阅读说明：本技术 基于谱方法的粘弹性材料复纵波波速反演方法、设备 (Method and equipment for inverting complex longitudinal wave velocity of viscoelastic material based on spectrum method ) 是由 王斌 谭力文 范军 周富霖 黎洁 于 2020-07-03 设计创作，主要内容包括：本发明提供了一种基于谱方法的粘弹性材料复纵波波速反演方法、设备,包括：获取被测粘弹性材料,在水声声管中利用双水听器传递函数法测量该被测粘弹性材料的复反射系数R；根据测量得到的复反射系数R,计算被测粘弹性材料湿面的平面导纳Y；选取声压表达的基函数以及干面边界条件和湿面边界条件,结合计算得到的平面导纳Y,建立Sturm-Liouville方程,将被测粘弹性材料的复纵波波速求解问题化为成矩阵的特征值求解问题；筛选特征值,得到复纵波波速。本发明实现了复纵波波速的快速、稳健解算,相对传统搜根方法计算效率高,无需确定初值且不易丢根。(The invention provides a spectrum method-based viscoelastic material complex longitudinal wave velocity inversion method and equipment, which comprises the following steps: obtaining a viscoelastic material to be measured, and measuring a complex reflection coefficient R of the viscoelastic material to be measured in an underwater acoustic pipe by using a hydrophone transfer function method; calculating the plane admittance Y of the wet surface of the viscoelastic material to be measured according to the complex reflection coefficient R obtained by measurement; selecting a basis function of sound pressure expression, a dry surface boundary condition and a wet surface boundary condition, combining a plane admittance Y obtained by calculation, establishing a Sturm-Liouville equation, and solving a problem of complex longitudinal wave velocity of the tested viscoelastic material into a matrix eigenvalue solving problem; and screening the characteristic value to obtain the wave velocity of the complex longitudinal wave. The method realizes the rapid and steady resolving of the wave velocity of the complex longitudinal wave, has high calculation efficiency compared with the traditional root searching method, does not need to determine an initial value and is not easy to lose the root.)

1. A viscoelastic material complex longitudinal wave velocity inversion method based on a spectrum method is characterized by comprising the following steps:

s1: obtaining a viscoelastic material to be measured, and measuring a complex reflection coefficient R of the viscoelastic material to be measured in an underwater acoustic pipe by using a hydrophone transfer function method;

s2: calculating the plane admittance Y of the wet surface of the viscoelastic material to be measured according to the complex reflection coefficient R measured in the S1;

s3: selecting a basis function of sound pressure expression, a dry surface boundary condition and a wet surface boundary condition, combining a plane admittance Y obtained by calculation in S2, establishing a Sturm-Liouville equation by adopting a spectrum method, and converting a complex longitudinal wave velocity solving problem of the tested viscoelastic material into a matrix characteristic value solving problem; and screening the characteristic value to obtain the wave velocity of the complex longitudinal wave.

2. The method for inverting the complex longitudinal wave velocity of the viscoelastic material based on the spectrum method as claimed in claim 1, wherein in S1, the viscoelastic material to be tested has a cylindrical structure, and the backing material of the viscoelastic material to be tested is selected according to the requirement.

3. The method for inverting complex longitudinal wave velocity of viscoelastic material based on spectrum method according to claim 2, wherein said backing material comprises: a free backing, a rigid backing, and/or a resistive backing.

4. The method for inverting the complex longitudinal wave velocity of the viscoelastic material based on the spectrum method according to claim 1, wherein in S1, the method for measuring the hydrophone transfer function of the complex reflection coefficient R of the viscoelastic material to be measured in the underwater acoustic tube comprises the following steps: two hydrophones are arranged in the underwater acoustic tube, a transfer function between sound pressures received by the two hydrophones is calculated, and the complex reflection coefficient R of the viscoelastic material to be measured is calculated according to the transfer function.

5. The method for inverting complex longitudinal wave velocity of viscoelastic material based on spectrum method as claimed in claim 1, wherein in S2, the method for calculating plane admittance Y of wet surface of viscoelastic material to be tested comprises: according to the following formula:

calculating the plane admittance of the wet surface of the viscoelastic material to be measured, wherein rho₀、c₀The density and the sound velocity of water, respectively.

6. The method for inverting complex longitudinal wave velocity of viscoelastic material based on spectrum method as claimed in claim 1, wherein in S3, the expression of Sturm-Liouville equation is:

wherein x is a coordinate variable representing the horizontal distance from any point in the viscoelastic material to the dry surface, p (x) represents the field point sound pressure varying with x,representing (-) the second derivative, k, with respect to the variable x_dRepresents the complex longitudinal wave number of the viscoelastic material to be tested.

7. The method for inverting the complex longitudinal wave velocity of the viscoelastic material based on the spectrum method as claimed in claim 1, wherein in S3, the wet boundary condition p (d) is:

wherein j is an imaginary unit and j²-1, ω is the angular frequency, ρ is the density of the viscoelastic material under test,

according to different backing materials of the tested viscoelastic material, the boundary conditions corresponding to different dry surfaces are respectively as follows:

wherein, Y₀Is the complex admittance of the backing material.

8. The method for inverting the complex longitudinal wave velocity of the viscoelastic material based on the spectrum method as claimed in claim 1, wherein in S3, the method for selecting the basis function of the sound pressure expression comprises: the internal sound field is expressed as a series form p (x) as follows:

wherein a is_nIn order to be the coefficient of expansion,

9. The method for inverting the complex longitudinal wave velocity of the viscoelastic material based on the spectrum method as claimed in claim 1, wherein in S3, the method for transforming the complex longitudinal wave velocity solution problem of the viscoelastic material to be tested into the eigenvalue solution problem of the matrix, and screening the eigenvalues to obtain the complex longitudinal wave velocity comprises:

combining the basis function and a Sturm-Liouville equation, and sorting out a matrix equation form of the undetermined coefficients expanded by the basis function according to the dry surface boundary condition and the wet surface boundary condition as follows:

wherein, { A_(N+1)×1Is the expansion coefficient a_nComposed column vector [ a₀,a₁,…,a_N]^TN is the truncation order, B_(N+1)×(N+1)A coefficient matrix which is a matrix equation;

calculating matrix eigenvalue, i.e. square of wave number of corresponding complex longitudinal wave

10. An apparatus comprising a memory, a processor and a computer program stored on the memory and operable on the processor, wherein the computer program, when executed by the processor, is operable to perform the method of any of claims 1 to 9.

Technical Field

The invention relates to the technical field of acoustics, in particular to a spectrum method-based viscoelastic material complex longitudinal wave velocity inversion method and equipment.

Background

The acoustic covering layer is widely applied to vibration suppression, noise reduction and noise elimination of an underwater vehicle by virtue of excellent acoustic performance, and the structure of the acoustic covering layer usually takes viscoelastic damping materials such as rubber and the like as a matrix, and special acoustic structures such as cavities and the like which are artificially designed are embedded in the viscoelastic damping materials so as to improve the low-frequency sound absorption performance or enable the materials to have broadband sound absorption performance. The accurate and rapid acquisition of the dynamic parameters of the viscoelastic material is important for the development, design, evaluation and optimization of the acoustic covering layer.

The dynamic parameter measuring method of the viscoelastic material is generally divided into two categories, one category is a vibration measuring method for calculating the mechanical parameters of the viscoelastic material by measuring the vibration characteristics of the material, and the vibration measuring method comprises a mass loading method, a vibration beam method, a laser vibration measuring method, a dynamic viscoelastic spectrometer method and the like, wherein the mechanical method is simple and mature, but the defects that the test frequency band is low, the requirement on sample manufacture is high, and the viscoelastic material is difficult to measure are also prominent; the other type is an acoustic measurement method for obtaining mechanical parameters or acoustic parameters of a material by measuring acoustic characteristics of the material, wherein when the complex longitudinal wave velocity is inverted according to a complex reflection coefficient measured by a cylindrical sound tube, the traditional root searching method for solving the Sturm-Liouville equation faces bottleneck problems of initial value dependence, low calculation efficiency, easy root leakage and the like.

At present, no explanation or report of the similar technology of the invention is found, and similar data at home and abroad are not collected.

Disclosure of Invention

The invention provides a spectrum method-based viscoelastic material complex longitudinal wave velocity inversion method and equipment aiming at low efficiency, easy root leakage and initial value dependence of a traditional root searching method.

The invention is realized by the following technical scheme.

According to one aspect of the invention, a method for inverting the complex longitudinal wave velocity of a viscoelastic material based on a spectrum method is provided, which comprises the following steps:

s1: obtaining a viscoelastic material to be measured, and measuring a complex reflection coefficient R of the viscoelastic material to be measured in an underwater acoustic pipe by using a hydrophone transfer function method;

s2: calculating the plane admittance Y of the wet surface of the viscoelastic material to be measured according to the complex reflection coefficient R measured in the S1;

s3: selecting a basis function of sound pressure expression, a dry surface boundary condition and a wet surface boundary condition, combining a plane admittance Y obtained by calculation in S2, establishing a Sturm-Liouville equation by adopting a spectrum method, and converting a complex longitudinal wave velocity solving problem of the tested viscoelastic material into a matrix characteristic value solving problem; and screening the characteristic value to obtain the wave velocity of the complex longitudinal wave.

Preferably, in S1, the viscoelastic material to be tested has a cylindrical structure, and the backing material of the viscoelastic material to be tested is selected according to the requirement.

Preferably, the backing material comprises: a free backing, a rigid backing, and/or a resistive backing.

Preferably, in S1, the method for measuring the complex reflection coefficient R of the viscoelastic material to be measured in the underwater acoustic tube by using a hydrophone transfer function includes: two hydrophones are arranged in the underwater acoustic tube, a transfer function between sound pressures received by the two hydrophones is calculated, and the complex reflection coefficient R of the viscoelastic material to be measured is calculated according to the transfer function.

Preferably, in S2, the method for calculating the planar admittance Y of the wet side of the viscoelastic material to be measured includes: according to the following formula:

calculating the plane admittance of the wet surface of the viscoelastic material to be measured, wherein rho₀、c₀The density and the sound velocity of water, respectively.

Preferably, in S3, the expression of the Sturm-Liouville equation is:

wherein x is a coordinate variable representing the horizontal distance from any point in the viscoelastic material to the dry surface, p (x) represents the field point sound pressure varying with x,representing (-) a second derivative with respect to a variable xNumber, k_dRepresents the complex longitudinal wave number of the viscoelastic material to be tested.

Preferably, in S3, the wet-face boundary condition p (d) is:

wherein j is an imaginary unit and j²-1, ω is the angular frequency, ρ is the density of the viscoelastic material under test,

is (-) with respect to the first derivative of the variable x, d is the thickness of the viscoelastic material being measured;

according to different backing materials of the tested viscoelastic material, the boundary conditions corresponding to different dry surfaces are respectively as follows:

wherein, Y₀Is the complex admittance of the backing material.

Preferably, in S3, the method for selecting a basis function of the sound pressure expression includes: the internal sound field is expressed as a series form p (x) as follows:

wherein a is_nIn order to be the coefficient of expansion,

is at [0, d]The basis of the orthogonal function defined in (1), i.e. the basis function of the sound pressure expression, the basis function satisfying

Wherein_nn′In the form of a Dirac function, the function,meanwhile, the selected basis function meets the requirement of dry surface edgeAnd (4) boundary conditions.

Preferably, in S3, the method for converting the complex longitudinal wave velocity solution problem of the viscoelastic material to a matrix eigenvalue solution problem, and screening eigenvalues to obtain the complex longitudinal wave velocity includes:

combining the basis function and a Sturm-Liouville equation, and sorting out a matrix equation form of the undetermined coefficients expanded by the basis function according to the dry surface boundary condition and the wet surface boundary condition as follows:

wherein, { A_(N+1)×1Is the expansion coefficient a_nComposed column vector [ a₀,a₁,…,a_N]^TN is the truncation order, B_(N+1)×(N+1)A coefficient matrix which is a matrix equation;

calculating matrix eigenvalue, i.e. square of wave number of corresponding complex longitudinal waveThen, the product of reciprocal and angular frequency is taken to obtain the square of the wave velocity of complex longitudinal wave

According to another aspect of the invention, there is provided an apparatus comprising a memory, a processor and a computer program stored on the memory and operable on the processor, the processor being operable when executing the computer program to perform any of the methods described above.

Compared with the prior art, the invention has the following beneficial effects:

according to the viscoelastic material complex longitudinal wave velocity inversion method and equipment based on the spectrum method, provided by the invention, the relation between the complex reflection coefficient measured by the underwater sound tube and the plane admittance is utilized, the spectrum method is introduced to solve the Sturm-Liouville equation, the complex plane root searching problem of the intrinsic equation is converted into the characteristic value decomposition problem, the fast and steady resolving of the complex longitudinal wave velocity is realized, the calculation efficiency is high compared with that of the traditional root searching method, the initial value does not need to be determined, and the root is not easy to lose.

The spectrum method-based viscoelastic material complex longitudinal wave velocity inversion method and equipment provided by the invention can be used for evaluating the shear modulus or shear wave velocity of a viscoelastic material and providing input parameters for the optimized design of the viscoelastic material and the underwater acoustic performance evaluation of a laid viscoelastic material structure.

Drawings

Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:

fig. 1 is a flowchart of a complex longitudinal wave velocity inversion method for a viscoelastic material based on a spectrum method according to a preferred embodiment of the present invention;

fig. 2 is a schematic diagram of an apparatus for an underwater acoustic hydrophone-in-tube method according to a preferred embodiment of the invention;

fig. 3 is a graph of a change of a complex reflection coefficient with frequency in a complex longitudinal wave velocity inversion method of a viscoelastic material based on a spectrum method according to a preferred embodiment of the present invention;

fig. 4 is a diagram of real parts of longitudinal wave velocity at different frequencies in a complex longitudinal wave velocity inversion method for a viscoelastic material based on a spectrum method according to a preferred embodiment of the present invention;

fig. 5 is a diagram of an imaginary part of longitudinal wave velocity at different frequencies in a complex longitudinal wave velocity inversion method for a viscoelastic material based on a spectrum method according to a preferred embodiment of the present invention.

Detailed Description

The following examples illustrate the invention in detail: the embodiment is implemented on the premise of the technical scheme of the invention, and a detailed implementation mode and a specific operation process are given. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention.

An embodiment of the present invention provides a method for inverting a complex longitudinal wave velocity of a viscoelastic material based on a spectrum method, as shown in fig. 1, the method includes the following steps:

step 1: obtaining a viscoelastic material to be measured, and measuring a complex reflection coefficient R of the viscoelastic material to be measured in an underwater acoustic pipe by using a hydrophone transfer function method;

step 2: calculating the plane admittance Y of the wet surface of the viscoelastic material to be measured according to the complex reflection coefficient obtained by measurement in the step 1;

and step 3: selecting a basis function of sound pressure expression, a dry surface boundary condition and a wet surface boundary condition, combining the plane admittance Y obtained by calculation in the step 2, establishing a Sturm-Liouville equation by adopting a spectrum method, and solving the problem of complex longitudinal wave velocity of the viscoelastic material to be measured into a matrix eigenvalue solving problem; and screening the characteristic value to obtain the wave velocity of the complex longitudinal wave.

As a preferred embodiment, in step 1, the viscoelastic material to be tested has a cylindrical structure, and the backing material of the viscoelastic material to be tested is selected according to the requirement.

As a preferred embodiment, the backing material comprises: a free backing, a rigid backing, and/or a resistive backing.

As a preferred embodiment, in step 1, a method for measuring a hydrophone transfer function of a complex reflection coefficient R of a viscoelastic material to be measured in an underwater acoustic pipe includes: referring to fig. 2, 2 hydrophones are arranged in the hydroacoustic tube, and the sound pressures received by the hydrophones are respectively recorded as p₁、p₂And calculating the transfer functions of the two:wherein H₁₂Is the amplitude of the transfer function, theta is the phase of the transfer function, | p₁|、|p₂| are the amplitude values of the received sound pressures respectively,respectively, the phases of the received sound pressures. And further calculating the complex reflection coefficient R of the tested viscoelastic material:wherein d is₁、d₂The distance between the two hydrophones and the wet surface of the viscoelastic material to be measured.

As a preferred embodiment, in step 2, the formula for calculating the plane admittance Y of the wet side of the viscoelastic material to be measured includes: according to the formula

Calculating the plane admittance of the wet surface of the viscoelastic material to be measured, wherein rho₀、c₀The density and the sound velocity of water, respectively.

As a preferred embodiment, in step 3, the expression of Sturm-Liouville equation is: when the complex reflection coefficient of the tested viscoelastic material is measured in the underwater sound tube, the incident sound wave can be approximate to a plane wave, only longitudinal waves propagate in the tested viscoelastic material, and the sound pressure p (x) in the tested viscoelastic material meets Sturm-Liouville equationWherein k is_dThe wave number of complex longitudinal wave of the viscoelastic material to be measured and the corresponding relation of the wave speed of the complex longitudinal wave are

Where f is the measurement frequency. Therefore, the wave velocity c of the complex longitudinal wave in this embodiment_dCan be equivalent to the complex longitudinal wave number k_dAnd (4) calculating.

As a preferred embodiment, in step 3, the dry-side boundary condition and the wet-side boundary condition are respectively: when a coordinate system is selected in the established Sturm-Liouville equation, the origin is located on the dry surface of the viscoelastic material to be measured, and x is 0 and corresponds to the dry surface, and x is d and corresponds to the wet surface. The boundary conditions on the wet side were:where ρ is the density of the viscoelastic material being measured. For different backing materials, corresponding to different dry-side boundary conditions:

wherein Y is₀Is the complex admittance of the backing material.

As a preferred embodiment, in step 3The method for selecting the basis function of the sound pressure expression in the tested viscoelastic material comprises the following steps: as the displacement inside the viscoelastic material to be detected is continuous at all positions and meets the continuous condition of the first derivative, the basis function can be selectedPerforming multi-mode orthogonal expansion on the internal sound field, namely expressing the internal sound field into a series form:

wherein a is_nIn order to be the coefficient of expansion,is at [0, d]The orthogonal function base defined in (1), which satisfies

The basis function can be selected from sine function, cosine function, Chebyshev polynomial, and the basis function satisfying the boundary condition of dry surface as much as possible, such as selecting the basis function under the condition of free backingIn the case of rigid backing, the basis functions are selectedIn the case of an impedance background, the same basis function can be chosen as in the case of a free backing; wherein x is a coordinate variable and represents the horizontal distance from any point in the tested viscoelastic material to the dry surface, and d is the thickness of the tested viscoelastic material and is the order of the basis function.

As a preferred embodiment, in step 3, the method for solving the problem of the complex longitudinal wave velocity of the viscoelastic material to be tested into a matrix eigenvalue solution problem, and screening the eigenvalues to obtain the complex longitudinal wave velocity includes: taking free backing as case analysis, and expressing the series of the viscoelastic materials to be detectedSubstituted into Sturm-Liouville equation, and multiplied byAnd is in [0, d ]]The upper integral, according to the boundary condition of the dry surface and the wet surface, can obtain:

arranged to obtain a coefficient of expansion a_nAnd taking the first N orders to perform truncation to obtain:

wherein, { A_(N+1)×1Is the expansion coefficient a_nComposed column vector

Can find that [ B ] is_(N+1)×(N+1)]Decomposing the eigenvalue to obtain the square of the wave number of complex longitudinal wave

Then, the product of reciprocal and angular frequency is taken to obtain the square of the wave velocity of complex longitudinal wave

In order to fully verify the effectiveness of the method provided by the embodiment of the present invention, a numerical sound tube is established by using CommolMultiphysics finite element software, and the complex reflection coefficients R of viscoelastic materials of different backing materials are calculated to obtain a graph of the variation of the complex reflection coefficients with frequency as shown in FIG. 3

According to the method flow shown in fig. 1, the Sturm-Liouville equation complex plane root search problem is converted into a eigenvalue solution problem, that is, the complex longitudinal wave velocity solution problem of the viscoelastic material to be measured is converted into a matrix eigenvalue solution problem, and the real part and the imaginary part of the inverse complex longitudinal wave velocity are calculated, as shown in fig. 4 and fig. 5. In the figure, the truncation number M of the matrix is 500, and the first 5 th order eigenvalues are retained. In the figure, the solid line is the theoretical value, and the five symbols in the figure represent the first five eigenvalues in amplitude order, respectively, and it can be seen that the first order eigenvalues agree well with the theoretical value.

As can be seen from fig. 4 and 5, the method provided by the embodiment of the invention can rapidly invert the complex longitudinal wave velocity of the viscoelastic material, has high calculation efficiency compared with the conventional root searching method, does not need to determine an initial value, and is not easy to lose roots.

A specific application example of the method provided by the embodiment of the present invention is given below.

Preparing a uniform viscoelastic material sample to be measured, measuring the complex reflection coefficient in the underwater acoustic tube, and rapidly inverting the longitudinal wave velocity by using the method. As a key input parameter, substituting the longitudinal wave velocity inverted by the method provided by the embodiment of the invention into a viscoelastic material finite element calculation model, and analyzing the influence of the acoustic performance of the viscoelastic material; or substituting the longitudinal wave velocity into a laying viscoelastic material structure acoustic radiation and scattering finite element calculation model, analyzing the radiation sound source level or the target intensity, and evaluating the acoustic stealth performance and the influence of the viscoelastic material.

Another embodiment of the invention provides an apparatus comprising a memory, a processor, and a computer program stored on the memory and capable of running on the processor, the processor being capable of performing the method of any of the above embodiments when executing the computer program.

Optionally, a memory for storing a program; a Memory, which may include a volatile Memory (abbreviated RAM), such as a Random-Access Memory (RAM), a static Random-Access Memory (SRAM), a Double Data Rate Synchronous Dynamic Random Access Memory (DDR SDRAM), and the like; the memory may also comprise a non-volatile memory, such as a flash memory. The memory 62 is used to store computer programs (e.g., applications, functional modules, etc. that implement the above-described methods), computer instructions, etc., which may be stored in one or more memories in a partitioned manner. And the computer programs, computer instructions, data, etc. described above may be invoked by a processor.

The computer programs, computer instructions, etc. described above may be stored in one or more memories in a partitioned manner. And the computer programs, computer instructions, data, etc. described above may be invoked by a processor.

A processor for executing the computer program stored in the memory to implement the steps of the method according to the above embodiments. Reference may be made in particular to the description relating to the preceding method embodiment.

The processor and the memory may be separate structures or may be an integrated structure integrated together. When the processor and the memory are separate structures, the memory, the processor may be coupled by a bus.

According to the inversion method and the inversion device for the complex longitudinal wave velocity of the viscoelastic material based on the spectrum method, provided by the embodiment of the invention, the relation between the complex reflection coefficient and the plane admittance measured by the underwater acoustic tube is utilized, the spectrum method is introduced to solve the Sturm-Liouville equation, the problem of searching the root of the complex plane of the eigen equation is converted into the problem of resolving the characteristic value, the fast and steady calculation of the complex longitudinal wave velocity is realized, the calculation efficiency is high compared with that of the traditional root searching method, the initial value does not need to be determined, and the root is not easy to lose. The spectrum method-based viscoelastic material complex longitudinal wave velocity inversion method provided by the embodiment of the invention evaluates the shear modulus or shear wave velocity of the viscoelastic material, and provides input parameters for the optimized design of the viscoelastic material and the underwater acoustic performance evaluation of the laid viscoelastic material structure.

The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes and modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention.