10) and (11), [K] ela is the elastic material stiffness matrix, [K] d is the equivalent particle damping stiffness matrix, e -ika [K] d is the periodic conditional stiffness matrix, [M] ela is the mass matrix of the elastomer material, [M] d is the equivalent particle damping mass matrix.

[0104] According to the frequency-dependent Rayleigh damping [C] = α(f)[M] in a finite period structure d +β(f)[K] d , after discretization by finite element method, the matrix equation is as follows:

[0105]

[0106] That is:

[0107] ([K] ela +[K] d )-ω 2 ([M] ela +[M] d ){U}={P} (13)

[0108] In formulas (12) and (13), is the acceleration matrix, is the velocity matrix, {U} is the displacement matrix, and {P} is the external excitation force.

[0109] Taking frequency as the independent variable, the time history of excitation and response is converted into frequency amplitude through Fourier transform. The vibration transmission spectrum of the finite structure is obtained through the amplitude ratio of response and excitation at the same frequency, which satisfies the following relationship:

[0110]

[0111] In formula (14), T is the transmission loss, w out and w inIt can be obtained from the external exciting array force {P}, w out is the output response, w in For input excitation.

[0112] Example 1

[0113] This embodiment provides a particle damping phononic crystal structure, the structure of which is as follows: Figure 1 As shown, it includes a base layer 10 aluminum plate, a damper 20 aluminum alloy shell 21 and steel damping particles 22.

[0114] Wherein, the thickness of the aluminum plate of the base layer 10 is h s =1mm, the height of the damper 20 aluminum alloy housing 21 is d S =32.5mm, the outer diameter of the aluminum alloy shell 21 of the damper 20 is D=23.6mm, the inner diameter of the aluminum alloy shell 21 of the damper 20 is d=18mm, the interior is filled with 2mm steel, spherical damping particles 22, the filling rate is 100%, and the length between the centers of two adjacent damper circles is a=38mm, then the ratio of the contact area between the damper 20 and the base layer 10 to the connection surface of the base layer 10 is f=π(D / 2) 2 / a 2 =0.268.

[0115] Example 2

[0116] This embodiment provides a method for constructing an equivalent theoretical model based on a particle-damped phononic crystal structure. The particle-damped phononic crystal structure in this embodiment is the particle-damped phononic crystal structure provided in Embodiment 1.

[0117] First, according to formulas (1) to (8), the following parameters can be obtained:

[0118] The relationship between the equivalent elastic modulus E and the frequency f is expressed by the following formula, and the relationship diagram is as follows: Figure 3 As shown in a:

[0119] E d (f) = 9 × 10 -8 f 4 -0.0004f 3 +0.4583f 2 -129.71f+415129

[0120] The relationship between the equivalent Rayleigh damping coefficient α and the frequency f is expressed by the following formula, and its approximate relationship diagram is as follows: Figure 3 As shown in b:

[0121] α(f)=-1.763×10 -14 f 6 +4.974×10 -11 f5 -5.52×10 -8 f 4 +3×10 -5 f 3 -7.92×10 -3 f 2 +0.6862f+113.3

[0122] The equivalent Rayleigh damping β coefficient and frequency f are expressed by the following formula, and the approximate relationship diagram is as follows: Figure 3 c:

[0123] β(f)=10 -9 f+0.65×10 -7

[0124] The equivalent dynamic Poisson's ratio is ν d ≈0.247; the equivalent dynamic mass is ρ d ≈5050kg / m 3 .

[0125] Finally, according to the above results and formulas (9) to (14), the finite structure transmission frequency response function curve is obtained. The results are as follows: Figure 3 As shown in Figure d, we can see that the transmission loss value obtained by the equivalent physical characteristic parameters calculated by the present invention is highly consistent with the transmission loss value obtained by actual measurement at the vibration frequency of 0 to 500 Hz, proving that the equivalent theoretical model construction method provided by the present invention can provide a new research paradigm for the research on the application of particle damping technology in the field of vibration. In addition, the increase in its transmission loss further proves that the particle damping phononic crystal structure provided by the present invention has excellent medium and low vibration reduction characteristics, extremely wide band gap characteristics, and also has vibration reduction characteristics in the full frequency domain of medium and low frequencies.

[0126] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for constructing an equivalent theoretical model of a particle damped phononic crystal structure, characterized in that: The particle damped phononic crystal structure comprises at least one layer of damping structure, and the damping structure comprises a base layer and a damper; A plurality of the dampers are fixedly arranged on the substrate layer and arranged in an orderly manner; the damper comprises an outer shell and damping particles filled in the inner cavity of the outer shell; a side of the substrate layer in one damping structure away from the damper is connected to a side of the damper in another damping structure that is not fixed to the substrate layer; the method for constructing an equivalent theoretical model of the particle damping phononic crystal structure is used to obtain equivalent physical characteristic parameters of the particle damping phononic crystal structure, and the method for constructing an equivalent theoretical model of the particle damping phononic crystal structure comprises the following steps: S101, obtaining physical characteristics of the particle damping phononic crystal structure; wherein the physical characteristics at least include the overall mass of the damping particles, the volume of the shell, the Young's modulus of the damping particle material, the Poisson's ratio of the damping particle material, the spherical radius of the damping particles, the mass of the damping particles, and the overlap between the damping particles; S102. Based on the physical characteristics and vibration frequency, construct equivalent physical characteristic parameters of the particle damping phononic crystal structure; wherein the equivalent physical characteristic parameters at least include equivalent elastic modulus, equivalent dynamic density, equivalent dynamic Poisson's ratio and dynamic Rayleigh damping; wherein the equivalent elastic modulus may be equivalent to the elastic modulus of the particle damping phononic crystal structure, the equivalent dynamic density may be equivalent to the dynamic density of the particle damping phononic crystal structure, the equivalent dynamic Poisson's ratio may be equivalent to the dynamic Poisson's ratio of the particle damping phononic crystal structure, and the dynamic Rayleigh damping may be equivalent to the energy consumption generated by the collision of the damping particles; S103. Based on the equivalent physical characteristic parameters, obtain the theoretical transmission loss value of the particle damping phononic crystal structure through Fourier transformation calculation, and measure the consistency between the theoretical transmission loss value and the actual measured transmission loss value.

2. The method for constructing an equivalent theoretical model of a particle damped phononic crystal structure according to claim 1, characterized in that: The filling rate of the damping particles of the damper is 10%-100%.

3. The method for constructing an equivalent theoretical model of a particle damped phononic crystal structure according to claim 1, characterized in that: The density of the damping particles is 1.2 g / cm 3 ~18.3g / cm 3 , the longest diameter is 0.1mm~12mm, the surface friction factor is 0.02~0.99, and the surface recovery coefficient is 0.1~1.

4. The method for constructing an equivalent theoretical model of a particle damped phononic crystal structure according to claim 1, characterized in that: The damper is cylindrical.

5. The method for constructing an equivalent theoretical model of a particle damped phononic crystal structure according to claim 4, characterized in that: The ratio of the contact area between the damper and the base layer to the connection area between the base layer and the damper satisfies the following relationship: Wherein, D is the outer diameter of the damper, a is the distance between the centers of two adjacent dampers, and f is the ratio of the contact area to the connection surface area.

6. The method for constructing an equivalent theoretical model of a particle damped phononic crystal structure according to claim 1, characterized in that: The damping particles are made of steel, glass or ceramic.

7. The method for constructing an equivalent theoretical model of a particle damped phononic crystal structure according to claim 1, characterized in that: The material of the base layer is steel, aluminum, carbon fiber or glass.

8. The method for constructing an equivalent theoretical model of a particle damped phononic crystal structure according to claim 1, characterized in that: The shell is made of steel or aluminum.

9. The method for constructing an equivalent theoretical model of a particle damped phononic crystal structure according to claim 1, characterized in that: Based on the physical characteristics and vibration frequency, constructing equivalent physical characteristic parameters of the particle damped phononic crystal structure comprises the following steps: The equivalent elastic modulus E d (f) satisfies the relationship with the vibration frequency f as follows: In formula (1), are the polynomial coefficients, is a constant; The equivalent dynamic density satisfies the following relationship: In formula (2), ρ d is the equivalent dynamic density, ρ sta is the static mass density, m to is the overall mass of the damping particles, and V is the volume of the shell; The relationship between the dynamic Rayleigh damping C(f) and the vibration frequency satisfies the following relationship: C d (f)=α(f)[M]+β(f)[K] (3) In formula (3), α, β are functions related to vibration frequency, stiffness matrix [K], and mass matrix [M]; in, α(f)=ξ1f 6 +ξ2f 5 +ξ3f 4 +ξ4f 3 +ξ5f 2 +ξ6f+ξ (4) In formula (4) and formula (5), ξ1, ξ2, ξ3, ξ4, ξ5, ξ6 are polynomial coefficients; ξ, ζ are constants; The equivalent dynamic Poisson's ratio ν satisfies the following relationship under a certain external pressure static equilibrium state: In formula (6), λ = k c-t / k n-e , k c-t is the tangential stiffness of the damping particle unit, k n-e is the normal stiffness of the damping particle element; in, In formula (7), E is the Young's modulus of the damping particle material, ν p is the Poisson's ratio of the damping particle material, R is the sphere radius of the damping particle, and m is the mass of the damping particle; In formula (8), δ is the overlap between the damping particles, and A is the dissipation coefficient, which is approximately 0.7071.

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