CN110414156B - A Method for Determining the Relative Radiation Acoustic Impedance of a Simply Supported Plate with Four Sides - Google Patents

Abstract

The invention discloses a method for determining the relative radiation acoustic impedance of a four-side simple support plate, which comprises the following steps: 1) Calculating bending vibration modes of the four-side simple support plate; 2) Calculating the modal sound radiation of the four-side simple support plate, and extracting the vibration speed of each node of the four-side simple support plate under a certain ka value; 3) Calculating the vibration speed of each unit; 4) Calculating the sound pressure generated by the vibration of other units at the unit ds and the sound pressure generated by all units on the radiation surface at the unit ds; 5) Calculating the acting force of the sound field received by the unit ds, the complex power provided for the sound field when the unit ds vibrates and the complex sound power radiated by the whole four-side simple support plate; 6) Calculating the surface average vibration speed of the whole four-side simple support plate; 7) And calculating the radiation impedance and the relative radiation impedance of the four-side simple support plate. The invention provides a simplified calculation method of the relative radiation acoustic impedance of the four-side simple support plate based on simulation data, which simplifies the solving process of the radiation acoustic impedance of the four-side simple support plate and has small result error.

Description

A Method for Determining the Relative Radiation Acoustic Impedance of a Simply Supported Plate with Four Sides

technical field

The invention relates to radiation impedance measurement technology, in particular to a method for determining the relative radiation acoustic impedance of a four-sided simply supported plate.

Background technique

In power transmission and transformation projects, especially in substations, various types of equipment such as transformers, reactors, and capacitors have a large proportion of plate structures. This type of structure has defects such as small wall thickness and poor rigidity. It is easy to generate vibration and noise under the action of the environment, which not only affects the performance of equipment operation, affects the physical and mental health of residents and staff, but also causes certain pollution to the surrounding environment. Therefore, the research on the radiated sound field of various plate structures has always attracted people's attention.

Radiation impedance is an important parameter of the acoustic system, which is of great significance for evaluating the acoustic characteristics of the system. The study of radiation impedance of various plate structures will promote the study of the radiation sound field of plate structures. In the bending vibration problem of a square thin plate, the free vibration with four sides simply supported is the simplest case and the only one for which an analytical solution can be obtained. Therefore, the research on the calculation method of the relative radiation acoustic impedance of the four-sided simply supported plate, and the verification by the analytical solution, have guiding significance for the research of the radiation impedance and radiation acoustic field of various plate structures.

The existing technical scheme is to derive and use the deflection function of a simply supported bending vibration square plate with four sides, calculate the vibration velocity distribution function with a differential method, and use the Rayleigh integral formula to calculate the unit sound pressure function and the unit sound pressure function on the basis of the vibration velocity distribution function. After the power function, the integral method is used to obtain the sound power of the whole four-sided simply supported plate, and the double integral is used to calculate the average vibration velocity of the plate surface, and finally the radiation acoustic impedance is obtained on the basis of the sound power of the four-sided simply supported plate and the average surface vibration velocity . In the process of calculating the analytical solution, in order to ensure the continuity of the calculation results, starting from the functional equation, the integral and differential methods are used many times, which has the disadvantages of complex calculation, high difficulty, and heavy workload.

Contents of the invention

The technical problem to be solved by the present invention is to provide a method for determining the relative radiation acoustic impedance of a simply supported plate with four sides in view of the defects in the prior art.

The technical solution adopted by the present invention to solve the technical problem is: a method for determining the relative radiation acoustic impedance of a four-sided simply supported plate, comprising the following steps:

1) Establish the three-dimensional model of the four-sided simply supported plate, and divide the mesh unit according to the size of the four-sided simply supported plate and the requirements of calculation accuracy, and then calculate the bending vibration mode of the four-sided simply supported plate;

2) Taking the flexural vibration mode of the four-sided simply supported plate as the boundary condition, calculate the modal acoustic radiation of the four-sided simply supported plate, set the ka value, and extract the vibration velocity of each node of the four-sided simply supported plate under this ka value; the nodes are the vertices of the grid cell;

3) Calculate the vibration velocity of each grid unit according to the vibration velocity of each node;

4) Take any one of the divided grid units as the unit ds, calculate the sound pressure dp _i generated by the vibration of other units d _i ' in the four-sided simply supported plate at the unit ds, and calculate all the units on the radiation surface in the unit The sound pressure p generated at ds;

5) Calculate the force dF of the sound field on the unit ds, the complex power dW provided to the sound field when the unit ds vibrates, and the complex sound power W radiated by the entire four-sided simply supported plate;

6) Calculate the surface average vibration velocity of the entire four-sided simply supported plate according to the vibration velocity of each grid unit;

7) Calculate the radiation impedance Zr and the relative radiation impedance R, X of the four-sided simply supported plate;

Among them, U is the surface average vibration velocity of the entire four-sided simply supported plate, and U ^* is the conjugate of the surface average vibration velocity U;

The relative radiation impedance R, X is related to the radiation impedance Zr of the four-sided simply supported plate, and its expression is as follows:

Zr=Rr+jXr

相对辐射抗：/>

Relative Radiation Resistance:

Relative radiation resistance: />

Among them, Rr is the radiation resistance, Xr is the radiation resistance, ρ is the medium density, c is the propagation velocity of the sound wave in the medium, and a is the side length of the four-sided simply supported plate.

According to the above scheme, the ka value in the step 2) is the product of the wave number k and the side length a of the four-sided simply supported plate.

According to the above scheme, in the step 1), the four-sided simply supported plate flexural vibration mode is carried out after establishing a four-sided simply supported plate three-dimensional model with a side length a in Ansys, dividing the mesh unit, setting materials and boundary conditions Calculation, wherein, the side length a of the three-dimensional model of the four-sided simply supported plate should be set according to the requirements; the boundary condition of the modal analysis is four-sided simply supported, and the implementation method is to constrain the degrees of freedom of the four sides of the radiation surface in the z direction, constrain the The degrees of freedom in the x and y directions of a corner point and the degrees of freedom in the y direction of the adjacent corner point are constrained.

According to the above scheme, in the step 1), the sound pressure _dpi is calculated by the following formula;

Among them, k is the wave number, ρ is the medium density, c is the propagation speed of sound wave in the medium, d _i ' is the area of other units, h _i is the distance between other units d _i ' and unit ds.

The beneficial effects produced by the present invention are:

The present invention jointly utilizes the modal analysis module of ansys workbench and the boundary element calculation module of LMS Virtual.Lab to simulate and calculate the modal acoustic radiation of the four-sided simply supported plate, and uses the mathematical relationship to process the simulation calculation result data, and the calculation is obtained The relative radiation acoustic impedance of the four-sided simply supported plate, the present invention overcomes the shortcomings of the four-sided simply supported plate, such as complex calculation process, high difficulty, and heavy workload when studying the analytical solution, and simplifies the radiation acoustic impedance of the four-sided simply supported plate to a certain extent The solution process also has certain guiding significance for the calculation of radiation impedance of other types of plate structures.

Description of drawings

The present invention will be further described below in conjunction with accompanying drawing and embodiment, in the accompanying drawing:

Fig. 1 is a flow chart of the method of the embodiment of the present invention.

Detailed ways

In order to make the object, technical solution and advantages of the present invention more clear, the present invention will be further described in detail below in conjunction with the examples. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention.

As shown in Figure 1, a method for determining the relative radiation acoustic impedance of a simply supported plate with four sides includes the following steps:

Step 1, calculating the flexural vibration mode of the four-sided simply supported plate;

In step 1, the bending vibration mode of the four-sided simply supported plate needs to be calculated after establishing a three-dimensional model of the four-sided simply supported plate with a side length a in Ansys, dividing mesh units, setting materials and boundary conditions.

Among them, the side length a of the three-dimensional model of the four-sided simply supported plate should be set by itself according to the requirements; the size of the divided grid unit should be set according to the size of the four-sided simply supported plate and the requirements of calculation accuracy; the modal analysis The boundary condition is simply supported on four sides, and the implementation method is to constrain the degree of freedom of the four sides of the radiating surface in the z direction, constrain the degree of freedom of one corner point in the x and y directions, and constrain the degree of freedom in the y direction of the other adjacent corner point.

Step 2, calculate the modal acoustic radiation of the four-sided simply supported plate, and extract the vibration velocity v of each node of the four-sided simply supported plate under a certain value of ka;

In step two, the modal acoustic radiation of the four-sided simply supported plate needs to use the four-sided simply supported plate's bending vibration mode obtained in step one as the boundary condition, and use the boundary element method for calculation in the virtual lab.

The ka value is the product of the wave number k and the side length a of the four-sided simply supported plate, and the wave number k is related to the angular frequency ω and the speed of sound c, and its expression is as follows:

Among them, f is the frequency.

Step 3, calculating the vibration velocity u of each unit;

In step 3, the vibration velocity u of each unit is related to the vibration velocity v of the nodes forming the unit, and it is necessary to take the four nodes forming a unit ds as objects, and use the vibration velocity v of each node obtained in step 2 to calculate, Its expression is as follows:

Step 4, calculate other each unit ds ' and the distance h of unit ds;

In step 4, the distance h between the other units ds' and the unit ds and the center abscissa x' of other units ds', the center ordinate y' of other units ds', the center abscissa x of unit ds, and the unit ds It is related to the center ordinate y, and its expression is as follows:

Step 5, calculating the sound pressure dp produced by the vibration of other units ds' at the unit ds place and the sound pressure p produced by all units on the radiation surface at the unit ds place;

In step five, the sound pressure dp generated by the vibration of the other units ds' at the unit ds is related to the vibration velocity u' of the other units ds', and the distance h between the other units ds' and the unit ds, according to The Rayleigh integral formula is calculated by using the vibration velocity u' of other units ds' obtained in step 3 and the distance h between other units ds' and unit ds obtained in step 4, and its expression is as follows:

Among them, k is the wave number, ρ is the density of the medium, c is the propagation speed of the sound wave in the medium, ds' is the area of other units, and the time factor is not considered in the calculation of the above formula.

The sound pressure p produced by all units on the radiating surface at the unit ds is related to the sound pressure dp produced at the unit ds by the vibration of other units ds', and its expression is as follows:

p=∑dp

Step 6, calculating the force dF of the sound field on the unit ds, the complex power dW provided to the sound field when the unit ds vibrates, and the complex sound power W radiated by the entire four-sided simply supported plate;

In step six, the force dF of the unit ds subjected to the sound field is related to the sound pressure p generated by all units at the unit ds, and it is necessary to use the sound pressure p generated by all units at the unit ds obtained in step five for calculation, where The expression is as follows:

dF=pds

Among them, ds is the unit area.

The complex power dW provided to the sound field when the unit ds vibrates is related to the force dF of the unit ds subjected to the sound field and the vibration velocity u of the unit ds. The speed u is calculated, and its expression is as follows:

dW＝dF·u ^*

Among them, u ^* is the conjugate of the vibration velocity u of the unit ds.

The complex sound power W radiated by the entire four-sided simply supported plate is related to the complex power dW provided to the sound field when each unit ds vibrates, and is the sum of the complex powers provided to the sound field when the unit ds vibrates in all divided units; that is, the ergodic All division units, taking it as unit ds, the sum of the complex powers provided to the sound field when all division units ds vibrate;

Its expression is as follows:

W = ΣdW

Step seven, calculate the surface average vibration velocity U of the entire four-sided simply supported plate;

In step seven, the surface average vibration velocity U of the entire four-sided simply supported plate is related to the vibration velocity u of each unit, and needs to be calculated using the vibration velocity u of each unit obtained in step three, and its expression is as follows:

Among them, m is the total number of units.

Step eight, calculate the radiation impedance Zr and the relative radiation impedance R, X of the four-sided simply supported plate.

In step 8, the radiation impedance Zr of the four-sided simply supported plate is related to the complex sound power W radiated by the entire four-sided simply supported plate and the surface average vibration velocity U. The complex sound power W is calculated with the surface average vibration velocity U obtained in step 7, and its expression is as follows:

Among them, U ^* is the conjugate of surface average vibration velocity U.

The relative radiation impedance R, X is related to the radiation impedance Zr of the four-sided simply supported plate, and its expression is as follows:

Zr=Rr+jXr

相对辐射抗：/>

Relative Radiation Resistance:

Relative radiation resistance: />

Among them, Rr is the radiation resistance, Xr is the radiation resistance, ρ is the medium density, c is the propagation velocity of the sound wave in the medium, and a is the side length of the four-sided simply supported plate.

Through the above steps, the present invention achieves the purpose of calculating the relative radiation impedance of the four-sided simply supported plate, overcomes the shortcomings of complex calculation process, high difficulty, and heavy workload when studying the analytical solution of the four-sided simply supported plate, and simplifies the four-sided simply supported plate to a certain extent. The solution process of radiation acoustic impedance of a simply supported plate is of guiding significance to the calculation of radiation impedance of other types of plate structures.

When ka is less than 4, the error between the radiation acoustic impedance calculated by this method and the analytical solution is less than 5%, so it can be concluded that this method can be used to calculate the radiation acoustic impedance of a four-sided simply supported plate in the low frequency range of 0-200Hz, and The error can be kept within the allowable range.

It should be understood that those skilled in the art can make improvements or changes based on the above description, and all these improvements and changes should belong to the protection scope of the appended claims of the present invention.

Claims (3)

1. A method for determining the relative radiation acoustic impedance of a four-sided simply supported plate, is characterized in that it may further comprise the steps: 1) Establish the three-dimensional model of the four-sided simply supported plate according to the four-sided simply supported plate, and divide the mesh unit according to the size of the four-sided simply supported plate and the requirements of calculation accuracy, and then calculate the bending vibration mode of the four-sided simply supported plate; 2) Taking the flexural vibration mode of the four-sided simply supported plate as the boundary condition, calculate the modal acoustic radiation of the four-sided simply supported plate, set the ka value, and extract the vibration velocity of each node of the four-sided simply supported plate under this ka value; the nodes are the vertices of the grid cell; Among them, ka is the product of the wave number k and the side length a of the four-sided simply supported plate; 3) Calculate the vibration velocity of each grid unit according to the vibration velocity of each node; 4) Take any one of the divided grid units as the unit ds, calculate the sound pressure dp _i generated by the vibration of other units d _i ' in the four-sided simply supported plate at the unit ds, and calculate all the units on the radiation surface in the unit The sound pressure p generated at ds; 5) Calculate the force dF of the sound field on the unit ds, the complex power dW provided to the sound field when the unit ds vibrates, and the complex sound power W radiated by the entire four-sided simply supported plate; 6) Calculate the surface average vibration velocity U of the entire four-sided simply supported plate according to the vibration velocity of each grid unit; 7) Calculate the radiation impedance Zr and the relative radiation impedance R, X of the four-sided simply supported plate;

Among them, U is the surface average vibration velocity of the entire four-sided simply supported plate, and U ^* is the conjugate of the surface average vibration velocity U; The relative radiation impedance R, X is related to the radiation impedance Zr of the four-sided simply supported plate, and its expression is as follows: Zr=Rr+jXr Relative Radiation Resistance:

Relative radiation resistance: />

Among them, Rr is the radiation resistance, Xr is the radiation resistance, ρ is the medium density, c is the propagation velocity of the sound wave in the medium, and a is the side length of the four-sided simply supported plate. 2. the method for determining the relative radiation acoustic impedance of four-sided simply supported plate according to claim 1, is characterized in that, in described step 1), described four-sided simply supported plate flexural mode is by establishing side length in Ansys as The three-dimensional model of the four-sided simply supported plate of a is calculated after dividing the mesh unit, setting the material and boundary conditions, wherein the side length a of the four-sided simply supported plate three-dimensional model should be set according to the requirements; the boundary conditions of the modal analysis It is simply supported on four sides, and the implementation method is to constrain the degree of freedom of the four sides of the radiating surface in the z direction, constrain the degree of freedom of one corner point in the x and y directions, and constrain the degree of freedom in the y direction of the adjacent corner point. 3. the method for determining the relative radiation acoustic impedance of four-sided simply supported plate according to claim 1, is characterized in that, in described step 4), sound pressure _dpi adopts following formula to calculate;

Among them, k is the wave number, ρ is the medium density, c is the propagation speed of sound wave in the medium, d _i ' is the area of other units, h _i is the distance between other units d _i ' and unit ds.

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