Method for determining sound reduction index of film type acoustic metamaterial

Abstract

The invention discloses a method for determining the sound reduction index of a film type acoustic metamaterial, and the method comprises the steps: 1, constructing a film type acoustic metamaterial model, and defining a coordinate system of the film type acoustic metamaterial model; 2, listing a transverse displacement calculation formula of the thin film bearing simple harmonic excitation; 3, listing a modal amplitude coefficient calculation formula of the thin film bearing simple harmonic excitation; 4, listing a speed potential calculation formula of the thin film bearing simple harmonic excitation; 5, constructing a vibration control equation of the thin film bearing simple harmonic excitation; step 6, substituting the transverse displacement of the thin film bearing simple harmonic excitation, the modal amplitude coefficient and the speed potential calculation formula into the vibration control equation to obtain a modal participation factor coefficient; step 7, calculating the transverse displacement, modal amplitude coefficient and speed potential of the thin film bearing harmonic excitation according to the modal participation factor coefficient of the thin film, and further calculating the equivalent surface density of the thin film; 8, calculating a sound energy transmission coefficient according to the equivalent surface density of the film; and 9, calculating the sound insulation index according to the sound energy transmission coefficient of the film.

Description

Technical Field

[0001] The present application belongs to the technical field of thin-film acoustic metamaterial design, and specifically relates to a method for determining the sound insulation value of a thin-film acoustic metamaterial. Background Art

[0002] Film-type acoustic metamaterials are used on aircraft for noise control. Compared with traditional homogeneous noise reduction materials, acoustic metamaterials are a special form of acoustic structure. Sound insulation is a key parameter in the design of film-type acoustic metamaterials.

[0003] Currently, the finite element method is mostly used to solve the sound insulation of thin-film acoustic metamaterials. During the finite element calculation, the selection of model element types, grid size and boundary conditions all have an impact on the calculation results. It is time-consuming and laborious, and it is difficult to obtain accurate results. It is difficult to provide effective support for the rapid design and improvement of thin-film acoustic metamaterials.

[0004] This application is proposed in view of the above-mentioned technical defects. Summary of the invention

[0005] The purpose of the present application is to provide a method for determining the sound insulation value of a thin-film acoustic metamaterial, so as to overcome or alleviate at least one of the technical defects of the known ones.

[0006] The technical solution of this application is:

[0007] A method for determining the sound insulation value of a thin film acoustic metamaterial, comprising:

[0008] Step 1: construct a thin film acoustic metamaterial model and define a coordinate system of the thin film acoustic metamaterial model;

[0009] Step 2: List the calculation formula for the lateral displacement of the film under simple harmonic excitation;

[0010] Step 3: List the calculation formula of the modal amplitude coefficient of the film subjected to simple harmonic excitation;

[0011] Step 4: List the velocity potential calculation formula for the film subjected to simple harmonic excitation;

[0012] Step 5: construct the vibration control equation of the film under simple harmonic excitation;

[0013] Step 6: Substitute the lateral displacement, modal amplitude coefficient, and velocity potential calculation formula of the film subjected to simple harmonic excitation into the vibration control equation to obtain the modal participation factor coefficient;

[0014] Step 7: Using the modal participation factor coefficient of the film, calculate the lateral displacement, modal amplitude coefficient, and velocity potential of the film under simple harmonic excitation, and then calculate the equivalent surface density of the film;

[0015] Step 8: Calculate the acoustic energy transmission coefficient based on the equivalent surface density of the film;

[0016] Step 9. Calculate the sound insulation value based on the sound energy transmission coefficient of the film.

[0017] Optionally, in the above-mentioned method for determining the sound insulation value of a thin film acoustic metamaterial, in step 1, a thin film acoustic metamaterial model is constructed, including a rectangular thin film and a plurality of circular mass blocks located on the thin film.

[0018] Optionally, in the above-mentioned method for determining the sound insulation value of the thin film type acoustic metamaterial, in step one, a coordinate system of the thin film type acoustic metamaterial model is defined, where the x-axis is along the length direction of the rectangular film, the y-axis is along the width direction of the rectangular film, and the z-axis is perpendicular to the rectangular film, conforming to the right-handed coordinate system.

[0019] Optionally, in the above-mentioned method for determining the sound insulation value of the film-type acoustic metamaterial, in step 2, a calculation formula for the lateral displacement of the film subjected to simple harmonic excitation is listed, specifically:

[0020]

[0021] in,

[0022] w(x,y,t) is the lateral displacement of the film, along the z direction;

[0023] m is the order of the film mode shape in the x-axis direction;

[0024] n is the order of the film mode shape in the y-axis direction;

[0025] ψ mn (x,y) is the vibration mode function of the film;

[0026] q mn (t) is the modal participation factor of the film.

[0027] Optionally, in the above method for determining the sound insulation value of a thin film acoustic metamaterial, step 2 includes:

[0028]

[0029] q mn (t) = A mn e jωt ;

[0030] in,

[0031] A mn is the modal participation factor coefficient of the film;

[0032] ω is the circular frequency of simple harmonic excitation;

[0033] j is the imaginary part.

[0034] Optionally, in the above-mentioned method for determining the sound insulation value of the film-type acoustic metamaterial, in step 3, a calculation formula for the modal amplitude coefficient of the film subjected to simple harmonic excitation is listed, including the modal amplitude coefficient α of the positive traveling wave in the incident sound field 1,mn , negative traveling wave modal amplitude coefficient β in the incident sound field 1,mn , transmitted sound wave modal amplitude coefficient α 2,mn Calculation formula.

[0035] Optionally, in the above method for determining the sound insulation value of a thin-film acoustic metamaterial, step three includes:

[0036]

[0037]

[0038]

[0039] in,

[0040] k z is the z-direction wave number of simple harmonic excitation.

[0041] Optionally, in the above-mentioned method for determining the sound insulation value of the thin film acoustic metamaterial, in step 4, a calculation formula for the velocity potential of the thin film subjected to simple harmonic excitation is listed, including the incident side velocity potential φ1(x, y, t) and the transmission side velocity potential φ2(x, y, t).

[0042] Optionally, in the above-mentioned method for determining the sound insulation value of a thin-film acoustic metamaterial, step 4 includes:

[0043]

[0044]

[0045] Optionally, in the above-mentioned method for determining the sound insulation value of the film-type acoustic metamaterial, in step 5, a vibration control equation of the film subjected to simple harmonic excitation is constructed, specifically:

[0046]

[0047] in,

[0048] D is the bending stiffness of the film;

[0049] ρ m is the mass density of the air in which the mass block is immersed;

[0050] ρ a is the air density;

[0051] F pq is the inertial force exerted by the p-th mass block on the membrane at the q-th distribution point;

[0052] δ is the Dirac delta function;

[0053] (x pq ,y pq ) is the global coordinate of the qth matching point where the pth mass block contacts the film.

[0054] Optionally, in the above-mentioned method for determining the sound insulation value of the thin film acoustic metamaterial, step five includes:

[0055]

[0056] Optionally, in the above-mentioned method for determining the sound insulation value of the thin film acoustic metamaterial, step five includes:

[0057]

[0058] in,

[0059] w(x pq ,y pq , t) is the lateral displacement of the film;

[0060] G(M p ) is the gain of the mass block.

[0061] Optionally, in the above-mentioned method for determining the sound insulation value of the thin film acoustic metamaterial, in step 7, the equivalent surface density of the thin film is calculated, specifically:

[0062]

[0063]

[0064]

[0065] in,

[0066] m″ is the equivalent surface density of the film;

[0067] Δp is the sound pressure difference between the incident side and the transmission side of the film;

[0068] a z is the surface average value of the z-component of the membrane vibration acceleration.

[0069] Optionally, in the above-mentioned method for determining the sound insulation value of the film-type acoustic metamaterial, in step eight, the sound energy transmission coefficient is calculated based on the equivalent surface density of the film, specifically:

[0070]

[0071]

[0072] in,

[0073] τ is the acoustic energy transmission coefficient of the film;

[0074] θ i is the azimuth of the incident wave on the film;

[0075] c a is the speed of sound in air;

[0076] T is the acoustic energy transfer matrix of the film, T 11 、T 12 、T 21 、T 22 For its elements.

[0077] Optionally, in the above-mentioned method for determining the sound insulation value of the film-type acoustic metamaterial, in step nine, the sound insulation value is calculated using the sound energy transmission coefficient of the film, specifically:

[0078] TL=-10log 10 τ

[0079] =f(L x , L y 、h m 、E m , η m , ν m 、M p );

[0080] in,

[0081] TL is the sound insulation of the film.

[0082] This application has at least the following beneficial technical effects:

[0083] A method for determining the sound insulation value of a thin film acoustic metamaterial is provided. The key parameters affecting the acoustic performance of the thin film acoustic metamaterial are used to perform calculations to obtain the sound insulation value of the thin film acoustic metamaterial. The method is efficient, convenient and has high accuracy, and can provide effective support for the rapid design and improvement of the thin film acoustic metamaterial. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 It is a schematic diagram of a method for determining the sound insulation value of a thin film acoustic metamaterial provided in an embodiment of the present application;

[0085] Figure 2 It is a schematic diagram of a thin film acoustic metamaterial model provided in an embodiment of the present application.

[0086] In order to better illustrate the present embodiment, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of the actual product. In addition, the drawings are only used for illustrative purposes and should not be construed as limitations on the present application. DETAILED DESCRIPTION

[0087] In order to make the technical solution and advantages of the present application clearer, the technical solution of the present application will be described in further detail in detail and in detail with reference to the accompanying drawings. It can be understood that the specific embodiments described here are only partial embodiments of the present application, which are only used to explain the present application, not to limit the present application. It should be noted that, for the convenience of description, only the parts related to the present application are shown in the accompanying drawings, and other related parts can refer to the general design.

[0088] In addition, unless otherwise defined, the technical terms or scientific terms used in the description of this application shall have the usual meanings understood by those of ordinary skill in the art to which this application belongs. The words used in the description of this application to indicate orientation are only used to indicate relative directions or positional relationships. When the absolute position of the described object changes, its relative positional relationship may also change accordingly. The word "include" used in the description of this application indicates that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, but does not exclude other elements or objects.

[0089] In addition, it should be noted that, unless otherwise clearly specified and limited, the words "installation", "connection" and similar terms used in the description of this application should be understood in a broad sense. For example, the connection can be a fixed connection or a detachable 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. Technical personnel in the field can understand its specific meaning in this application according to the specific circumstances.

[0090] This application is based on the theoretical analysis of the distribution parameters of thin-film acoustic metamaterials to obtain the key parameters that affect the acoustic performance, and provides a method for determining the sound insulation of thin-film acoustic metamaterials, such as Figure 1 shown.

[0091] Step 1: Construct a thin film acoustic metamaterial model and define a coordinate system of the thin film acoustic metamaterial model.

[0092] The film-type acoustic metamaterial model includes a rectangular film and multiple circular mass blocks located on the film, such as Figure 2 As shown. The parameters of the film-type acoustic metamaterial model include the film length L x , Film width L y , film thickness h m , Young's modulus E of the film material m , damping loss factor η of thin film material m , Poisson's ratio ν of the film material m 、Mass block weight M p .

[0093] The x-axis of the coordinate system of the film-type acoustic metamaterial model is along the length direction of the rectangular film, the y-axis is along the width direction of the rectangular film, and the z-axis is perpendicular to the rectangular film, which conforms to the right-hand coordinate system. The origin of the coordinate is located at the intersection of the x-axis and the y-axis of the rectangular film, which can be located at the center of the film.

[0094] Step 2: List the calculation formula for the lateral displacement of the film under simple harmonic excitation.

[0095]

[0096] in,

[0097] w(x,y,t) is the lateral displacement of the film, along the z direction;

[0098] m is the order of the film mode shape in the x-axis direction;

[0099] n is the order of the film mode shape in the y-axis direction;

[0100] ψ mn (x,y) is the vibration mode function of the film;

[0101] q mn (t) is the modal participation factor of the film.

[0102]

[0103] q mn (t) = A mn e jωt ;

[0104] in,

[0105] A mn is the modal participation factor coefficient of the film;

[0106] ω is the circular frequency of simple harmonic excitation;

[0107] j is the imaginary part.

[0108] Step 3: List the calculation formulas for the modal amplitude coefficients of the film subjected to simple harmonic excitation.

[0109] The modal amplitude coefficient of the film includes the modal amplitude coefficient of the positive wave in the incident acoustic field α 1,mn , negative traveling wave modal amplitude coefficient β in the incident sound field 1,mn , transmitted sound wave modal amplitude coefficient α 2,mn .

[0110] According to the z-direction velocity continuity condition of the interface between the film and the air, we have:

[0111]

[0112]

[0113]

[0114] in,

[0115] k z is the z-direction wave number of simple harmonic excitation.

[0116] Step 4: List the velocity potential calculation formula for the film subjected to simple harmonic excitation.

[0117] The velocity potential of the film includes the incident side velocity potential φ1(x, y, t) and the transmission side velocity potential φ2(x, y, t).

[0118] The vibration mode function of the film is expanded in series, and we have:

[0119]

[0120]

[0121] Step 5: Construct the vibration control equation of the membrane subjected to simple harmonic excitation.

[0122]

[0123] in,

[0124] D is the bending stiffness of the film;

[0125] ρ m is the mass density of the air in which the mass block is immersed;

[0126] ρ a is the air density;

[0127] F pq is the inertial force exerted by the p-th mass block on the membrane at the q-th distribution point;

[0128] δ is the Dirac delta function;

[0129] (x pq ,y pq ) is the global coordinate of the qth matching point where the pth mass block contacts the film.

[0130]

[0131]

[0132] in,

[0133] w(x pq ,y pq , t) is the lateral displacement of the film;

[0134] G(M p ) is the gain of the mass block.

[0135] Step 6: Substitute the lateral displacement, modal amplitude coefficient, and velocity potential calculation formula of the membrane under simple harmonic excitation into the vibration control equation to obtain the modal participation factor coefficient.

[0136] Step 7: Using the modal participation factor coefficient of the film, calculate the lateral displacement, modal amplitude coefficient, and velocity potential of the film under simple harmonic excitation, and then calculate the equivalent surface density of the film.

[0137]

[0138]

[0139]

[0140] in,

[0141] m″ is the equivalent surface density of the film;

[0142] Δp is the sound pressure difference between the incident side and the transmission side of the film;

[0143] a z is the surface average value of the z-component of the membrane vibration acceleration.

[0144] Step 8: Calculate the acoustic energy transmission coefficient based on the equivalent surface density of the film.

[0145]

[0146]

[0147] in,

[0148] τ is the acoustic energy transmission coefficient of the film;

[0149] θ i is the azimuth of the incident wave on the film;

[0150] c a is the speed of sound in air;

[0151] T is the acoustic energy transfer matrix of the film, T 11 、T 12 、T 21 、T 22 For its elements.

[0152] Step 9. Calculate the sound insulation value based on the sound energy transmission coefficient of the film.

[0153] TL=-10log 10 τ

[0154] =f(L x , L y 、h m 、E m , η m , ν m 、M p );

[0155] in,

[0156] TL is the sound insulation of the film, and L is the length of the film. x , Film width L y , film thickness h m , Young's modulus E of the film material m , damping loss factor η of thin film material m , Poisson's ratio ν of the film material m 、Mass block weight M p function.

[0157] The method for determining the sound insulation value of the thin film acoustic metamaterial disclosed in the above embodiment uses the key parameters that affect the acoustic performance of the thin film acoustic metamaterial to perform calculations to obtain the sound insulation value of the thin film acoustic metamaterial. The method is efficient, convenient, and has high accuracy, and can provide effective support for the rapid design and improvement of the thin film acoustic metamaterial.

[0158] So far, the technical solution of the present application has been described in conjunction with the preferred embodiments shown in the accompanying drawings. Those skilled in the art should understand that the scope of protection of the present application is obviously not limited to these specific embodiments. Without departing from the principles of the present application, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will fall within the scope of protection of the present application.

Claims

1. A method for determining the sound insulation value of a thin-film acoustic metamaterial, characterized in that: include: Step 1: construct a thin film acoustic metamaterial model and define a coordinate system of the thin film acoustic metamaterial model; Step 2: List the calculation formula for the lateral displacement of the film under simple harmonic excitation; Step 3: List the calculation formula of the modal amplitude coefficient of the film subjected to simple harmonic excitation; Step 4: List the velocity potential calculation formula for the film subjected to simple harmonic excitation; Step 5: construct the vibration control equation of the film under simple harmonic excitation; Step 6: Substitute the lateral displacement, modal amplitude coefficient, and velocity potential calculation formula of the film subjected to simple harmonic excitation into the vibration control equation to obtain the modal participation factor coefficient; Step 7: Using the modal participation factor coefficient of the film, calculate the lateral displacement, modal amplitude coefficient, and velocity potential of the film under simple harmonic excitation, and then calculate the equivalent surface density of the film; Step 8: Calculate the acoustic energy transmission coefficient based on the equivalent surface density of the film; Step 9. Calculate the sound insulation value based on the sound energy transmission coefficient of the film.

2. The method for determining the sound insulation value of a thin film acoustic metamaterial according to claim 1, characterized in that: In step one, a thin film acoustic metamaterial model is constructed, including a rectangular thin film and a plurality of circular mass blocks located on the thin film.

3. The method for determining the sound insulation value of a thin film acoustic metamaterial according to claim 2, characterized in that: In step 1, a coordinate system of the film-type acoustic metamaterial model is defined, where the x-axis is along the length direction of the rectangular film, the y-axis is along the width direction of the rectangular film, and the z-axis is perpendicular to the rectangular film, conforming to a right-handed coordinate system.

4. The method for determining the sound insulation value of a thin film acoustic metamaterial according to claim 3, characterized in that: In step 2, the calculation formula for the lateral displacement of the film under simple harmonic excitation is listed as follows: in, w(x,y,t) is the lateral displacement of the film, along the z direction; m is the order of the film mode shape in the x-axis direction; n is the order of the film mode shape in the y-axis direction; ψ mn (x,y) is the vibration mode function of the film; q mn (t) is the modal participation factor of the film.

5. The method for determining the sound insulation value of a thin film acoustic metamaterial according to claim 4, characterized in that: In step 2, there are: q mn (t)=A mn e jωt ; in, A mn is the modal participation factor coefficient of the film; ω is the circular frequency of simple harmonic excitation; j is the imaginary part.

6. The method for determining the sound insulation value of a thin film acoustic metamaterial according to claim 5, characterized in that: In step 3, the modal amplitude coefficient calculation formula for the film subjected to simple harmonic excitation is listed, including the modal amplitude coefficient α of the positive traveling wave in the incident sound field 1,mn , negative traveling wave modal amplitude coefficient β in the incident sound field 1,mn , transmitted sound wave modal amplitude coefficient α 2,mn Calculation formula.

7. The method for determining the sound insulation value of a thin film acoustic metamaterial according to claim 6, characterized in that: In step three, there are: in, k z is the z-direction wave number of simple harmonic excitation.

8. The method for determining the sound insulation value of a thin film acoustic metamaterial according to claim 7, characterized in that: In step 4, the velocity potential calculation formula for the film subjected to simple harmonic excitation is listed, including the incident side velocity potential φ1(x, y, t) and the transmission side velocity potential φ2(x, y, t).

9. The method for determining the sound insulation value of a thin film acoustic metamaterial according to claim 8, characterized in that: In step 4, there are:

10. The method for determining the sound insulation value of a thin film acoustic metamaterial according to claim 9, characterized in that: In step 5, the vibration control equation of the film subjected to simple harmonic excitation is constructed, which is: in, D is the bending stiffness of the film; ρ m is the mass density of the air in which the mass block is immersed; ρ a is the air density; F pq is the inertial force exerted by the p-th mass block on the membrane at the q-th distribution point; δ is the Dirac delta function; (x pq ,y pq ) is the global coordinate of the qth matching point where the pth mass block contacts the film.

11. The method for determining the sound insulation value of a thin film acoustic metamaterial according to claim 10, characterized in that: In step five, there are:

12. The method for determining the sound insulation value of a thin film acoustic metamaterial according to claim 11, characterized in that: In step five, there are: in, w(x pq ,y pq , t) is the lateral displacement of the film; G(M p ) is the gain of the mass block.

13. The method for determining the sound insulation value of a thin film acoustic metamaterial according to claim 12, characterized in that: In step 7, the equivalent surface density of the film is calculated, specifically: in, m″ is the equivalent surface density of the film; Δp is the sound pressure difference between the incident side and the transmission side of the film; a z is the surface average value of the z-component of the membrane vibration acceleration.

14. The method for determining the sound insulation value of a thin film acoustic metamaterial according to claim 13, characterized in that: In step eight, the acoustic energy transmission coefficient is calculated based on the equivalent surface density of the film, specifically: in, τ is the acoustic energy transmission coefficient of the film; θ i is the azimuth of the incident wave on the film; c a is the speed of sound in air; T is the acoustic energy transfer matrix of the film, T 11 , T 12 , T 21 , T 22 For its elements.

15. The method for determining the sound insulation value of a thin film acoustic metamaterial according to claim 14, characterized in that: In step nine, the sound insulation is calculated using the sound energy transmission coefficient of the film, specifically: TL=-10log 10 t =f(L x 、L y 、h m 、E m ,or m ,n m 、M p ); in, TL is the sound insulation of the film.

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