CN113640388A - Method and device for calculating sound absorption coefficient of porous material with periodic non-flat interface - Google Patents
Method and device for calculating sound absorption coefficient of porous material with periodic non-flat interface Download PDFInfo
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Abstract
The invention belongs to the technical field of acoustic measurement of porous sound-absorbing materials, and particularly relates to a method and a device for calculating the sound-absorbing coefficient of a porous material with a periodic non-flat interface, wherein the method comprises the following steps: obtaining equivalent acoustic parameters of the porous material with the periodic non-flat interface; carrying out layering treatment on the periodic non-flat interface porous material, wherein each thin layer material is equivalent to an acoustic material modulated by a periodic rectangle; acquiring sound pressure and related acoustic parameters in the acoustic material equivalently modulated by the periodic rectangles of each thin-layer material, expanding the sound pressure and the related acoustic parameters into a hierarchical number expression form, substituting the hierarchical number expression form into a sound wave equation, and calculating the eigen state form of the sound pressure in each thin-layer material; calculating intensity coefficient vectors of all orders of eigen state forms of reflected sound pressure and intensity coefficient vectors of all orders of eigen state forms of transmitted sound pressure by adopting an iterative optimization algorithm according to the interlayer boundary continuity condition; and determining the total reflection coefficient and the total transmission coefficient according to the calculation result, and calculating the sound absorption coefficient of the porous material with the periodic non-flat interface.
Description
Technical Field
The invention belongs to the technical field of acoustic measurement of porous sound absorption materials, and particularly relates to a method and a device for calculating a sound absorption coefficient of a porous material with a periodic non-flat interface.
Background
Porous materials are widely used in the field of noise control because they convert acoustic energy into heat. A plurality of porous materials with a wedge-shaped or semi-elliptical surface and a periodic corrugated structure are arranged on a wall body to achieve the purpose of sound absorption. Compared with a plane porous material, the porous material with the periodic corrugated structure has better sound absorption performance in a wider frequency range.
At present, the research on the sound absorption performance of the porous material with the periodic non-flat interface mainly takes experimental tests as main points. Through experimental test research and optimization of the sound absorption performance of the porous material, a large number of sample pieces with different material parameters, different geometric shapes and different structural parameters are generally required to be prepared, a large number of repeated measurement works are carried out, and then all test data are summarized and counted and the rule is summarized. Such an experimental test procedure is tedious to operate, time-consuming and labor-consuming, and is not favorable for rapid optimization design in engineering application.
Aiming at the calculation of the sound absorption coefficient of the porous material with the periodic non-flat interface, the conventional calculation method mainly comprises theoretical calculation methods such as finite elements, boundary elements, time domain finite difference and the like, the conventional method mainly needs geometric modeling and grid division, the calculation complexity and difficulty are very high, and the measurement efficiency and the measurement precision are greatly reduced.
Disclosure of Invention
In order to solve the defects in the prior art, the invention provides a method for calculating the sound absorption coefficient of a porous material with a periodic non-flat interface, which comprises the following steps:
obtaining equivalent acoustic parameters of the porous material with the periodic non-flat interface; wherein the equivalent acoustic parameters include: equivalent refractive index and equivalent density;
carrying out layering treatment on the periodic non-flat interface porous material, wherein each thin layer material is equivalent to an acoustic material modulated by a periodic rectangle;
according to the obtained equivalent acoustic parameters of the porous material, sound pressure and related acoustic parameters in the acoustic material which is equivalently modulated by the periodic rectangles of each thin-layer material are obtained and expanded into a graded number expression form, and are brought into a sound wave equation, and the eigen state form of the sound pressure in each thin-layer material is calculated;
calculating intensity coefficient vectors of all orders of eigen state forms of reflected sound pressure and intensity coefficient vectors of all orders of eigen state forms of transmitted sound pressure by adopting an iterative optimization algorithm according to the interlayer boundary continuity condition;
and determining the total reflection coefficient and the total transmission coefficient according to the calculation result, and calculating the sound absorption coefficient of the porous material with the periodic non-flat interface.
As an improvement of the above technical solution, the periodic non-flat interface porous material comprises: a periodic array of non-flat, non-completely filled porous material tips and a completely filled porous material substrate.
As one improvement of the technical scheme, the equivalent acoustic parameters of the porous material with the periodic non-flat interface are acquired; the specific process comprises the following steps:
the first thickness obtained by measurement is t1Reflection coefficient R of planar structure of porous material1And a second thickness t2Reflection coefficient R of planar structure of porous material2Respectively calculating the first thickness as t1Surface resistance zeta of planar structure of porous material1And a second thickness t2Surface resistance zeta of planar structure of porous material2；
ζ1＝(1+R1)/(1-R1)
ζ2＝(1+R2)/(1-R2)
Therein, ζ1＝Zpcoth(γt1)；ζ2＝Zpcoth(γt2)；
According to ζ1tanh(γt1)-ζ2tanh(γt2)＝0；
Combining the above formula, calculating to obtain a complex propagation constant gamma and a normalized characteristic impedance Zp；
Calculating the equivalent refractive index n according to the following formulapAnd equivalent secretDegree rhop：
np＝ω/(-jγc0)；
ρp＝(-jγρ0c0Zp)/ω；
Wherein, c0Is the speed of sound of air; rho0Is the density of air; omega is angular frequency; j is an imaginary unit; .
And taking the calculated equivalent refractive index and equivalent density as equivalent acoustic parameters.
As one improvement of the above technical solution, the periodic non-flat interface porous material is subjected to a layering treatment, and each thin layer material is equivalent to a periodic rectangular modulated acoustic material; the specific process comprises the following steps:
the tip of the periodic non-flat interface porous material is a non-flat, non-completely filled porous material with a plurality of thin layers; carrying out layering treatment on the periodic non-flat interface porous material to obtain a plurality of thin layer materials, wherein each thin layer material is equivalent to an acoustic material modulated by a periodic rectangle;
the substrate of the periodic non-flat interfacial porous material is a completely filled porous material, which is a completely filled, periodic rectangular modulated acoustic material with a fill factor of 1.
As one improvement of the above technical solution, the sound pressure and related acoustic parameters in the acoustic material, which is obtained according to the equivalent acoustic parameters of the porous material and is equivalently modulated by the periodic rectangle, of each thin layer material are expanded into a hierarchical number expression form and are brought into a sound wave equation, and the eigen state form of the sound pressure in each thin layer material is calculated; the specific process comprises the following steps:
the sound pressure series expression form in the acoustic material with equivalent periodic rectangular modulation of each thin layer material is as follows:
wherein, PIThe sound pressure series expression form of the incident and reflection areas; pIIIs a sound pressure level expression form of the transmission region, PlIs a sound pressure series expression form in the acoustic material with the equivalent periodic rectangular modulation of the first thin material of the porous material; wherein, L is 1,2, …, L-1, L;
kx0＝k0sinθ，kz0＝k0cosθ，kxi＝k0sin theta + iK, and the subscript i is a positive integer greater than 0, which represents the ith order number expansion; k is 2 pi/T, and K is an inverted space basis vector;
when k isxi<k0When there is
When k isxi>k0When there is
Wherein j is an imaginary unit; k is a radical of0Is the wave number in air; k is a radical ofxiA wave vector representing the x direction; k is a radical ofziA wave vector representing the z direction; θ is the angle of incidence; t represents the period of the porous material; d represents the total thickness of the porous material; riAnd TiRespectively representing a reflection coefficient and a transmission coefficient of the normalized ith-order sound pressure; sli(z) is the ith order sound pressure coefficient of the layer l periodic porous material; exp () represents an exponential function with a natural constant e as the base;
the series expression of the relevant acoustic parameters is in the form of:
where ρ isl(x) Is the equivalent density of the l layer of periodic porous material; n isl(x) Is the equivalent refractive index of the l layer of periodic porous material;
wherein f islIs the duty cycle of the porous material in the l-th layer of periodic porous material; n isp，ρpThe equivalent refractive index and the equivalent density of the porous material, respectively; n is0，ρ0Refractive index and density of air, respectively; j is an imaginary unit; m is the expansion order; k is an inverse spatial basis vector;
the obtained sound pressure of each thin-layer material and the series expression form of the related acoustic parameters are brought into a sound wave equation; in the one-dimensional periodic acoustic structure, an acoustic wave equation in a density non-uniform medium is as follows:
wherein,
is a Laplace operator; p is a sound pressure series expression form; p is the sound pressure level expression form P of the incident and reflection regionsISound pressure level expression form P of transmission regionIIOr sound pressure level order expression form P in periodic rectangular modulated acoustic material equivalent to porous materiall(ii) a n (x) is a series expression of the equivalent refractive index of the porous material of the periodic porous material;
obtaining a coupling equation of each order of coefficient:
writing the above coupling equation in matrix form:
[Sl″]＝[Al][Sl]
wherein S islIs formed by SliA column vector of components; sl"is composed of2Sli/dz2A column vector of components; matrix array
Wherein, the matrix XlAnd YlAre respectively
And
wherein m1 is the number of rows; n1 is the number of columns;
and
are all coefficients; diagonal matrix KxElement K ofi,i＝kxi；
Computing the matrix AlEigenvalue and eigenvector to obtain square root of mth eigenvalue
And corresponding feature vectors
Then the sound pressure coefficient Sli(z) expression:
wherein, l is 1;
is a positive eigenstate form of sound pressure in the first thin-layer material;
is the reverse eigenstate form of sound pressure in the first thin layer material;
an intensity coefficient in the form of a forward propagating eigenstate;
intensity coefficients in the form of counter-propagating eigenstates; d1Is the thickness of the first thin layer; z is the position in the z direction;
wherein L is 2,3, …, L; dpIs the thickness of the pth thin layer;
according to the sound pressure coefficient Sli(z) determining the positive eigenstate form of the acoustic pressure in the first thin-layer material
And the inverse eigenstate form of the sound pressure in the first thin-layer material
As one improvement of the above technical solution, the intensity coefficient vector of each order of eigen state of the reflected sound pressure and the intensity coefficient vector of each order of eigen state of the transmitted sound pressure are calculated by using an iterative optimization algorithm according to the interlayer boundary continuity condition; the specific process comprises the following steps:
the boundary continuity condition comprises that the sound pressure and the normal direction particle vibration speed are continuous;
normal direction particle vibration velocity vzExpression is
Wherein j is an imaginary unit; omega is angular frequency;
is the inverse of the normalized density;
expanding the reciprocal of the normalized density into a corresponding series form
Where ρ is0Is the air density; rhol(x) Is the equivalent density of the l lamellae;
is the expansion coefficient;
i-th order particle vibration velocity
The method comprises the following steps:
wherein, l is 1;
wherein L is 2,3, …, L;
an expansion coefficient that is the inverse of the normalized density;
the interfacial continuity conditions for the incident, reflective regions and the first layer of periodic porous material are:
the continuity conditions for the interfaces in between are:
the interfacial continuity conditions for the last layer of periodic porous material and the transmissive region are:
wherein R is the reflection intensity coefficient RiA column vector of components; t is the transmission intensity coefficient TiA column vector of components;
intensity coefficients in the form of forward propagating eigenstates
A column vector of components; and
intensity coefficients in the form of counter-propagating eigenstates
A column vector of components; wlIs a feature vector
A constructed matrix, I being an identity matrix; deltai0Is 0 order with a corresponding coefficient of 1, and the other terms areA column vector of 0; first thin layer matrix Vl＝ZlWlQlAnd matrix ZlIs an element of
First thin diagonal matrix Ql，ElAnd KzAre respectively an element
Element(s)
And element kziA matrix of compositions; wLAs feature vectors
A matrix of formations; eLAs feature vectors
A matrix of formations; l thin layer VL＝ZLWLQL；
Through matrix calculation, a matrix equation about the sound pressure reflection coefficient and the transmission coefficient is obtained:
calculating intensity coefficient vectors R of all orders of eigenstates of reflected sound pressure and intensity coefficient vectors T of all orders of eigenstates of transmitted sound pressure by adopting an iterative optimization algorithm; the method comprises the following specific steps:
the last four terms of the above matrix equation are expressed as:
introduces an iteration matrix fL+1And gL+1And has fL+1＝I，gL+1＝jKz(ii) a And then introducing the following iteration matrix:
wherein, aL、bLRespectively introducing a first column intermediate matrix and a second column intermediate matrix;
is provided with
The following relationships were obtained by collation:
then the iteration matrix expression is:
through iterative computation, a matrix equation is obtained:
solving the matrix equation to obtain R and T1；
Vector of transmission coefficients T1＝(g1+jKzf1)-1(jKzΔi0+jk0cosθΔi0)；
Intensity coefficient vector R ═ f of each order eigenstate of reflected sound pressure1T1-Δi0；
Intensity coefficient vector of each order eigenstate of transmission sound pressure
As one improvement of the technical scheme, the total reflection coefficient and the total transmission coefficient are determined, and the sound absorption coefficient of the porous material with the periodic non-flat interface is calculated; the specific process comprises the following steps:
calculating the total reflection coefficient R:
wherein,
is the reflection intensity coefficient R in the intensity coefficient vector R of each order eigenstate of the reflection sound pressureiTaking conjugation;
calculating the total transmission coefficient T:
T＝∑iTiTi*Re(kzi/kz0)；
wherein, Ti *Transmission intensity coefficient T in intensity coefficient vector T of each order eigenstate of transmission sound pressureiTaking conjugation; re () is a real part;
calculating the sound absorption coefficient alpha of the porous material with the periodic uneven interface according to the calculated total reflection coefficient R and the total transmission coefficient T;
α＝1-R-T。
the invention also provides a device for measuring the sound absorption coefficient of the porous material with the periodic non-flat interface, which comprises:
the acoustic parameter acquisition module is used for acquiring equivalent acoustic parameters of the porous material with the periodic uneven interface; wherein the equivalent acoustic parameters include: equivalent refractive index and equivalent density;
the layering module is used for layering the periodic non-flat interface porous material, and each thin layer material is equivalent to a periodic rectangular modulated acoustic material;
the eigen-state calculation module is used for acquiring the equivalent acoustic parameters of the porous material, expanding the sound pressure and the related acoustic parameters in the acoustic material which is equivalently modulated by the thin-layer material in a periodic rectangular mode into a hierarchical number expression form, bringing the hierarchical number expression form into an acoustic wave equation, and calculating the eigen-state form of the sound pressure in each thin-layer material;
the intensity coefficient calculation module is used for calculating intensity coefficient vectors of all orders of eigen state forms of the reflected sound pressure and intensity coefficient vectors of all orders of eigen state forms of the transmitted sound pressure by adopting an iterative optimization algorithm according to the interlayer boundary continuity condition; and
and the sound absorption coefficient acquisition module is used for determining the total reflection coefficient and the total transmission coefficient according to the calculation result and calculating the sound absorption coefficient of the porous material with the periodic non-flat interface.
Compared with the prior art, the invention has the beneficial effects that:
1. according to the method, equivalent acoustic parameters of the porous material to be tested are obtained, namely only two samples of the planar porous material with different thicknesses are required to be measured, sample pieces with different geometric shapes and structural sizes are not required to be prepared, and a large number of repeated experimental tests are not required, so that the measurement efficiency is greatly improved, and the sound absorption coefficient of the porous material with a periodic uneven interface can be measured more quickly;
2. the method considers the influence of periodic modulation on the sound absorption performance, wherein the influence comprises a high-order mode including evanescent waves, and the accuracy of the measured sound absorption coefficient is improved;
3. after the geometric parameters of the structure are determined, the method can accurately predict the broadband sound absorption coefficient of the porous material with the periodic non-flat interface only by bringing in equivalent acoustic parameters of each frequency, simplifies the calculation complexity, saves the time cost, greatly improves the measurement efficiency, and has important significance for the application in the field of noise control.
Drawings
FIG. 1 is a flow chart of a method for calculating the sound absorption coefficient of a periodic non-flat interfacial porous material according to the present invention;
FIG. 2 is a schematic diagram of a structure for measuring the reflection coefficient R of the porous material in a two-microphone impedance tube;
FIG. 3 is a schematic structural view of a tip and a substrate of a periodic non-planar interfacial porous material in the method of FIG. 1;
FIG. 4 is a schematic structural view of a single layer periodically modulated porous material after delamination of the periodic non-planar interfacial porous material in the method of FIG. 1;
FIG. 5a is a graphical representation of the equivalent refractive index of the porous material over a broad frequency range in the method of FIG. 1;
FIG. 5b is a graphical representation of the equivalent density of the porous material over a wide frequency range in the method of FIG. 1;
FIG. 6a is a schematic structural diagram of the geometric shape of the acoustic absorbent cotton with triangular periodic modulation as a sample to be measured;
FIG. 6b is a schematic structural diagram of the geometric shape of the acoustic absorbent cotton with rectangular periodic modulation of the sample to be measured;
fig. 7 is a result of calculation of the sound absorption coefficient of the sample to be tested and an experimental test result in the method of fig. 1.
Detailed Description
The invention will now be further described with reference to the accompanying drawings and examples.
As shown in figure 1, the invention provides a method for calculating the sound absorption coefficient of the porous material with the periodic non-flat interface, and the method can accurately predict the broadband sound absorption coefficient of the porous material with the periodic non-flat interface only by bringing in equivalent acoustic parameters of each frequency after determining the geometric parameters of the structure, thereby simplifying the calculation complexity, saving the time cost and having great significance for the application in the field of noise control.
The method comprises the following steps:
obtaining equivalent acoustic parameters of the porous material with the periodic non-flat interface; wherein the equivalent acoustic parameters include: equivalent refractive index and equivalent density;
specifically, as shown in fig. 2,3 and 4, in the two-microphone impedance tube, a planar structure of a porous material having a thickness t is mounted on a rigid backing, and the reflection coefficient R of the porous material is measured;
ζ＝(1+R)/(1-R)
wherein ζ is the surface resistance of the porous material, which is a known value; wherein, Zpcoth(γt)；
Wherein gamma is a complex propagation constant of the periodic non-flat interface porous material; zpNormalized characteristic impedance of the periodic non-flat interface porous material;
based on the above formula, the first thickness obtained by measurement is t1Reflection coefficient R of planar structure of porous material1And a second thickness t2Reflection coefficient R of planar structure of porous material2Respectively calculating the first thickness as t1Surface resistance zeta of planar structure of porous material1And a second thickness t2Surface resistance zeta of planar structure of porous material2；
ζ1＝(1+R1)/(1-R1)
ζ2＝(1+R2)/(1-R2)
Therein, ζ1＝Zpcoth(γt1)；ζ2＝Zpcoth(γt2)；
According to ζ1tanh(γt1)-ζ2tanh(γt2)＝0；
Combining the above formula, calculating to obtain a complex propagation constant gamma and a normalized characteristic impedance Zp；
Calculating the equivalent refractive index n according to the following formulapAnd equivalent density ρp：
np＝ω/(-jγc0)；
ρp＝(-jγρ0c0Zp)/ω；
Wherein, c0Is the speed of sound of air; rho0Is the density of air; omega is angular frequency; j is an imaginary unit; .
And taking the calculated equivalent refractive index and equivalent density as equivalent acoustic parameters.
Carrying out layering treatment on the periodic non-flat interface porous material, wherein each thin layer material is equivalent to an acoustic material modulated by a periodic rectangle;
specifically, the tip of the periodic non-flat interfacial porous material is a non-flat, non-completely filled porous material having a plurality of thin layers; carrying out layering treatment on the periodic non-flat interface porous material to obtain a plurality of thin layer materials, wherein each thin layer material is equivalent to an acoustic material modulated by a periodic rectangle;
the substrate of the periodic non-flat interfacial porous material is a completely filled porous material, which is a completely filled, periodic rectangular modulated acoustic material with a fill factor of 1.
Wherein the periodic non-planar interfacial porous material comprises: a periodic array of non-flat, non-completely filled porous material tips and a completely filled porous material substrate.
According to the obtained equivalent acoustic parameters of the porous material, sound pressure and related acoustic parameters in the acoustic material which is equivalently modulated by the periodic rectangles of each thin-layer material are obtained and expanded into a graded number expression form, and are brought into a sound wave equation, and the eigen state form of the sound pressure in each thin-layer material is calculated;
specifically, the sound pressure level expression in the periodic rectangular modulated acoustic material equivalent to each thin layer material is in the form of:
wherein, PIThe sound pressure series expression form of the incident and reflection areas; pIIIs a sound pressure level expression form of the transmission region, PlIs a sound pressure series expression form in the acoustic material with the equivalent periodic rectangular modulation of the first thin material of the porous material; wherein, L is 1,2, …, L-1, L;
kx0＝k0sinθ，kz0＝k0cosθ，kxi＝k0sin theta + iK, and the subscript i is a positive integer greater than 0, which represents the ith order number expansion; k is 2 pi/T, and K is an inverted space basis vector;
when k isxi<k0When there is
When k isxi>k0When there is
Wherein j is an imaginary unit; k is a radical of0Is the wave number in air; k is a radical ofxiA wave vector representing the x direction; k is a radical ofziA wave vector representing the z direction; θ is the angle of incidence; t represents the period of the porous material; d represents the total thickness of the porous material; riAnd TiRespectively representing a reflection coefficient and a transmission coefficient of the normalized ith-order sound pressure; sli(z) is the ith order sound pressure coefficient of the layer l periodic porous material; exp () represents an exponential function with a natural constant e as the base;
the series expression of the relevant acoustic parameters is in the form of:
where ρ isl(x) Is the equivalent density of the l layer of periodic porous material; n isl(x) Is the equivalent refractive index of the l layer of periodic porous material;
wherein f islIs the duty cycle of the porous material in the l-th layer of periodic porous material; n isp，ρpThe equivalent refractive index and the equivalent density of the porous material, respectively; n is0，ρ0Refractive index and density of air, respectively; j is an imaginary unit; m is an expansionThe order; k is an inverse spatial basis vector;
the obtained sound pressure of each thin-layer material and the series expression form of the related acoustic parameters are brought into a sound wave equation; in the one-dimensional periodic acoustic structure, an acoustic wave equation in a density non-uniform medium is as follows:
wherein,
is a Laplace operator; p is a sound pressure series expression form; p is the sound pressure level expression form P of the incident and reflection regionsISound pressure level expression form P of transmission regionIIOr sound pressure level order expression form P in periodic rectangular modulated acoustic material equivalent to porous materiall(ii) a n (x) is a series expression of the equivalent refractive index of the porous material of the periodic porous material;
obtaining a coupling equation of each order of coefficient:
writing the above coupling equation in matrix form:
[Sl″]＝[Al][Sl]
wherein S islIs formed by SliA column vector of components; sl"is composed of2Sli/dz2A column vector of components; matrix array
Wherein, the matrix XlAnd YlAre respectively
And
wherein m1 is the number of rows; n1 is the number of columns;
and
are all coefficients; diagonal matrix KxElement K ofi，i＝kxi；
Computing the matrix AlEigenvalue and eigenvector to obtain square root of mth eigenvalue
And corresponding feature vectors
Then the sound pressure coefficient Sli(z) expression:
wherein, l is 1;
is a positive eigenstate form of sound pressure in the first thin-layer material;
is the reverse eigenstate form of sound pressure in the first thin layer material;
an intensity coefficient in the form of a forward propagating eigenstate;
intensity coefficients in the form of counter-propagating eigenstates; d1Is the thickness of the first thin layer; z is the position in the z direction;
wherein L is 2,3, …, L; dpIs the thickness of the pth thin layer;
according to the sound pressure coefficient Sli(z) determining the positive eigenstate form of the acoustic pressure in the first thin-layer material
And the inverse eigenstate form of the sound pressure in the first thin-layer material
Calculating intensity coefficient vectors of all orders of eigen state forms of reflected sound pressure and intensity coefficient vectors of all orders of eigen state forms of transmitted sound pressure by adopting an iterative optimization algorithm according to the interlayer boundary continuity condition;
specifically, the boundary continuity condition includes that the sound pressure and the normal direction particle vibration velocity are continuous;
normal direction particle vibration velocity vzExpression is
Wherein j is an imaginary unit; omega is angular frequency;
is the inverse of the normalized density;
expanding the reciprocal of the normalized density into a corresponding series form
Where ρ is0Is the air density; rhol(x) Is the equivalent density of the l lamellae;
is the expansion coefficient;
i-th order particle vibration velocity
The method comprises the following steps:
wherein, l is 1;
wherein L is 2,3, …, L;
an expansion coefficient that is the inverse of the normalized density;
the interfacial continuity conditions for the incident, reflective regions and the first layer of periodic porous material are:
the continuity conditions for the interfaces in between are:
the interfacial continuity conditions for the last layer of periodic porous material and the transmissive region are:
wherein R is the reflection intensity coefficient RiA column vector of components; t is the transmission intensity coefficient TiA column vector of components;
intensity coefficients in the form of forward propagating eigenstates
A column vector of components; and
intensity coefficients in the form of counter-propagating eigenstates
A column vector of components; wlIs a feature vector
A constructed matrix, I being an identity matrix; deltai0Is a column vector with 0 order corresponding coefficient of 1 and other terms of 0; first thin layer matrix Vl＝ZlWlQlAnd matrix ZlIs an element of
First thin diagonal matrix Ql，ElAnd KzAre respectively an element
Element(s)
And element kziA matrix of compositions; wLAs feature vectors
A matrix of formations; eLAs feature vectors
A matrix of formations;l thin layer VL＝ZLWLQL；
Through matrix calculation, a matrix equation about the sound pressure reflection coefficient and the transmission coefficient is obtained:
calculating intensity coefficient vectors R of all orders of eigenstates of reflected sound pressure and intensity coefficient vectors T of all orders of eigenstates of transmitted sound pressure by adopting an iterative optimization algorithm; the method comprises the following specific steps:
the last four terms of the above matrix equation are expressed as:
introduces an iteration matrix fL+1And gL+1And has fL+1＝I，gL+1＝jKz(ii) a And then introducing the following iteration matrix:
wherein, aL、bLRespectively introducing a first column intermediate matrix and a second column intermediate matrix;
is provided with
The following relationships were obtained by collation:
then the iteration matrix expression is:
through iterative computation, a matrix equation is obtained:
solving the matrix equation to obtain R and T1；
Vector of transmission coefficients T1＝(g1+jKzf1)-1(jKzΔi0+jk0cosθΔi0)；
Intensity coefficient vector R ═ f of each order eigenstate of reflected sound pressure1T1-Δi0；
Intensity coefficient vector of each order eigenstate of transmission sound pressure
And determining the total reflection coefficient and the total transmission coefficient according to the calculation result, and calculating the sound absorption coefficient of the porous material with the periodic non-flat interface.
Specifically, the total reflection coefficient R is calculated:
wherein,
is the reflection intensity coefficient R in the intensity coefficient vector R of each order eigenstate of the reflection sound pressureiTaking conjugation;
calculating the total transmission coefficient T:
T＝∑iTiT* iRe(kzi/kz0)；
wherein, Ti *Transmission intensity coefficient T in intensity coefficient vector T of each order eigenstate of transmission sound pressureiTaking conjugation; re () is a real part;
calculating the sound absorption coefficient alpha of the porous material with the periodic uneven interface according to the calculated total reflection coefficient R and the total transmission coefficient T;
α＝1-R-T。
the invention also provides a device for measuring the sound absorption coefficient of the porous material with the periodic non-flat interface, which comprises:
the acoustic parameter acquisition module is used for acquiring equivalent acoustic parameters of the porous material with the periodic uneven interface; wherein the equivalent acoustic parameters include: equivalent refractive index and equivalent density;
the layering module is used for layering the periodic non-flat interface porous material, and each thin layer material is equivalent to a periodic rectangular modulated acoustic material;
the eigen-state calculation module is used for acquiring the equivalent acoustic parameters of the porous material, expanding the sound pressure and the related acoustic parameters in the acoustic material which is equivalently modulated by the thin-layer material in a periodic rectangular mode into a hierarchical number expression form, bringing the hierarchical number expression form into an acoustic wave equation, and calculating the eigen-state form of the sound pressure in each thin-layer material;
the intensity coefficient calculation module is used for calculating intensity coefficient vectors of all orders of eigen state forms of the reflected sound pressure and intensity coefficient vectors of all orders of eigen state forms of the transmitted sound pressure by adopting an iterative optimization algorithm according to the interlayer boundary continuity condition; and
and the sound absorption coefficient acquisition module is used for determining the total reflection coefficient and the total transmission coefficient according to the calculation result and calculating the sound absorption coefficient of the porous material with the periodic non-flat interface.
As shown in fig. 5a and 5b, a conventional porous sound absorbing material, i.e., high-density sound absorbing cotton, was purchased, the equivalent acoustic parameters of the porous material were first tested by a two-microphone impedance tube system, the reflection coefficients of the planar sound absorbing cotton with thicknesses of 2cm and 4.8cm were experimentally tested, and the equivalent refractive index and the equivalent density of the porous material were obtained by numerical calculation, and the results are shown in fig. 5a and 5 b.
By adopting the method for measuring the sound absorption coefficient of the porous material with the periodic non-flat interface, the sound absorption coefficients of the high-density sound absorption cotton with the two periodic non-flat interfaces are measured, the two sound absorption cotton are subjected to experimental tests in a two-microphone impedance tube system, and the sound absorption coefficients of the experimental tests are compared with the calculation results. The porous materials of the two periodic non-flat interfaces are triangular and rectangular periodic modulated sound absorption cotton respectively, and specific parameters are shown in fig. 6a and 6b, so that the calculation method provided by the invention can be determined to have higher accuracy.
As shown in FIG. 6a, the geometric parameters of the triangular periodically modulated sound absorbing cotton include the period Tt5cm, substrate thickness dt1cm, triangular tip thickness ht＝3.7cm：
As shown in FIG. 6b, the geometric parameters of the rectangular periodic modulated acoustic wool include the period Tr3.3cm, substrate thickness dr1.9cm, rectangular tip thickness hr2.8cm and a rectangular tip width wr＝1.5cm：
The sound absorption coefficient of the porous material measured by the method and the experimental test result are shown in fig. 7, and the two calculation results are very close to each other, which shows that the method for calculating the sound absorption coefficient of the porous material with the periodic non-flat interface provided by the invention is very effective.
Finally, it should be noted that the above embodiments are only used for illustrating the technical solutions of the present invention and are not limited. Although the present invention has been described in detail with reference to the embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (8)
1. A method for calculating the sound absorption coefficient of a porous material with a periodic non-flat interface comprises the following steps:
obtaining equivalent acoustic parameters of the porous material with the periodic non-flat interface; wherein the equivalent acoustic parameters include: equivalent refractive index and equivalent density;
carrying out layering treatment on the periodic non-flat interface porous material, wherein each thin layer material is equivalent to an acoustic material modulated by a periodic rectangle;
according to the obtained equivalent acoustic parameters of the porous material, sound pressure and related acoustic parameters in the acoustic material which is equivalently modulated by the periodic rectangles of each thin-layer material are obtained and expanded into a graded number expression form, and are brought into a sound wave equation, and the eigen state form of the sound pressure in each thin-layer material is calculated;
calculating intensity coefficient vectors of all orders of eigen state forms of reflected sound pressure and intensity coefficient vectors of all orders of eigen state forms of transmitted sound pressure by adopting an iterative optimization algorithm according to the interlayer boundary continuity condition;
and determining the total reflection coefficient and the total transmission coefficient according to the calculation result, and calculating the sound absorption coefficient of the porous material with the periodic non-flat interface.
2. The method of calculating the sound absorption coefficient of a periodic non-flat interfacial porous material of claim 1, wherein the periodic non-flat interfacial porous material comprises: a periodic array of non-flat, non-completely filled porous material tips and a completely filled porous material substrate.
3. The method for calculating the sound absorption coefficient of the periodic non-flat interface porous material according to claim 1, wherein equivalent acoustic parameters of the periodic non-flat interface porous material are obtained; the specific process comprises the following steps:
the first thickness obtained by measurement is t1Reflection coefficient R of planar structure of porous material1And a second thickness t2Reflection coefficient R of planar structure of porous material2Respectively calculating the first thickness as t1Surface resistance zeta of planar structure of porous material1And a second thickness t2Surface resistance zeta of planar structure of porous material2；
ζ1＝(1+R1)/(1-R1)
ζ2＝(1+R2)/(1-R2)
Therein, ζ1＝Zpcoth(γt1)；ζ2＝Zpcoth(γt2)；
According to ζ1tanh(γt1)-ζ2tanh(γt2)＝0；
Combined upper, calculated to obtainComplex propagation constant gamma and normalized characteristic impedance Zp；
Calculating the equivalent refractive index n according to the following formulapAnd equivalent density ρp：
np＝ω/(-jγc0)；
ρp＝(-jγρ0c0Zp)/ω；
Wherein, c0Is the speed of sound of air; rho0Is the density of air; omega is angular frequency; j is an imaginary unit;
and taking the calculated equivalent refractive index and equivalent density as equivalent acoustic parameters.
4. The method for calculating the sound absorption coefficient of the periodic non-flat interface porous material as claimed in claim 1, wherein the periodic non-flat interface porous material is subjected to layering treatment, and each thin layer material is equivalent to a periodic rectangular modulated acoustic material; the specific process comprises the following steps:
the tip of the periodic non-flat interface porous material is a non-flat, non-completely filled porous material with a plurality of thin layers; carrying out layering treatment on the periodic non-flat interface porous material to obtain a plurality of thin layer materials, wherein each thin layer material is equivalent to an acoustic material modulated by a periodic rectangle;
the substrate of the periodic non-flat interfacial porous material is a completely filled porous material, which is a completely filled, periodic rectangular modulated acoustic material with a fill factor of 1.
5. The method for calculating the sound absorption coefficient of the porous material with the periodic non-flat interface according to claim 1, wherein the sound pressure and the related acoustic parameters in the acoustic material which is obtained according to the equivalent acoustic parameters of the porous material and is subjected to equivalent periodic rectangular modulation of each thin-layer material are expanded into a graded number expression form and are brought into a sound wave equation to calculate the eigen-state form of the sound pressure in each thin-layer material; the specific process comprises the following steps:
the sound pressure series expression form in the acoustic material with equivalent periodic rectangular modulation of each thin layer material is as follows:
wherein, PIThe sound pressure series expression form of the incident and reflection areas; pIIIs a sound pressure level expression form of the transmission region, PlIs a sound pressure series expression form in the acoustic material with the equivalent periodic rectangular modulation of the first thin material of the porous material; wherein, L is 1,2,. said, L-1, L;
kx0＝k0sinθ，kz0＝k0cosθ，kxi＝k0sin theta + iK, and the subscript i is a positive integer greater than 0, which represents the ith order number expansion; k is 2 pi/T, and K is an inverted space basis vector;
when k isxi＜k0When there is
When k isxi＞k0When there is
Wherein j is an imaginary unit; k is a radical of0Is the wave number in air; k is a radical ofxiA wave vector representing the x direction; k is a radical ofziA wave vector representing the z direction; θ is the angle of incidence; t represents the period of the porous material; d represents the total thickness of the porous material; riAnd TiRespectively representing a reflection coefficient and a transmission coefficient of the normalized ith-order sound pressure; sli(z) is the l-th layer periodThe ith order sound pressure coefficient of the porous material; exp () represents an exponential function with a natural constant e as the base;
the series expression of the relevant acoustic parameters is in the form of:
where ρ isl(x) Is the equivalent density of the l layer of periodic porous material; n isl(x) Is the equivalent refractive index of the l layer of periodic porous material;
wherein f islIs the duty cycle of the porous material in the l-th layer of periodic porous material; n isp，ρpThe equivalent refractive index and the equivalent density of the porous material, respectively; n is0，ρ0Refractive index and density of air, respectively; j is an imaginary unit; m is the expansion order; k is an inverse spatial basis vector;
the obtained sound pressure of each thin-layer material and the series expression form of the related acoustic parameters are brought into a sound wave equation; in the one-dimensional periodic acoustic structure, an acoustic wave equation in a density non-uniform medium is as follows:
wherein,
is a Laplace operator; p is a sound pressure series expression form; p is the sound pressure level expression form P of the incident and reflection regionsISound pressure level expression form P of transmission regionIIOr sound pressure level order expression form P in periodic rectangular modulated acoustic material equivalent to porous materiall(ii) a n (x) is a series expression of the equivalent refractive index of the porous material of the periodic porous material;
obtaining a coupling equation of each order of coefficient:
writing the above coupling equation in matrix form:
[Sl″]＝[Al][Sl]
wherein S islIs formed by SliA column vector of components; sl"is composed of2Sli/dz2A column vector of components; matrix array
Wherein, the matrix XlAnd YlAre respectively
And
wherein m1 is the number of rows; n1 is the number of columns;
and
are all coefficients; diagonal matrix KxElement K ofi，i＝kxi；
Computing the matrix AlEigenvalue and eigenvector to obtain square root of mth eigenvalue
And corresponding feature vectors
Then the sound pressure coefficient Sli(z) expression:
wherein, l is 1;
is a positive eigenstate form of sound pressure in the first thin-layer material;
is the reverse eigenstate form of sound pressure in the first thin layer material;
an intensity coefficient in the form of a forward propagating eigenstate;
intensity coefficients in the form of counter-propagating eigenstates; d1Is the thickness of the first thin layer; z is the position in the z direction;
wherein, L is 2, 3.., L; dpIs the thickness of the pth thin layer;
according to the sound pressure coefficient Sli(z) determining the positive eigenstate form of the acoustic pressure in the first thin-layer material
And the inverse eigenstate form of the sound pressure in the first thin-layer material
6. The method for calculating the sound absorption coefficient of the porous material with the periodically non-flat interface as claimed in claim 1, wherein the intensity coefficient vector of each order of eigenstates of reflected sound pressure and the intensity coefficient vector of each order of eigenstates of transmitted sound pressure are calculated by an iterative optimization algorithm according to the continuity condition of the boundary between layers; the specific process comprises the following steps:
the boundary continuity condition comprises that the sound pressure and the normal direction particle vibration speed are continuous;
normal direction particle vibration velocity vzExpression is
Wherein j is an imaginary unit; omega is angular frequency;
is the inverse of the normalized density;
expanding the reciprocal of the normalized density into a corresponding series form
Where ρ is0Is the air density; rhol(x) Is the equivalent density of the l lamellae;
is the expansion coefficient;
i-th order particle vibration velocity
The method comprises the following steps:
wherein, l is 1;
wherein,
an expansion coefficient that is the inverse of the normalized density;
the interfacial continuity conditions for the incident, reflective regions and the first layer of periodic porous material are:
the continuity conditions for the interfaces in between are:
the interfacial continuity conditions for the last layer of periodic porous material and the transmissive region are:
wherein R is selected from the group consisting ofCoefficient of radiation intensity RiA column vector of components; t is the transmission intensity coefficient TiA column vector of components;
intensity coefficients in the form of forward propagating eigenstates
A column vector of components; and
intensity coefficients in the form of counter-propagating eigenstates
A column vector of components; wlIs a feature vector
A constructed matrix, I being an identity matrix; deltai0Is a column vector with 0 order corresponding coefficient of 1 and other terms of 0; first thin layer matrix Vl＝ZlWlQlAnd matrix ZlIs an element of
First thin diagonal matrix Ql，ElAnd KzAre respectively an element
Element(s)
And element kziA matrix of compositions; wLAs feature vectors
A matrix of formations; eLAs feature vectors
A matrix of formations; l thin layer VL＝ZLWLQL；
Through matrix calculation, a matrix equation about the sound pressure reflection coefficient and the transmission coefficient is obtained:
calculating intensity coefficient vectors R of all orders of eigenstates of reflected sound pressure and intensity coefficient vectors T of all orders of eigenstates of transmitted sound pressure by adopting an iterative optimization algorithm; the method comprises the following specific steps:
the last four terms of the above matrix equation are expressed as:
introduces an iteration matrix fL+1And gL+1And has fL+1＝I，gL+1＝jKz(ii) a And then introducing the following iteration matrix:
wherein, aL、bLRespectively introducing a first column intermediate matrix and a second column intermediate matrix;
is provided with
The following relationships were obtained by collation:
then the iteration matrix expression is:
through iterative computation, a matrix equation is obtained:
solving the matrix equation to obtain R and T1；
Vector of transmission coefficients T1＝(g1+jKzf1)-1(jKzΔi0+jk0cosθΔi0)；
Intensity coefficient vector R ═ f of each order eigenstate of reflected sound pressure1T1-Δi0；
Intensity coefficient vector of each order eigenstate of transmission sound pressure
7. The method for calculating the sound absorption coefficient of the periodic non-flat interface porous material according to claim 6, wherein the total reflection coefficient and the total transmission coefficient are determined, and the sound absorption coefficient of the periodic non-flat interface porous material is calculated; the specific process comprises the following steps:
calculating the total reflection coefficient R:
wherein,
is the reflection intensity coefficient R in the intensity coefficient vector R of each order eigenstate of the reflection sound pressureiTaking conjugation;
calculating the total transmission coefficient T:
wherein,
transmission intensity coefficient T in intensity coefficient vector T of each order eigenstate of transmission sound pressureiTaking conjugation; re () is a real part;
calculating the sound absorption coefficient alpha of the porous material with the periodic uneven interface according to the calculated total reflection coefficient R and the total transmission coefficient T;
α＝1-R-T。
8. a device for measuring sound absorption coefficient of porous material with periodic non-flat interface is characterized in that the device comprises:
the acoustic parameter acquisition module is used for acquiring equivalent acoustic parameters of the porous material with the periodic uneven interface; wherein the equivalent acoustic parameters include: equivalent refractive index and equivalent density;
the layering module is used for layering the periodic non-flat interface porous material, and each thin layer material is equivalent to a periodic rectangular modulated acoustic material;
the eigen-state calculation module is used for acquiring the equivalent acoustic parameters of the porous material, expanding the sound pressure and the related acoustic parameters in the acoustic material which is equivalently modulated by the thin-layer material in a periodic rectangular mode into a hierarchical number expression form, bringing the hierarchical number expression form into an acoustic wave equation, and calculating the eigen-state form of the sound pressure in each thin-layer material;
the intensity coefficient calculation module is used for calculating intensity coefficient vectors of all orders of eigen state forms of the reflected sound pressure and intensity coefficient vectors of all orders of eigen state forms of the transmitted sound pressure by adopting an iterative optimization algorithm according to the interlayer boundary continuity condition; and
and the sound absorption coefficient acquisition module is used for determining the total reflection coefficient and the total transmission coefficient according to the calculation result and calculating the sound absorption coefficient of the porous material with the periodic non-flat interface.
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|---|---|---|---|---|
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| CN111651874A (en) * | 2020-05-25 | 2020-09-11 | 国网江西省电力有限公司电力科学研究院 | Method for calculating sound absorption performance of fiber material |
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Non-Patent Citations (3)
| Title |
|---|
| YUZHEN YANG ET AL.: "Study on asymmetric diffraction of acoustic parity-time-symmetric gratings using rigorous coupled-wave analysis", 《J. ACOUST. SOC. AM.》 * |
| 沈岳等: "活性炭纤维材料吸声性能预测模型", 《纺织学报》 * |
| 马晓文等: "梯度穿缝型双孔隙率多孔材料的吸声性能", 《声学学报》 * |
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| CN114371224A (en) * | 2021-12-03 | 2022-04-19 | 华南理工大学 | Test method for ABA structure random incidence sound absorption coefficient |
| CN114371224B (en) * | 2021-12-03 | 2023-08-22 | 华南理工大学 | Test method for random incidence sound absorption coefficient of ABA structure |
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