Composite phononic crystal mechanism and sound insulation frequency band regulation method

Abstract

The application discloses a kind of composite phononic crystal mechanism and sound insulation frequency band regulation and control method, mechanism includes composite phononic crystal unit cell, composite phononic crystal unit cell includes base material, scatterer and oscillator, scatterer is cylindrical metal material, inlay in the middle of base material, oscillator is cylindrical, set in the four around of scatterer;Method includes selecting material parameter and known geometry parameter base material, scatterer and oscillator, establish the new bending vibration equation of substrate, according to classic laminated plate theory, obtain the equivalent of the density, bending stiffness of oscillator and the base material with the same area of the bottom of oscillator, by equivalent medium method, obtain the equivalent density and equivalent bending stiffness of oscillator and base material, by improved plane wave expansion method, combined with new bending vibration equation, the band gap of composite phononic crystal is solved, adjust known material parameters and geometric parameters, so that the band gap of composite phononic crystal is consistent with target sound insulation frequency band;The band gap of the application is wide, effectively realizes the sound insulation effect in low frequency band.

Description

Technical Field

[0001] This invention relates to the technical field of acoustic sound insulation materials, and in particular to a composite phonon crystal structure and a method for controlling the sound insulation frequency band. Background Technology

[0002] Phononic crystals, proposed in analogy to photonic crystals, are formed by combining two or more elastic materials in a periodic structure. Because elastic waves propagate within a periodic elastic structure, a specific dispersion relation is generated; the frequency range of this dispersion relation is called a bandgap. Similar to the bandgap in photonic crystals, the bandgap in phononic crystals can suppress the propagation of elastic waves, effectively creating a sound-insulating bandgap.

[0003] To address the noise reduction problem of multiple noise peaks existing simultaneously in the low, mid, and high frequency ranges during equipment operation, and considering that ordinary phononic crystals have narrow band gaps, are difficult to shift, and have poor sound insulation performance in the low and mid frequency ranges, this invention proposes a composite phononic crystal structure and a sound insulation frequency band control method, which uses an improved plane wave expansion method for sound insulation control. Summary of the Invention

[0004] The purpose of this section is to outline some aspects of embodiments of the present invention and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents; however, such simplifications or omissions should not be construed as limiting the scope of the invention.

[0005] In view of the problems of existing phononic crystals, such as narrow band gap, difficulty in shifting, and poor sound insulation effect in the high-frequency band, the present invention is proposed.

[0006] Therefore, the purpose of this invention is to provide a composite phononic crystal mechanism and a sound insulation frequency band control method. The purpose is to achieve effective sound insulation by using an improved plane wave expansion method on the composite phononic crystal mechanism to control the sound insulation of multiple target frequency bands according to the different noise reduction requirements of different products in different fields.

[0007] To solve the above-mentioned technical problems, the present invention provides the following technical solution: including a composite phononic crystal unit cell 100, wherein the composite phononic crystal unit cell 100 is periodically connected in series to form a composite phononic crystal structure;

[0008] The composite phononic crystal unit cell 100 includes a substrate 101, a scatterer 102, and four oscillators 103. The substrate 101 is made of square rubber material; the scatterer 102 is made of cylindrical metal material and is embedded in the middle of the substrate 101; the oscillators 103 are cylindrical and are disposed around the scatterer 102 and are fixedly connected to the top surface of the substrate 101.

[0009] As a preferred embodiment of the composite phonon crystal mechanism of the present invention, the scatterer 102 is made of a metal material with a density, elastic modulus, and shear modulus that are all much greater than those of rubber material, and the oscillator 103 is made of a metal material with a density, elastic modulus, and shear modulus that are even greater than those of the scatterer 102 material.

[0010] In a preferred embodiment of the composite phonon crystal mechanism of the present invention, the radius of the scatterer 102 is greater than the radius of the oscillator 103, and the thickness of the scatterer 102 is equal to that of the substrate 101.

[0011] As a preferred embodiment of the sound insulation frequency band control method of the present invention, the method includes the following specific steps: selecting a substrate, a scatterer, and an oscillator with known material and geometric parameters; obtaining a new bending vibration equation for the substrate by considering the rotational inertia and shear deformation of the composite phonon crystal structure, and inputting the material and geometric parameters of the substrate and the scatterer; obtaining the equivalent density and bending stiffness of the oscillator and the substrate with the same area as the bottom of the oscillator according to classical laminate theory, and inputting the material and geometric parameters of the oscillator; obtaining the equivalent density and equivalent bending stiffness of the oscillator and the substrate through the equivalent medium method; obtaining the Fourier series expansion of each parameter by using the improved plane wave expansion method, and solving the matrix eigenvalues ​​by combining the new bending vibration equation to obtain the band gap of the composite phonon crystal; adjusting the material and geometric parameters of the substrate, the scatterer, and the oscillator to make the band gap of the composite phonon crystal consistent with the target sound insulation frequency band.

[0012] As a preferred embodiment of the sound insulation frequency band control method of the present invention, the material parameters include the material type, density, elastic modulus and shear modulus; the geometric parameters include the side length of the unit cell, the radius of the scatterer, the thickness of the substrate and the scatterer, the radius of the oscillator and the thickness of the oscillator.

[0013] As a preferred embodiment of the sound insulation frequency band control method of the present invention, the bending vibration equation is as follows:

[0014]

[0015] In the formula, ρ represents the density of the substrate; ω represents the frequency; D=Eh 3 / 12(1-v 2 ) represents the bending stiffness, where E represents the elastic modulus; h represents the thickness of the substrate and the scatterer; μ is the shear modulus; κ = 5 / 6 is the shear coefficient; and J = h 3 / 12 represents the moment of inertia; x and y represent a rectangular coordinate system with a right angle as the origin, and the two directions of the coordinate system are the x and y directions, respectively; t represents time.

[0016] The simplified calculation yields the following new bending vibration equation:

[0017]

[0018] In the formula, let γ1=ρh.

[0019] As a preferred embodiment of the sound insulation frequency band control method described in this invention, the equivalent formulas for density and bending stiffness are:

[0020] ρ aeq =ρ z +ρ b

[0021]

[0022] In the formula, E b E z v represents the elastic modulus of the substrate and the oscillator. b v z ρ represents the Poisson's ratio of the substrate and the oscillator. b ρ z For the density of the substrate and the oscillator, h and h z The thickness of the substrate and the oscillator.

[0023] As a preferred embodiment of the sound insulation frequency band control method of the present invention, the equivalent density and equivalent bending stiffness of the oscillator and the substrate are:

[0024] ρ eq =ρ a P f2 +ρ b (1-P f2 )

[0025]

[0026] In the formula, P f2 P represents the ratio of the oscillator area to the substrate area. f3 This represents the ratio of the area of ​​the oscillator to the area of ​​the square region containing the oscillator.

[0027] As a preferred embodiment of the sound insulation frequency band control method of the present invention, the Fourier series expansion is shown below, and each parameter, including density, elastic modulus, and shear modulus, is represented by f:

[0028]

[0029] In the formula, f eq Represents the equivalent parameters of the substrate and oscillator;

[0030] The new bending vibration equation is then used to obtain:

[0031] ω 4∑ G′ β1(G″-G′)w k (G′)-ω 2 ∑ G′ [-α1(G″-G′)((k+G′) x ·(k+G″) x +(k+G′) y ·(k+G″) y )-γ1(G″-G′)]w k (G′)+∑ G′ [D(G″-G′)*((k+G′) x ·(k+G″) x +(k+G′) y ·(k+G″) y ) 2 ]w k (G′)=0

[0032] Since the above formula contains ω 4 and ω 2 The band gap of a composite phononic crystal cannot be directly calculated from the given formula; it needs to be processed into the following equation:

[0033] m 2 AY-mBY+CY=0;

[0034] Where m=ω 2 Y = w k (G′), A=β 1 (G″-G′),

[0035] B=[-α1(G″-G′)((k+G′) x ·( k +G″) x +(k+G′) v ·(k+G″) v )-γ1(G″-G′)],

[0036] C = [D(G″-G′)((k+G′)] x ·(k+G″) x +(k+G′)v·(k+G″) v ) 2 ];

[0037] Let X = mY, then the formula for solving the matrix eigenvalues ​​is as follows:

[0038]

[0039] By using the improved plane wave expansion method, N reciprocal lattice vectors are taken in the reciprocal lattice vector space for calculation, and the Fourier series expansion of each parameter is obtained. Combined with the new bending vibration equation, the above equation is transformed into solving the eigenvalues ​​of a 2N*2N order matrix, and the band gap of the acoustic metamaterial of the oscillator containing phononic crystal is obtained, that is, the band gap of the composite phononic crystal.

[0040] As a preferred embodiment of the sound insulation frequency band control method of the present invention, the material size parameters of the substrate, scatterer and oscillator are adjusted according to the parameters of the target sound insulation frequency band, and the operation is repeated until the band gap of the composite phonon crystal is consistent with the target sound insulation frequency band.

[0041] The beneficial effects of this invention are as follows: By adding an oscillator to a traditional phononic crystal, a composite phononic crystal structure is obtained. An improved plane wave expansion method is used on the composite phononic crystal structure to control the sound insulation of multiple target frequency bands according to the different noise reduction requirements of different products in different fields, thereby achieving effective sound insulation. Attached Figure Description

[0042] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0043] Figure 1 This is a schematic diagram of the overall structure of the composite phonon crystal mechanism of the present invention.

[0044] Figure 2 This is a schematic diagram of the unit cell structure of the composite phononic crystal mechanism of the present invention.

[0045] Figure 3 This is a diagram showing the noise frequency band situation of the sound insulation frequency band control method of the present invention.

[0046] Figure 4 This is a flowchart of the sound insulation frequency band control method of the present invention.

[0047] Figure 5 This is a schematic diagram of the band gap of a common phononic crystal structure in the sound insulation frequency band control method of the present invention.

[0048] Figure 6 This is a schematic diagram of the bandgap of the composite phonon crystal mechanism in the sound insulation frequency band control method of the present invention. Detailed Implementation

[0049] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0050] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0051] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0052] Secondly, the present invention is described in detail with reference to the schematic diagrams. When detailing the embodiments of the present invention, for ease of explanation, the cross-sectional views illustrating the device structure may be partially enlarged, not according to the usual scale. Furthermore, the schematic diagrams are merely examples and should not limit the scope of protection of the present invention. In addition, actual fabrication should include three-dimensional spatial dimensions of length, width, and depth.

[0053] Example 1

[0054] Reference Figures 1-2 The first embodiment of the present invention provides a composite phononic crystal mechanism, which includes a composite phononic crystal unit cell 100, which are periodically connected in series to form the composite phononic crystal mechanism.

[0055] The composite phononic crystal unit cell 100 includes a substrate 101, a scatterer 102, and four oscillators 103. The substrate 101 is made of square rubber material; the scatterer 102 is made of cylindrical metal material and is embedded in the middle of the substrate 101; the oscillators 103 are cylindrical and are disposed around the scatterer 102 and are fixedly connected to the top surface of the substrate 101.

[0056] The scatterer 102 is made of a metal material with a density, elastic modulus, and shear modulus that are much greater than those of rubber material. The oscillator 103 is made of a metal material with a density, elastic modulus, and shear modulus that are even greater than those of the scatterer 102. The radius of the scatterer 102 is greater than the radius of the oscillator 103. The thickness of the scatterer 102 is the same as that of the substrate 101.

[0057] During use, by adding an oscillator to a regular phononic crystal to widen its band gap, the sound insulation effect in the high-frequency band can be improved.

[0058] Example 2

[0059] Reference Figure 4 This is the second embodiment of the present invention, which differs from the first embodiment in that it provides a method for controlling the sound insulation frequency band, the specific steps of which are as follows:

[0060] S1, select a substrate, scatterer and oscillator whose material parameters and geometric parameters are known.

[0061] Material parameters include the material type, density, elastic modulus, and shear modulus; geometric parameters include the side length of the unit cell, the radius of the scatterer, the thickness of the substrate and the scatterer, the radius of the oscillator, and the thickness of the oscillator.

[0062] S2, by considering the rotational inertia and shear deformation of the composite phonon crystal mechanism, obtains a new bending vibration equation for the substrate, with the material and geometric parameters of the substrate and the scatterer as input.

[0063] The equation for bending vibration is as follows:

[0064]

[0065] In the formula, ρ represents the density of the substrate; ω represents the frequency; D=Eh 3 / 12(1-v 2 ) represents the bending stiffness, where E represents the elastic modulus; h represents the thickness of the substrate and the scatterer; μ is the shear modulus; κ = 5 / 6 is the shear coefficient; and J = h 3 / 12 represents the moment of inertia; x and y represent a rectangular coordinate system with a right angle as the origin, and the two directions of the coordinate system are the x and y directions, respectively; t represents time.

[0066] The simplified calculation yields the following new bending vibration equation:

[0067]

[0068] In the formula, let γ1=ρh.

[0069] S3, based on classical laminate theory, obtains the equivalent density and bending stiffness of the oscillator and the substrate with the same area as the bottom of the oscillator, and inputs the material and geometric parameters of the oscillator.

[0070] The equivalent formulas for density and bending stiffness are:

[0071] ρ aeq =ρ z +ρ b

[0072]

[0073] In the formula, E b E z v represents the elastic modulus of the substrate and the oscillator. b v z ρ represents the Poisson's ratio of the substrate and the oscillator. b ρ z For the density of the substrate and the oscillator, h and h zThe thickness of the substrate and the oscillator.

[0074] S4. The equivalent density and equivalent bending stiffness of the oscillator and the substrate are obtained by using the equivalent medium method.

[0075] The equivalent density and equivalent bending stiffness of the oscillator and the substrate are:

[0076] ρ eq =ρ a P f2 +ρ b (1-P f2 )

[0077]

[0078] In the formula, P f2 P represents the ratio of the oscillator area to the substrate area. f3 This represents the ratio of the area of ​​the oscillator to the area of ​​the square region containing the oscillator.

[0079] S5. The equivalent density and equivalent bending stiffness are obtained by using the improved plane wave expansion method to obtain the Fourier series expansion of each parameter. Combined with the new bending vibration equation, the matrix eigenvalues ​​are solved to obtain the band gap of the composite phonon crystal.

[0080] The Fourier series expansion is shown below, where all parameters, including density, elastic modulus, and shear modulus, are represented by f:

[0081]

[0082] In the formula, f eq Represents the equivalent parameters of the substrate and oscillator;

[0083] The new bending vibration equation is then used to obtain:

[0084] ω 4 ∑ G′ β1(G″-G′)w k (G′)-ω 2 ∑ G ′[-α1(G″-G′)((k+G′) x ·(k+G″) x +(k+G′) y ·(k+G″) y )-γ1(G″-G′)]w k (G′)+∑ G′ [D(G″-G′)*((k+G′) x ·(k+G″) x +(k+G′) y ·(k+G″) y ) 2 ]wk (G′)=0

[0085] Since the above formula contains ω 4 and ω 2 The band gap of a composite phononic crystal cannot be directly calculated from the given formula; it needs to be processed into the following equation:

[0086] m 2 AY-mBY+CY=0;

[0087] Where m=ω 2 Y = w k (G′), A=β1(G″-G′),

[0088] B=[-α1(G″-G′)((k+G′) x ·(k+G″) x +(k+G′) v ·((k+G″) v )-γ1(G″-G′)],

[0089] C = [D(G″-G′)((k+G′)] x ·(k+G″) x +(k+G′)v·(k+G″) v ) 2 ];

[0090] Let X = mY, then the formula for solving the matrix eigenvalues ​​is as follows:

[0091]

[0092] By using the improved plane wave expansion method, N reciprocal lattice vectors are taken in the reciprocal lattice space for calculation, and the Fourier series expansion of each parameter is obtained. Then, combined with the new bending vibration equation, an equation is obtained. The equation is transformed into solving the eigenvalues ​​of a 2N*2N order matrix, and the band gap of the acoustic metamaterial of the phononic crystal is obtained, that is, the band gap of the composite phononic crystal.

[0093] S6 adjusts the material and geometric parameters of the substrate, scatterer, and oscillator to make the band gap of the composite phonon crystal consistent with the target sound insulation frequency band.

[0094] The material dimensions of the substrate, scatterer, and oscillator are adjusted according to the parameters of the target sound insulation frequency band, and the operation is repeated until the band gap of the composite phonon crystal matches the target sound insulation frequency band.

[0095] In summary, by using the improved plane wave expansion method in the mechanism of this invention, sound insulation control is applied to multiple target frequency bands according to the different noise reduction requirements of different products in different fields, thereby achieving effective sound insulation.

[0096] Example 3

[0097] Reference Figures 1-6 This is the third embodiment of the present invention, which differs from the second embodiment in that it targets the sound insulation requirements of a certain compressor, such as... Figure 3 As shown, the main noise frequency band of the compressor is 1000-5000Hz, specifically distributed in the frequency bands of 60-300Hz, 600-800Hz, 1250-1450Hz, and 2100-3200Hz. These frequency bands contain noise peaks generated by vibration, which are used as the target frequency bands.

[0098] The geometric parameters of the substrate, scatterer, and oscillator selected in this invention are as follows: unit cell lattice side length a = 0.02 m, scatterer radius r = 0.008 m, substrate and scatterer thickness h = 0.002 m, and oscillator radius r z =0.002m, thickness h z =0.002m.

[0099] The material parameters of the substrate, scatterer, and oscillator selected in this invention are as follows: the scatterer material is lead, with a density ρ a =11600kg / m 3 Elastic modulus E a =4.08×10 10 Pa, shear modulus μ a =1.49×10 10 Pa; The base material is nitrile rubber, with a density ρ. b =1300kg / m 3 Elastic modulus E b =1.175×10 7 Pa, shear modulus μ b =4×10 6 Pa, the oscillator material is tungsten, density ρ z =19100kg / m 3 Elastic modulus E z =35.41×10 10 Pa.

[0100] To verify the superiority of the acoustic metamaterial structure containing a phononic crystal of the present invention, the bandgap of a conventional phononic crystal of the same size with lead as the scatterer and nitrile rubber as the matrix material was calculated. Since elastic waves propagate within a periodic elastic structure and exhibit specific dispersion relations, the frequency range between these dispersion relations is called the bandgap. The bandgap can suppress the propagation of elastic waves. Therefore, by using a suitable phononic crystal, its bandgap range can be made to correspond to the noise frequency, achieving the desired noise reduction effect.

[0101] like Figure 5 and Figure 6As shown, the horizontal axis represents frequency, and the vertical axis represents the direction of the Brillouin zone composed of TXMs (Tube, Trough, Mesh, and Scale). This corresponds to the two-dimensional plane coordinate direction, where TXM points are points in several special reciprocal lattice spaces. The curves represent stable acoustic modes. The frequency bands through which no curve passes, i.e., the dark and gray regions, represent band gaps. The dark regions are complete band gaps, and the gray regions are directional band gaps.

[0102] Figure 5 The diagram shown is a bandgap result for a conventional phononic crystal consisting only of a substrate and a scatterer, while the bandgap result of the present invention is for a composite phononic crystal structure. Figure 6 As shown.

[0103] from Figure 5 , 6 It is not difficult to find that both ordinary phononic crystals and composite phononic crystal structures have a complete bandgap above 3000Hz, as shown in the dark-covered area in the figure, which has good high-frequency sound insulation performance.

[0104] However, the composite phonon crystal mechanism of the present invention has multiple directional band gaps and one complete band gap in the mid-to-low frequency band. Specifically, in the XM direction, there are directional band gaps of 0Hz-329Hz and 1250Hz-3092Hz; in the TX direction, there are directional band gaps of 329Hz-1178Hz and 1600Hz-3224Hz; and there is a complete band gap of 3460Hz-5453Hz.

[0105] Ordinary phononic crystals, such as Figure 5 There are two directional band gaps and two complete band gaps, namely 0Hz-775Hz in the XM direction, 2015Hz-2652Hz in the MT direction, and the frequency range of the complete band gaps is 2652Hz-3139Hz and 3353Hz-5046Hz.

[0106] Therefore, the composite phonon crystal mechanism of the present invention exhibits superior sound insulation performance in the required target sound insulation frequency bands of 60-300Hz, 600-800Hz, 1250-1450Hz and 2100-3200Hz.

[0107] In summary, the composite phononic crystal mechanism and sound insulation frequency band control method of the present invention exhibit more accurate sound insulation band gaps and has more band gaps than ordinary phononic crystals for the needs of multiple sound insulation frequency bands, indicating that the mechanism and method of the present invention are more suitable for broadband sound insulation.

[0108] 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 it. 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 spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A composite phonon crystal mechanism, characterized in that: include, A composite phononic crystal unit cell (100) is formed by periodically connecting the composite phononic crystal unit cells (100) to form a composite phononic crystal structure; The composite phonon crystal unit cell (100) includes a substrate (101), a scatterer (102), and four oscillators (103). The substrate (101) is made of square rubber; the scatterer (102) is made of cylindrical metal and is embedded in the center of the substrate (101); the oscillators (103) are cylindrical and are disposed around the scatterer (102), and are fixedly connected to the top surface of the substrate (101). The scatterer (102) is made of a metal material with a density, elastic modulus, and shear modulus that are all much greater than those of rubber material, and the oscillator (103) is made of a metal material with a density, elastic modulus, and shear modulus that are even greater than those of the scatterer (102). The radius of the scatterer (102) is greater than the radius of the oscillator (103), and the thickness of the scatterer (102) is the same as that of the substrate (101).

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