Sound velocity calculation method and system based on pulse tube experiment

Abstract

The invention provides a sound velocity calculation method and system based on a pulse tube experiment, and relates to the technical field of sound velocity measurement, and the method comprises the steps: obtaining a first complex reflection coefficient of a tested sample under an air backing and a second complex reflection coefficient of the tested sample under a rigid backing through the pulse tube experiment; based on the first complex reflection coefficient and the second complex reflection coefficient, a real part and an imaginary part of a calculation result are obtained through combination; obtaining the density of water, the sound velocity and the frequency in the water, the density of the tested sample and the thickness of the tested sample, and calculating to obtain a constant term; and according to the thickness, the real part, the imaginary part, the constant term and the frequency of the tested sample, calculating the sound velocity and the attenuation coefficient of the tested sample. According to the method, the technical problems of unstable numerical value, low calculation efficiency and inaccurate result caused by difficulty in solving a transcendental equation in sound velocity calculation of an existing pulse tube experimental method are solved.

Description

Technical Field

[0001] This invention relates to the field of sound velocity measurement technology, and in particular to a sound velocity calculation method and system based on pulse tube experiments, which can be used to measure the sound velocity of any structure. Background Technology

[0002] Accurate measurement of structural acoustic velocity is a crucial foundation for achieving acoustic metasurface design and acoustic impedance matching. Currently, the main methods for measuring structural acoustic velocity include the pulse tube experiment and the transient method. The pulse tube experiment-based method primarily establishes the relationship between input acoustic impedance and reflection coefficient by measuring the reflection coefficient of the sample under air backing (soft acoustic end) and rigid backing (hard acoustic end) conditions, thereby solving for the acoustic velocity and attenuation coefficient. However, this method involves transcendental equations, including two unknown variables: acoustic velocity and attenuation coefficient. During numerical solutions, due to the nonlinear nature of the equations, it often relies on numerical iterative algorithms such as gradient descent, which can easily get trapped in local optima, leading to inaccurate and unstable calculation results. Furthermore, experimental measurement errors further exacerbate the inconsistency between the results under the two backing conditions, making it difficult to guarantee the self-consistency of the acoustic velocity and attenuation coefficient. In addition, although the transient method can directly calculate the acoustic velocity through time difference, it requires both transmitting and receiving devices, making the system complex and low-frequency measurements difficult.

[0003] Therefore, existing methods have significant limitations in terms of numerical stability, accuracy, efficiency, and applicability. Summary of the Invention

[0004] To address the aforementioned problems, this invention provides a method and system for calculating the speed of sound based on pulse tube experiments. The aim is to solve the technical problems of numerical instability, low computational efficiency, and inaccurate results caused by the difficulty in solving transcendental equations in existing pulse tube experimental methods for calculating the speed of sound.

[0005] In a first aspect, the present invention provides a method for calculating the velocity of sound based on a pulse tube experiment, the method comprising: The first complex reflection coefficient of the test sample under air backing and the second complex reflection coefficient under rigid backing were obtained using a pulse tube experiment. Based on the first complex reflection coefficient and the second complex reflection coefficient, the real part and imaginary part of the calculation result are obtained together; The density of water, the speed of sound in water, the frequency, the density of the test sample, and the thickness of the test sample are obtained, and the constant term is calculated. The sound velocity and attenuation coefficient of the test sample are calculated based on the thickness, real part, imaginary part, constant term, and frequency of the test sample.

[0006] Furthermore, the real part and the virtual part They are respectively: ; in, This represents the magnitude of the first complex reflection coefficient; This represents the magnitude of the second complex reflection coefficient; The phase angle represents the first complex reflection coefficient; The phase angle represents the second complex reflection coefficient.

[0007] Furthermore, the constant term The calculation formula is: ; in, Indicates the density of water; Indicates the speed of sound in water; Indicates frequency; Indicates the density of the tested sample; This indicates the thickness of the sample being tested.

[0008] Furthermore, the sound speed of the tested sample The calculation formula is: ,and ; in, This represents the attenuation coefficient of the tested sample; Indicates frequency; Indicates the thickness of the tested sample; Represents the constant term; Denotes the real part; This represents the imaginary part.

[0009] Furthermore, the attenuation coefficient of the tested sample The calculation formula is: ,and .

[0010] Furthermore, based on the first complex reflection coefficient and the second complex reflection coefficient, the real and imaginary parts of the calculation result are jointly obtained, specifically including: The first relationship between the sound velocity and attenuation coefficient of the test sample under air backing and the modulus and phase angle of the first complex reflection coefficient, and the second relationship between the sound velocity and attenuation coefficient of the test sample under rigid backing and the modulus and phase angle of the second complex reflection coefficient are obtained respectively. make And because Then, multiplying the transformed first and second relations yields the first formula: ; The first formula and After being disassembled separately, the air backing was obtained. The first simplified form and under the rigid backing The second simplified form; The real and imaginary parts of the first formula are obtained by combining the first and second simplified expressions.

[0011] Furthermore, the first simplified formula is: ; The second simplified form is: .

[0012] Furthermore, the method for calculating the sound velocity of the test sample specifically includes: Based on the real part, the imaginary part, and the constant term, the first formula is rewritten as the second formula: ; Will Substituting into the second formula, we obtain the third formula; By decomposing both sides of the third equation into real and imaginary parts, and ensuring that the real and imaginary parts on both sides of the equation are equal, the sound velocity and attenuation coefficient of the tested sample can be calculated.

[0013] Furthermore, the first and second complex reflection coefficients are obtained through any of the following methods: experimental measurement, finite element simulation, or theoretical calculation.

[0014] In a second aspect, the present invention provides a sound speed calculation system based on a pulse tube experiment, comprising a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of any of the methods described above.

[0015] In summary, this invention provides a method and system for calculating the speed of sound based on pulse tube experiments. Compared with existing technologies, the technical solution conceived in this invention can achieve the following beneficial effects: (1) This invention combines the reflection coefficient data under two backing conditions to construct an analytical formula including real and imaginary parts, and transforms the solution of sound velocity and attenuation coefficient into a direct calculation process through analytical means; it not only effectively avoids the numerical instability problem caused by solving transcendental equations using a single set of data in traditional methods, but also eliminates the inconsistency problem when solving under a single backing condition, so that sound velocity and attenuation coefficient have a unified physical meaning in the whole frequency band, ensuring that the sound velocity and attenuation coefficient results calculated under different backing conditions are consistent and unified, and significantly improving the consistency, accuracy and reliability of the calculation results.

[0016] (2) This invention transforms the complex transcendental equation problem that traditionally requires iterative numerical solution into an analytical expression based on explicit algebraic relations without unknowns; it directly solves the speed of sound and attenuation coefficient through algebraic operations, which not only saves the time-consuming iterative process and avoids the risk of local optima in the iterative method, but also significantly improves the accuracy and efficiency of calculation, and realizes the fast and direct solution of the speed of sound; it is particularly suitable for scenarios that require rapid analysis or processing of a large amount of frequency data.

[0017] (3) The present invention only requires the magnitude and phase of the complex reflection coefficient of any structure as input, without the need for complex transmission and reception dual devices to measure the time difference as in the transient method. It can achieve accurate calculation of sound velocity and obtain parameters such as the sound absorption coefficient of the material simultaneously. It reduces the requirements for experimental equipment, simplifies the measurement process, and makes sound velocity measurement easier to realize on conventional pulse tube experimental platforms, thus reducing the technical threshold and implementation cost.

[0018] (4) This invention is applicable to any structural type. The reflection coefficient can be obtained through experiments, simulations or theoretical analysis. It does not depend on a specific model and has strong versatility. At the same time, based on the same reflection coefficient data, this method can not only calculate the sound velocity, but also synchronously and conveniently obtain various acoustic parameters such as the attenuation coefficient and even the sound absorption coefficient. It realizes one measurement and multi-parameter analysis, providing an efficient and universal solution for acoustic material design and performance evaluation, and enriching the data output and application value of pulse tube experiments. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0020] Figure 1 This is a schematic diagram of the method steps of a sound velocity calculation method and system based on a pulse tube experiment provided by the present invention; Figure 2 This is a schematic diagram of an experimental apparatus for measuring sound velocity using a pulse tube experiment, which is a method and system for calculating sound velocity based on a pulse tube experiment provided by this invention. Figure 3 This is a schematic diagram of a hollow cylindrical sample structure provided by the present invention; Figure 4 This is a schematic diagram showing the real and imaginary parts of the complex reflection coefficient of a hollow cylindrical tube under air and rigid backing as a function of frequency, provided by the present invention. Figure 5This is a schematic diagram comparing the sound velocity calculation method and system based on pulse tube experiments provided by this invention with the theoretical calculation results of the attenuation coefficient. Figure 6 This is a schematic diagram comparing the sound velocity calculation method and system based on pulse tube experiments provided by this invention with the theoretical calculation results of sound velocity. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings and embodiments. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0022] It should be noted that, in the description of the embodiments of the present invention, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a method, step, or apparatus that includes a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to the method, step, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of additional identical elements in the method, step, or apparatus that includes the element.

[0023] Due to the relationship between the test wavelength and the structural dimensions, it is very difficult to experimentally measure the structural sound velocity at low frequencies, but obtaining the reflection coefficient is very easy. Therefore, this invention provides a sound velocity calculation method and system based on pulse tube experiments. Instead of solving transcendental equations, it integrates reflection coefficient data under two backing conditions after obtaining the reflection coefficient, and transforms the solution of sound velocity and attenuation coefficient into a calculation process through analytical means, directly calculating the sound velocity value. This calculation method simplifies the sound velocity testing method, avoids the uncertainty of iterative algorithms, and solves the technical problems of numerical instability, low calculation efficiency, and inaccurate results caused by the difficulty of solving transcendental equations in existing pulse tube experimental methods for sound velocity calculation, thereby improving the consistency and reliability of measurement results.

[0024] Specifically, such as Figure 1 As shown, the method includes: S100: The first complex reflection coefficient of the test sample under air backing and the second complex reflection coefficient under rigid backing were obtained using a pulse tube experiment.

[0025] It should be noted that the test sample can be an acoustic material of any structure.

[0026] Specifically, the magnitude and phase angle of the complex reflection coefficient of any structure under air backing and rigid backing can be obtained through any of the following methods: experimental measurement, finite element simulation, or theoretical calculation.

[0027] like Figure 2 The diagram shows an experimental setup for measuring sound velocity using the pulse tube method. It mainly includes a pulse tube experimental setup and a signal processing and control system. The two work together to accurately measure the acoustic characteristic parameters of the sample being tested.

[0028] The pulse tube experimental setup includes: The pulse tube cavity is filled with water as the sound wave propagation medium; and one end of the tube is a rigid backing to provide ideal acoustic hard boundary conditions. The test sample contains an acoustic material or structural sample to be tested inside the pulse tube; The transducer, as a sound source, is located at the bottom of the pulse tube and is used to convert electrical signals into sound wave signals, emitting pulsed sound waves of a specific frequency into the tube.

[0029] The hydrophone, located inside the pulse tube, includes two high-precision sound pressure sensors arranged along the direction of sound wave propagation; it is used to receive incident sound waves and reflected sound wave signals after being reflected by the sample, and is a key component for acquiring raw acoustic data.

[0030] Signal processing and control include: A signal processor is used to generate the required initial electrical signal; The power amplifier is used to receive weak electrical signals from the signal processor, amplify them, and drive the transducer at the bottom. The data acquisition and analysis system is used to acquire voltage signals from hydrophone 1 and hydrophone 2, and calculate the complex reflection coefficient (including magnitude and phase) of the sample surface by analyzing the amplitude and phase difference of the two signals. The computer, as the central control and computing center, controls the entire measurement process and receives complex reflection coefficient data from the data acquisition system. Based on the sound velocity calculation method of this invention, the computer runs dedicated software to directly analyze and calculate the acoustic characteristic parameters of the sample, such as sound velocity and attenuation coefficient.

[0031] The workflow of the pulse tube experimental method for measuring sound velocity is as follows: During operation, the computer-controlled signal processor generates a signal, which is amplified by the power amplifier and drives the transducer to emit sound waves; the sound waves propagate in the water-filled pulse tube and are reflected when they encounter the test sample; hydrophones 1 and 2 record the sound wave information respectively, the data acquisition system calculates the complex reflection coefficient based on this, and finally the computer completes the accurate calculation of the sound velocity using the analytical algorithm proposed in this invention.

[0032] It should be noted that when a plane wave enters the pulse tube, according to acoustic theory, the input acoustic impedance of the test sample can be determined under both air-backed and rigid-backed conditions.

[0033] When the end of the test sample is an air-backed terminal (i.e., an acoustic soft terminal), the input acoustic impedance of the test sample is calculated as follows: ; When the end of the test sample is a rigid backing (i.e., an acoustic hard end), the input acoustic impedance of the test sample is calculated as follows: ; in, Represents the imaginary unit; Indicates frequency; Indicates the density of the tested sample; Indicates the attenuation coefficient; Indicates the speed of sound of the tested sample; Indicates the thickness of the tested sample; The hyperbolic tangent function describes the standing wave effect caused by multiple reflections at the front and rear ends of a wave as it propagates in a plate of finite thickness. Let represent the hyperbolic cotangent function. Since the boundary condition at the end changes from zero sound pressure to zero velocity, therefore... The function describing the standing wave effect changes from hyperbolic tangent to hyperbolic cotangent.

[0034] It should be noted that, and Both describe a longitudinal wave at a thickness of The propagation of sound waves in solid materials is derived from theoretical models of sound wave propagation in solid materials, linking the input acoustic impedance to the intrinsic properties of the tested sample. Among these, The end of the test sample is air or a vacuum, and the acoustic impedance is much smaller than that of the sample. At the end, the sound pressure is approximately zero, so it is considered a soft boundary. The end of the test sample is firmly attached to a rigid wall. At the end, the vibration velocity of the particle is zero, so it is considered a hard boundary.

[0035] The input acoustic impedance is calculated from the complex reflection coefficient of the front interface of the test sample. Therefore, the calculation method for the input acoustic impedance of the test sample is as follows: ; in, Indicates the density of water; Indicates the speed of sound in water; Represents the complex reflection coefficient, used to describe reflection behavior; The magnitude of the complex reflection coefficient is used to describe the amplitude attenuation of the reflected wave. The phase angle represents the complex reflection coefficient and is used to describe the phase change of the reflected wave relative to the incident wave.

[0036] It should be noted that, This paper describes how to calculate the input acoustic impedance of a sample by experimentally measuring the reflection coefficient. When a plane wave in a pulse tube is incident perpendicularly to the surface of the test sample, a portion of the sound wave is reflected back. By measuring the amplitude and phase of the incident and reflected waves using a hydrophone, the modulus can be obtained. and phase angle This allows for the direct calculation of the input acoustic impedance of the surface of the tested sample, without relying on any intrinsic properties of the tested sample.

[0037] In other words, for an acoustic soft terminal, the modulus of the first complex reflection coefficient under air backing is obtained. and phase angle For acoustic hard ends, the modulus of the second complex reflection coefficient under a rigid backing is obtained. and phase angle .

[0038] S200: Based on the first complex reflection coefficient and the second complex reflection coefficient, the real part and imaginary part of the calculation result are obtained by combining them.

[0039] As one embodiment, based on the first complex reflection coefficient and the second complex reflection coefficient, the real part and imaginary part of the calculation result are jointly obtained, specifically including: S2001: Obtain the first relationship between the sound velocity and attenuation coefficient of the test sample under air backing and the modulus and phase angle of the first complex reflection coefficient, and the second relationship between the sound velocity and attenuation coefficient of the test sample under rigid backing and the modulus and phase angle of the second complex reflection coefficient.

[0040] It should be noted that by combining these three formulas for calculating the input acoustic impedance of the front surface of the test sample, the sound velocity of the test sample under the two end boundary conditions can be obtained. and attenuation coefficient With the magnitude of the complex reflection coefficient and phase angle The relational expression.

[0041] For acoustic soft terminals, based on We can obtain the first relation: ; For acoustic hard terminals, based on We can obtain the second relation: ; in, , These represent the magnitude and phase angle of the complex reflection coefficient under the acoustic soft terminal, respectively, which are also the magnitude and phase angle of the first complex reflection coefficient; , These represent the magnitude and phase angle of the complex reflection coefficient under acoustic hard ends, respectively, which are also the magnitude and phase angle of the second complex reflection coefficient.

[0042] It should be noted that both the first and second relations after the equations are formed contain two unknowns: the speed of sound. and attenuation coefficient The first or second relation is itself a complex transcendental equation that cannot be solved analytically directly.

[0043] In numerical solutions, due to the nonlinear nature of the equations, existing methods often rely on numerical iterative algorithms such as gradient descent. However, this method is computationally complex, slow, and prone to getting trapped in local optima due to improper initial value selection, leading to inaccurate results. Furthermore, the sound velocity calculated using air-backed and rigid-backed data respectively... and attenuation coefficient They may not be entirely consistent in theory, and there may be inconsistencies.

[0044] Therefore, after obtaining the first complex reflection coefficient of the test sample under an air backing and the second complex reflection coefficient under a rigid backing using a pulse tube experiment, this invention does not process the equations for the air backing or the rigid backing separately, but combines the two equations to eliminate the difficult-to-solve hyperbolic function, and directly uses the real and imaginary parts to calculate the structural sound velocity and attenuation coefficient. Thus, it is possible to directly calculate the sound velocity value without solving transcendental equations.

[0045] S2002: Order And because Then, multiplying the transformed first and second relations yields the first formula: .

[0046] It should be noted that variables It is a complex number that incorporates the real part. The attenuation and the imaginary part are reflected This reflects the phase change in wave propagation.

[0047] The specific method for obtaining the first formula is as follows: variables Substituting these into the first and second relations respectively, we obtain the first model expression. Second model ; Multiply the collateral edges of the equations of the first and second models respectively, based on , This simplifies to the first formula.

[0048] By multiplying both sides of the first and second model expressions, using and The property of reciprocals eliminates the difficulty of handling transcendental functions. and I got a result about The relationship includes only known experimental measurements: , , , And material constants. This transforms the problem from solving transcendental equations to substituting known quantities into a complex expression and then directly calculating... .

[0049] S2003: The first formula and After being disassembled separately, the air backing was obtained. The first simplified form and under the rigid backing The second simplified form.

[0050] It should be noted that splitting the right-hand side of the first equation into real and imaginary parts, that is, requiring consideration of the imaginary part under air background... With a rigid backing Each part is broken down and simplified.

[0051] Specifically, the methods for obtaining the first simplified form include: First use Euler's formula The first exponent formula in exponential form Replace the first rectangular coordinate formula with rectangular coordinates; then simplify the numerator and denominator of the first rectangular coordinate formula to obtain the first simplified formula with real part plus imaginary part.

[0052] The formula for the first rectangular coordinate is: ; The denominator of the first rectangular coordinate formula is simplified as follows: ; The numerator of the first rectangular coordinate formula is simplified as follows: ; This leads to the result under air backing. The first simplified form is: ; Among them, the real part is The imaginary part is .

[0053] because and The only difference is the subscript symbol; the calculation method is the same. Therefore, under a rigid backing... The second simplified form is: ; Among them, the real part is The imaginary part is .

[0054] S2004: Obtain the real and imaginary parts of the first formula by combining the first and second simplified expressions.

[0055] make Let be the real part of the first formula. The imaginary part of the first formula, This is the constant term in the first formula.

[0056] As an example, the real part and the virtual part They are respectively: ; in, This represents the magnitude of the first complex reflection coefficient; This represents the magnitude of the second complex reflection coefficient; The phase angle represents the first complex reflection coefficient; The phase angle represents the second complex reflection coefficient.

[0057] This achieves the goal of multiplying the two equations on the right side of the air backing and the rigid backing, and then further separating them into real and imaginary parts.

[0058] S300: Obtain the density of water, the speed of sound in water, the frequency, the density of the test sample, and the thickness of the test sample, and calculate the constant term.

[0059] Specifically, substituting the first and second simplified expressions into the first formula yields the constant term. As an example, the constant term... The calculation formula is: ; in, Indicates the density of water; Indicates the speed of sound in water; Indicates frequency; Indicates the density of the tested sample; This indicates the thickness of the sample being tested.

[0060] S400: The sound velocity and attenuation coefficient of the test sample are calculated based on the thickness, real part, imaginary part, constant term and frequency of the test sample.

[0061] Specifically, the method for calculating the speed of sound of the tested sample includes: Based on the real part, imaginary part, and constant term, the first formula is rewritten as the second formula: ; Will Substituting into the second formula, we obtain the third formula; By decomposing both sides of the third equation into real and imaginary parts, and ensuring that the real and imaginary parts on both sides are equal, the sound velocity and attenuation coefficient of the tested sample can be calculated.

[0062] The third formula is as follows: .

[0063] The third equation can be broken down into real and imaginary parts, as follows: .

[0064] For the third formula to hold true, the real and imaginary parts of both sides of the equation must be equal, that is: ; because and All values ​​should be greater than 0. Therefore, the sound velocity and attenuation coefficient of the tested sample can be calculated.

[0065] Specifically, the speed of sound of the tested sample The calculation formula is: ,and ; in, Indicates the attenuation coefficient of the tested sample; Indicates frequency; Indicates the thickness of the tested sample; Represents a constant term; Indicates the real part; Indicates the imaginary part.

[0066] attenuation coefficient of the test sample The calculation formula is: ,and .

[0067] Since the attenuation coefficient only has a definite physical meaning when it is a real number, it is always greater than 0. The sign in the middle can be determined based on the actual situation.

[0068] It should be noted that a discriminant was used in deriving the sound velocity and attenuation coefficient of the test sample. Because the discriminant... This principle holds true under all circumstances. Therefore, the calculation formulas for sound velocity and attenuation coefficient of this invention are valid under all circumstances. In other words, it can be used to measure the sound velocity of any structure.

[0069] After obtaining the magnitude and phase angle of the complex reflection coefficient under two backing conditions, the accurate sound velocity and attenuation coefficient can be obtained analytically using the calculation formulas for sound velocity and attenuation coefficient. This not only eliminates the time-consuming iterative process and avoids the risk of local optima in the iterative method, but also significantly improves the accuracy and efficiency of the calculation, realizing a fast and direct solution for the sound velocity. It is particularly suitable for scenarios that require rapid analysis or processing of large amounts of frequency data.

[0070] To verify the feasibility of the sound speed calculation results of this invention, the sound speed calculation results of this invention were compared with the theoretical values.

[0071] As a specific embodiment, utilizing such Figure 3 The hollow cylinder shown is used as the test sample. The sound velocity and complex reflection coefficient of this structure can also be calculated theoretically. The complex reflection coefficient of this structure under rigid and flexible backing is as follows: Figure 4 As shown. The first complex reflection coefficient, the second complex reflection coefficient, and other relevant parameters are directly substituted into the sound speed. Calculation formula and attenuation coefficient The corresponding speed of sound can be obtained from the calculation formula. and attenuation coefficient .

[0072] like Figure 5 As shown, the attenuation coefficient calculation curve (PTM) of this invention almost completely overlaps with the theoretical curve (Theory) across the entire frequency band, indicating that the method of this invention can very accurately infer the attenuation coefficient of the material and has extremely high accuracy in calculating the attenuation coefficient.

[0073] like Figure 6 As shown, the sound velocity calculation curve (PTM) of this invention matches the theoretical curve (Theory) very well across the entire frequency range. The trends and fluctuation patterns of the two curves are basically consistent, which can accurately reflect the complex relationship between sound velocity and frequency.

[0074] As can be seen, through comparison with theoretical values, this invention achieves a high degree of consistency between the calculated results (PTM) of sound velocity and attenuation coefficient and the theoretical model (Theory) through joint solution. This not only avoids the numerical instability problem of traditional iterative methods, but also solves for the two key parameters of sound velocity and attenuation coefficient with high precision at the same time. This highlights the great advantages of this invention in terms of result consistency and calculation accuracy.

[0075] On the other hand, the present invention provides a sound speed calculation system based on a pulse tube experiment, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of any of the above methods.

[0076] Specifically, the system includes: The data acquisition module is used to acquire the first complex reflection coefficient of the test sample under an air backing and the second complex reflection coefficient under a rigid backing, as well as to acquire physical parameters (density and thickness of the test sample) and environmental parameters (density of water, speed of sound in water, and frequency), and send them to the parameter calculation module. The parameter calculation module, connected to the data acquisition module, is used to calculate the real part, imaginary part, and constant term based on the acquired data.

[0077] The sound velocity analysis module, connected to the parameter calculation module, is used to calculate and output the sound velocity of the measured sample based on the real part, imaginary part, and constant term output by the parameter calculation module.

[0078] Furthermore, the technical features of the system are consistent, and will not be elaborated upon here.

[0079] In summary, this invention directly calculates the structural sound velocity and attenuation coefficient using the real and imaginary parts of the reflection coefficient obtained from pulse tube experiments, offering significant advantages over traditional methods. Improving numerical stability. Traditional methods rely on only one set of results from either air-backed or rigid-backed solutions, which can easily lead to inconsistencies between the two sets of numerical results. However, theoretically, the attenuation coefficients and sound velocities obtained from the two sets of data should be equal. Therefore, this invention combines the reflection coefficient data from both backing conditions to construct an analytical formula including real and imaginary parts. After rigorous derivation, a corresponding analytical solution is proposed, eliminating the inconsistency problem when solving under a single backing condition and significantly improving the numerical stability and reliability of the calculation results.

[0080] Improving the accuracy and speed of measurement. Traditional methods often use equations with two unknowns, typical of transcendental equations. This leads to significant difficulties and inaccuracies in numerical solutions. Theoretically, the attenuation coefficient is a frequency-dependent quantity. Through derivation, this invention decouples the attenuation coefficient from frequency in calculation, integrating their relationship into the calculation of the reflection coefficient, making the frequency only related to the speed of sound. In other words, this invention transforms the original problem with two unknowns into an analytical problem with no unknowns, greatly improving the accuracy of the results and computational efficiency.

[0081] This invention simplifies the method for measuring sound velocity. Current methods for measuring structural sound velocity include pulse tube experiments and transient methods. However, transient methods require two monitoring devices: a transmitter and a receiver, using the time difference and distance between the two devices to measure the sound velocity. In contrast, this invention only requires obtaining the complex reflection coefficient of the structure, simplifying the device requirements. Furthermore, it can further obtain other parameters such as the absorption coefficient of the structure under test, offering richer measurement capabilities. Compared to transient methods, measuring the reflection coefficient is much easier.

[0082] It should be noted that, for the sake of simplicity, the foregoing embodiments are all described as a series of actions. However, those skilled in the art should understand that this application is not limited to the described order of actions, as some steps may be performed in other orders or simultaneously according to this application. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to this application.

[0083] In the above embodiments, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0084] In the several embodiments provided in this application, it should be understood that the disclosed methods or systems can be implemented in other ways. For example, the embodiments described above are merely illustrative. For instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed.

[0085] The foregoing description is merely an exemplary embodiment of this disclosure and should not be construed as limiting the scope of this disclosure. Any equivalent changes and modifications made in accordance with the teachings of this disclosure shall still fall within the scope of this disclosure. Those skilled in the art will readily conceive of embodiments of this disclosure upon considering the specification and practicing the disclosure herein. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not described herein. The specification and embodiments are to be considered exemplary only, and the scope and spirit of this disclosure are defined by the claims.

[0086] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0087] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for calculating the velocity of sound based on a pulse tube experiment, characterized in that, The method includes: The first complex reflection coefficient of the test sample under air backing and the second complex reflection coefficient under rigid backing were obtained using a pulse tube experiment. Based on the first complex reflection coefficient and the second complex reflection coefficient, the real part and imaginary part of the calculation result are obtained together; The density of water, the speed of sound in water, the frequency, the density of the test sample, and the thickness of the test sample are obtained, and the constant term is calculated. The sound velocity and attenuation coefficient of the test sample are calculated based on the thickness, real part, imaginary part, constant term, and frequency of the test sample.

2. The method for calculating the speed of sound based on a pulse tube experiment according to claim 1, characterized in that, Real part and the virtual part They are respectively: ； in, This represents the magnitude of the first complex reflection coefficient; This represents the magnitude of the second complex reflection coefficient; The phase angle represents the first complex reflection coefficient; The phase angle represents the second complex reflection coefficient.

3. The method for calculating the speed of sound based on a pulse tube experiment according to claim 1, characterized in that, The constant term The calculation formula is: ； in, Indicates the density of water; Indicates the speed of sound in water; Indicates frequency; Indicates the density of the tested sample; This indicates the thickness of the sample being tested.

4. A method for calculating the velocity of sound based on a pulse tube experiment according to any one of claims 1 to 3, characterized in that, The speed of sound of the tested sample The calculation formula is: ,and ; in, This represents the attenuation coefficient of the tested sample; Indicates frequency; Indicates the thickness of the tested sample; Represents the constant term; Denotes the real part; This represents the imaginary part.

5. The method for calculating the speed of sound based on a pulse tube experiment according to claim 4, characterized in that, The attenuation coefficient of the tested sample The calculation formula is: ,and .

6. A method for calculating the velocity of sound based on a pulse tube experiment according to any one of claims 1 to 3, characterized in that, Based on the first complex reflection coefficient and the second complex reflection coefficient, the real and imaginary parts of the calculation result are obtained jointly, specifically including: The first relationship between the sound velocity and attenuation coefficient of the test sample under air backing and the modulus and phase angle of the first complex reflection coefficient, and the second relationship between the sound velocity and attenuation coefficient of the test sample under rigid backing and the modulus and phase angle of the second complex reflection coefficient are obtained respectively. make And because Then, multiplying the transformed first and second relations yields the first formula: ; The first formula and After being disassembled separately, the air backing was obtained. The first simplified form and under the rigid backing The second simplified form; The real and imaginary parts of the first formula are obtained by combining the first and second simplified expressions.

7. The method for calculating the speed of sound based on a pulse tube experiment according to claim 6, characterized in that, The first simplified form is: ； The second simplified form is: 。 8. The method for calculating the speed of sound based on a pulse tube experiment according to claim 6, characterized in that, The method for calculating the sound velocity of the tested sample specifically includes: Based on the real part, the imaginary part, and the constant term, the first formula is rewritten as the second formula: ; Will Substituting into the second formula, we obtain the third formula; By decomposing both sides of the third equation into real and imaginary parts, and ensuring that the real and imaginary parts on both sides of the equation are equal, the sound velocity and attenuation coefficient of the tested sample can be calculated.

9. The method for calculating the speed of sound based on a pulse tube experiment according to claim 1, characterized in that, The first and second complex reflection coefficients are obtained by any of the following methods: experimental measurement, finite element simulation, or theoretical calculation.

10. A sound velocity calculation system based on a pulse tube experiment, comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 9.

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