Cylindrical open-hole rigid plate internal vector sound field calculation method, program, equipment and storage medium

Abstract

For a cylindrical open hole rigid plate arranged in a fluid area where a sound source is located, according to a Helmholtz equation met by a simple harmonic plane sound source excitation sound pressure field, circular piston radiation acoustic impedance on an infinite baffle plate is adopted to represent radiation impedance at an opening of a cylindrical open hole; constructing a sound field analytic solution of any depth in the open pore of the cylindrical open-pore rigid plate; the method comprises the following steps: drawing a frequency response curve of sound pressure amplitude and a frequency response curve of vibration velocity amplitude by measuring the opening cross section radius and the opening total depth of a cylindrical opening rigid plate, and taking a resonance peak and frequency values within a certain range on the two sides of the resonance peak as a resonance frequency interval; and selecting a fixed frequency in a non-resonant frequency interval range, measuring the sound pressure amplitude and the vibration velocity amplitude at any depth of the cylindrical open pore through a vector hydrophone, and correcting and restoring the real incident sound pressure amplitude and the vibration velocity amplitude of the cylindrical open pore rigid plate by using a calibration coefficient.

Description

Technical Field

[0001] This invention belongs to the field of acoustic technology, specifically relating to a method, program, device, and storage medium for calculating the vector sound field inside a cylindrical perforated rigid plate. Background Technology

[0002] In the field of acoustics, accurate calculation and prediction of sound field distribution are core requirements for acoustic device design, acoustic measurement, and related engineering applications. Under traditional free-field conditions, sound wave propagation exhibits relatively simple and regular characteristics, and vector sound field analysis techniques have become quite mature. However, in practical applications, it is often necessary to embed vector hydrophones within perforated rigid plates to measure the sound field. Inside a cylindrical perforated rigid plate, sound waves are constrained by the opening, sidewalls, and bottom rigid boundaries, undergoing multiple reflections, refractions, and interferences, resulting in complex directional distortions of sound field quantities such as sound pressure and vibration velocity in space. Therefore, researching a method that can accurately describe and calculate the vector sound field inside perforated rigid plates has become a crucial problem urgently needing to be solved in the field of acoustics. Summary of the Invention

[0003] The purpose of this invention is to provide a method, program, device, and storage medium for calculating the vector sound field inside a cylindrical perforated rigid plate. This invention derives the sound pressure field form solution by clarifying the Helmholtz equation and boundary conditions, substituting the boundary conditions to obtain coefficients, and adding sound source conditions to accurately calculate the sound pressure and vibration velocity, etc., inside a cylindrical perforated rigid plate under perpendicular plane wave incidence.

[0004] A method for calculating the vector sound field inside a cylindrical perforated rigid plate includes the following steps:

[0005] For a cylindrical rigid plate with an opening arranged in the fluid region where the sound source is located, according to the Helmholtz equation satisfied by the sound pressure field excited by the simple harmonic plane sound source, the radiation impedance at the opening of the cylindrical opening is represented by the radiation acoustic impedance of the circular piston on the infinite baffle, and the analytical solution of the sound field at any depth inside the opening of the cylindrical rigid plate with an opening is constructed.

[0006] Measure the cross-sectional radius and total depth of the opening of the cylindrical perforated rigid plate. Based on the analytical solution of the sound field at any depth inside the opening of the cylindrical perforated rigid plate, take the sound pressure amplitude as one and plot the frequency response curves of the sound pressure amplitude and the vibration velocity amplitude.

[0007] Take the frequency point corresponding to the resonant peak in the frequency response curve of sound pressure amplitude and the frequency point corresponding to the resonant peak in the frequency response curve of vibration velocity amplitude, and take the frequency value corresponding to the frequency point and the frequency value within a certain range on both sides as the resonant frequency range.

[0008] A fixed frequency is selected within the non-resonant frequency range, and the sound pressure amplitude and vibration velocity amplitude at any depth of the cylindrical opening are measured using a vector hydrophone.

[0009] Based on the analytical solution of the sound field at any depth inside the opening of the cylindrical perforated rigid plate, a sound pressure amplitude calibration coefficient and a vibration velocity amplitude calibration coefficient are constructed. The measured values ​​of sound pressure amplitude and vibration velocity amplitude are corrected using the calibration coefficients to restore the true incident sound pressure amplitude and vibration velocity amplitude of the cylindrical perforated rigid plate.

[0010] Furthermore, the Helmholtz equation satisfied by the sound pressure field excited by the simple harmonic plane sound source is:

[0011]

[0012] Where x is the direction from the center of the opening of the cylindrical opening to the center of the bottom of the cylindrical opening; t is the time variable; k is the wave number, k = ω / c0, ω is the angular frequency of the sound source, and c0 is the speed of sound in the fluid region.

[0013] Furthermore, the radiation acoustic impedance at the opening of the cylindrical aperture is represented by the radiation impedance of a circular piston on an infinitely large baffle. s Specifically:

[0014]

[0015] Where r0 is the radius of the circular piston, numerically made the same as the cross-sectional radius of the cylindrical opening; J1(·) is the first-order Bessel function; H1(·) is the first-order Struff function; ρ0 is the density of the fluid region;

[0016] The input impedance Z inside the cylindrical aperture at x=0 a0 for:

[0017]

[0018] Where j is the imaginary unit; L is the total depth of the cylindrical opening.

[0019] Furthermore, the analytical solution for the acoustic field at any depth inside the opening of the constructed cylindrical perforated rigid plate is specifically as follows:

[0020]

[0021] Where p(x) and u(x) are the sound pressure and vibration velocity at depth x of the cylindrical opening, x∈[0,L]; p0 is the incident wave sound pressure amplitude; u0 is the incident wave vibration velocity amplitude.

[0022] Furthermore, the cross-sectional radius r0 and total depth L of the cylindrical perforated rigid plate are measured. Based on the analytical solution of the sound field at any depth inside the perforation of the cylindrical perforated rigid plate, the sound pressure amplitude p0 = 1 is set, and the frequency response curves of the sound pressure amplitude and the vibration velocity amplitude are plotted.

[0023] Furthermore, the sound pressure amplitude calibration coefficient K is constructed based on the analytical solution of the sound field at any depth inside the opening of the cylindrical perforated rigid plate. p With vibration amplitude calibration coefficient K u Specifically:

[0024]

[0025] Furthermore, a fixed frequency is selected within the non-resonant frequency range, and the sound pressure amplitude |p(x0)| and vibration velocity amplitude |u(x0)| at any depth x0 of the cylindrical opening are measured using a vector hydrophone. The measured values ​​of sound pressure amplitude and vibration velocity amplitude are corrected using calibration coefficients to restore the true incident sound pressure amplitude p0 and vibration velocity amplitude u0 of the rigid plate with the cylindrical opening.

[0026] p0 = K p ·|p(x0)|

[0027] u0 = K u ·|u(x0)|

[0028] A computer device / equipment / system includes a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the above-described method for calculating the internal vector sound field of a cylindrical perforated rigid plate.

[0029] A computer-readable storage medium storing a computer program / instructions that, when executed by a processor, implement the steps of the above-described method for calculating the vector sound field inside a cylindrical perforated rigid plate.

[0030] A computer program product includes a computer program / instructions that, when executed by a processor, implement the steps of the above-described method for calculating the internal vector sound field of a cylindrical perforated rigid plate.

[0031] The beneficial effects of this invention are as follows:

[0032] This invention has low computational complexity and can overcome the influence of sound field changes under non-free field conditions, ensuring the stability and reliability of calculations under complex boundary conditions. It can be used to calculate the sound field quantity inside a cylindrical perforated rigid plate under the condition of plane sound source incident, accurately obtain the precise sound pressure, vibration velocity and other sound field quantities inside a cylindrical perforated rigid plate under the condition of plane wave perpendicular incident, with small error and wide application range. Attached Figure Description

[0033] Figure 1 This is the overall flowchart of the present invention.

[0034] Figure 2 This is a schematic diagram of a cylindrical perforated rigid plate arranged in the fluid region where the sound source is located, as described in this invention.

[0035] Figure 3 This is a comparison chart of the amplitude, phase, and frequency response of the sound pressure and vibration velocity at a depth x = 4 cm on the axis of a cylindrical perforated rigid plate under perpendicular incidence of a 1000Hz-10000Hz plane wave, calculated using the method of this invention, with the results calculated by finite element software. Detailed Implementation

[0036] The present invention will now be further described with reference to the accompanying drawings.

[0037] This invention provides a method for calculating the vector sound field inside a cylindrical perforated rigid plate, comprising the following steps:

[0038] Step 1: For a cylindrical rigid plate with an opening arranged in the fluid region where the sound source is located, according to the Helmholtz equation satisfied by the sound pressure field excited by the simple harmonic plane sound source, the radiation impedance at the opening of the cylindrical opening is represented by the radiation acoustic impedance of the circular piston on the infinite baffle, and the analytical solution of the sound field at any depth inside the opening of the cylindrical rigid plate with an opening is constructed.

[0039] The cylindrical perforated rigid plate is made of a material with high rigidity and low sound absorption performance. Its surface has cylindrical perforations with a cross-section of a circle with a radius of r0 and a total depth of L. The center of the opening of the rigid plate is the origin of the coordinate system, and the x-direction points to the bottom of the opening along the axis of the cylindrical perforation.

[0040] A simple harmonic plane sound source is incident along the positive x-axis;

[0041] Considering sound propagation in one dimension, the sound pressure generated by a simple harmonic sound source satisfies the following Helmholtz equation:

[0042]

[0043] Where x is the direction from the axis at the opening of the cylindrical opening to the axis at the bottom of the cylindrical opening; t is the time variable; k = ω / c0 is the wave number; ω is the angular frequency of the sound source; c0 is the speed of sound in the fluid region; p is the sound pressure.

[0044] The formal solution to the Helmholtz equation is:

[0045] p=(Ae -jkx +Be jkx )e jωt

[0046]

[0047] Where j is the imaginary unit, u is the vibration velocity, and the vibration velocity exists only in the x direction; ρ0 is the density of the fluid, and A and B are undetermined coefficients;

[0048] The bottom of the perforated rigid plate satisfies the rigid boundary condition that the normal vibration velocity is 0:

[0049]

[0050] The relationship between A and B is:

[0051] B = Ae -2jkL

[0052] The radiation impedance Z at the opening of the cylindrical aperture is represented by the radiation acoustic impedance of a circular piston with radius r0 on an infinitely large baffle. s :

[0053]

[0054] Where J1(·) is a first-order Bessel function; H1(·) is a first-order Struff function; ρ0 is the density of the fluid region;

[0055] Based on the standing wave expression within a cylindrical rigid plate with an opening, the input impedance Z at the opening is obtained. a0 for:

[0056]

[0057] A series equivalent circuit is constructed using acoustic-electric analogy, with a total impedance Z. total =Z s +Z a0 According to the voltage source at Z a0 The pressure drop across the surface can be used to calculate the true open-mouth sound pressure level.

[0058]

[0059] For a plane incident wave, its sound wave expression is:

[0060] p i =p0e j(ωt-kx)

[0061] Where, p i p0 is the incident wave sound pressure level;

[0062] The coefficient A is obtained as follows:

[0063]

[0064] We obtain the following from the relationship between A and B:

[0065]

[0066] The analytical solution for the sound field at any depth x inside the opening of a cylindrical rigid plate with an opening is:

[0067]

[0068] Where u0 is the incident wave velocity amplitude; and 0 ≤ x ≤ L, the time factor e is omitted in the formula. jωt .

[0069] Step 2: Measure the radius r0 of the opening cross section and the total depth L of the opening of the cylindrical rigid plate with opening. Based on the analytical solution of the sound field at any depth inside the opening of the cylindrical rigid plate with opening, set p0 to 1 and plot the frequency response curves of the sound pressure amplitude and the vibration velocity amplitude. Take the frequency point corresponding to the resonance peak in the frequency response curve of the sound pressure amplitude and the frequency point corresponding to the resonance peak in the frequency response curve of the vibration velocity amplitude, and take the frequency value corresponding to the frequency point and the frequency value within a certain range on both sides as the resonant frequency range.

[0070] Step 3: Select a fixed frequency within the non-resonant frequency range, and measure the sound pressure amplitude |p(x0)| and vibration velocity amplitude |u(x0)| at any depth x0 of the cylindrical opening using a vector hydrophone;

[0071] Step 4: Based on the analytical solution of the sound field at any depth x inside the opening of the cylindrical perforated rigid plate, construct the sound pressure amplitude calibration coefficient and the vibration velocity amplitude calibration coefficient. Use the calibration coefficients to correct the measured values ​​of sound pressure amplitude and vibration velocity amplitude, and restore the true incident sound pressure amplitude p0 and vibration velocity amplitude u0 of the cylindrical perforated rigid plate.

[0072] p0 = K p ·|p(x0)|

[0073] u0 = K u ·|u(x0)|

[0074] in,

[0075] Example 1:

[0076] A cylindrical rigid plate with an opening, characterized by rigid boundaries on both the sidewalls and bottom, is selected as the research object. The opening radius is r0 = 9 cm, and the depth is L = 8 cm. The fluid inside the rigid plate is water, with a water density ρ0 = 1000 kg / m³. 3 The speed of sound in water is c0 = 1500 m / s. A planar sound source emits sound waves in the x-axis direction. The sound pressure amplitude of the incident plane wave is p0 = 1 Pa. A cylindrical rigid plate model with an opening is shown below. Figure 2 As shown.

[0077] The amplitude-frequency response of the sound pressure and vibration velocity at a depth x = 4 cm on the axis of a cylindrical perforated rigid plate under perpendicular incident plane wave of 1000Hz-10000Hz is obtained by calculating using the method of this invention. Figure 3 As shown in the figure; it can be seen from the figure that the sound pressure resonant frequency is about 2520Hz and the vibration velocity resonant frequency is about 2660Hz.

[0078] As demonstrated by the examples, this method constructs an analytical solution by substituting the parameters of the cylindrical perforated rigid plate as boundary conditions into the Helmholtz equation, and combining this with the radiation impedance characteristics at the opening into the Helmholtz equation. This solution is then coupled with sound source conditions for derivation and calculation. It can quickly and accurately solve for sound pressure, vibration velocity, and other sound field quantities at any depth inside the opening under plane wave incidence conditions without relying on complex numerical simulations. This method has a wide range of applications, laying the foundation for future calculations of sound field quantities in more complex acoustic structures, and has positive guiding significance for practical applications in the field of acoustic engineering.

[0079] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., 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 vector sound field inside a cylindrical perforated rigid plate, characterized in that: For a cylindrical rigid plate with an opening arranged in the fluid region where the sound source is located, according to the Helmholtz equation satisfied by the sound pressure field excited by the simple harmonic plane sound source, the radiation impedance at the opening of the cylindrical opening is represented by the radiation acoustic impedance of the circular piston on the infinite baffle, and the analytical solution of the sound field at any depth inside the opening of the cylindrical rigid plate with an opening is constructed. Measure the cross-sectional radius and total depth of the opening of the cylindrical perforated rigid plate. Based on the analytical solution of the sound field at any depth inside the opening of the cylindrical perforated rigid plate, take the sound pressure amplitude as one and plot the frequency response curves of the sound pressure amplitude and the vibration velocity amplitude. Take the frequency point corresponding to the resonant peak in the frequency response curve of sound pressure amplitude and the frequency point corresponding to the resonant peak in the frequency response curve of vibration velocity amplitude, and take the frequency value corresponding to the frequency point and the frequency value within a certain range on both sides as the resonant frequency range. A fixed frequency is selected within the non-resonant frequency range, and the sound pressure amplitude and vibration velocity amplitude at any depth of the cylindrical opening are measured using a vector hydrophone. Based on the analytical solution of the sound field at any depth inside the opening of the cylindrical perforated rigid plate, a sound pressure amplitude calibration coefficient and a vibration velocity amplitude calibration coefficient are constructed. The measured values ​​of sound pressure amplitude and vibration velocity amplitude are corrected using the calibration coefficients to restore the true incident sound pressure amplitude and vibration velocity amplitude of the cylindrical perforated rigid plate.

2. The method for calculating the vector sound field inside a cylindrical perforated rigid plate according to claim 1, characterized in that: The Helmholtz equation satisfied by the sound pressure field excited by the simple harmonic plane sound source is: Where x is the direction from the center of the opening of the cylindrical opening to the center of the bottom of the cylindrical opening, t is the time variable, p is the sound pressure, k is the wave number, k = ω / c0, ω is the angular frequency of the sound source, and c0 is the sound speed in the fluid region.

3. The method for calculating the vector sound field inside a cylindrical perforated rigid plate according to claim 2, characterized in that: The radiation impedance Z at the opening of the cylindrical aperture is represented by the radiation acoustic impedance of a circular piston on an infinitely large baffle. s Specifically: Where r0 is the radius of the circular piston, numerically made the same as the cross-sectional radius of the cylindrical opening; J1(·) is the first-order Bessel function; H1(·) is the first-order Struff function; ρ0 is the density of the fluid region; The input impedance Z inside the cylindrical aperture at x=0 a0 for: Where j is the imaginary unit; L is the total depth of the cylindrical opening.

4. The method for calculating the vector sound field inside a cylindrical perforated rigid plate according to claim 3, characterized in that: The analytical solution for the acoustic field at any depth inside the opening of the cylindrical perforated rigid plate is as follows: Where p(x) and u(x) are the sound pressure and vibration velocity at depth x of the cylindrical opening, x∈[0,L]; p0 is the incident wave sound pressure amplitude.

5. The method for calculating the vector sound field inside a cylindrical perforated rigid plate according to claim 4, characterized in that: The measurement of the cross-sectional radius r0 and total depth L of the cylindrical perforated rigid plate is based on the analytical solution of the sound field at any depth inside the perforation of the cylindrical perforated rigid plate. The sound pressure amplitude p0 = 1 is set, and the frequency response curves of the sound pressure amplitude and the vibration velocity amplitude are plotted.

6. The method for calculating the vector sound field inside a cylindrical perforated rigid plate according to claim 5, characterized in that: The sound pressure amplitude calibration coefficient K is constructed based on the analytical solution of the sound field at any depth inside the opening of the cylindrical perforated rigid plate. p With vibration amplitude calibration coefficient K u Specifically:

7. The method for calculating the vector sound field inside a cylindrical perforated rigid plate according to claim 6, characterized in that: The process involves selecting a fixed frequency within the non-resonant frequency range, measuring the sound pressure amplitude |p(x0)| and vibration velocity amplitude |u(x0)| at any depth x0 of the cylindrical opening using a vector hydrophone, and correcting the measured values ​​of the sound pressure amplitude and vibration velocity amplitude using calibration coefficients to restore the true incident sound pressure amplitude p0 and vibration velocity amplitude u0 of the rigid plate with the cylindrical opening. p0=K p ·|p(x0)| u0=K u ·|u(x0)|。 8. A computer device / equipment / system, 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 7.

9. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that: When the computer program / instructions are executed by the processor, they implement the steps of the method according to any one of claims 1 to 7.

10. A computer program product comprising a computer program / instructions, characterized in that: When the computer program / instructions are executed by the processor, they implement the steps of the method according to any one of claims 1 to 7.

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