Wave Function Superposition Method Based On Plane Element And Its Application In Nearfield Acoustic Holography

Near-field acoustic holography is an effective technique for identifying noise sources and visualizing sound fields.This technology utilizes the measurement of sound pressure or particle velocity data on a holographic surface near the sound source,and reconstructs acoustic quantities at any position including the sound source surface through calculation,such as sound pressure,particle velocity,and sound intensity.In recent decades,many transformation algorithms have been developed to realize near-field acoustic holography,such as spatial Fourier transform,statistical optimization method,boundary element method,wave superposition method,etc.Among many methods,the wave superposition method has attracted much attention due to its simple principle,convenient calculation,and strong adaptability to sound sources.However,in the traditional wave superposition method,the external sound field of the vibrating body is obtained by integrating and superposing the Green function on the virtual divergent boundary.When there are many discrete elements and a large number of calculated field points,a large number of numerical integration calculations are required,which is inefficient.If a monopole point source is used to replace the discrete element,although the simplified wave superposition method has high computational efficiency,there is a significant integration approximation error in the process of simplifying the point source with a surface source.To solve these problems,this paper proposes to construct a wave function instead of the numerical integration of the Green function of the discrete element in the wave superposition method.The improved wave function superposition method is applied to near-field acoustic holography,and numerical simulation is used to verify the effectiveness and accuracy of the method in acoustic field reconstruction.The main research work of this article is as follows:(1)The research status and development trend of near-field acoustic holography are discussed,and several main acoustic field space transformation algorithms of near-field acoustic holography are described.Aiming at the advantages,disadvantages and existing problems of the existing acoustic field space transformation algorithms,the numerical integration of Green function of discrete units in the construction of wave function instead of wave superposition method is determined as the main research topic in this paper.(2)The traditional wave superposition method needs repeated numerical integration for each discrete element on the virtual surface when calculating the sound pressure at different points of the external radiation sound field of the sound source,and the calculation efficiency is low.The simplified wave superposition method is not as accurate as direct integration due to its overly simplified elements,and its applicability is limited.In this paper,an equivalent wave function is proposed to replace the integration of Green function in the unit area in the traditional wave superposition method,and it is applied to near-field acoustic holography to avoid repeated integration calculation in the acoustic field calculation,and to maximize the calculation accuracy.(3)According to the sound field generated by the sound source in external space,it can be replaced by the weighted sum of the product of the spherical Hankel function and the spherical harmonic function.In this paper,the solution of Helmholtz equation in spherical coordinates is used to derive an equivalent wave function instead of Green’s function in the traditional wave superposition method,and the expansion coefficient of wave function is determined by constructing an artificial boundary.Since the expansion coefficient of the general wave function is more complex,it is further proposed to set the artificial boundary in the far field,simplify the expansion coefficient of the wave function,and derive the internal wave function with higher calculation efficiency.(4)First,taking the commonly used quadrilateral element as an example,the general form of wave function to replace the quadrilateral element integration is derived,and taking the special rectangular element as an example,the general form and the extrapolation form of the rectangular element integration wave function,as well as the simplified extrapolation wave function when the element is square are derived.Then,taking the triangle element which has the most extensive adaptability as an example,the general form and the extrapolation form of wave function instead of the triangle constant element are derived.In order to improve the accuracy of wave function,the general form of triangular linear element and the interpolation form of wave function are derived.Finally,through numerical simulation,using these constructed wave function and direct integration to compare the external sound field of the calculation unit,the calculation accuracy and efficiency of wave function are verified.The simplified extrapolated wave function in the circular domain and the extrapolated wave function in the triangular linear unit are applied to the simulation example of near-field acoustic holography.Compared with the point source superposition method,the external radiation sound field of the simply supported plate sound source,the cube box sound source,and the pulsating sphere sound source is reconstructed,which further verifies the effectiveness and stability of the wave function constructed in this paper.(5)A summary of the main research work of this article is provided,and prospects for future research directions are provided.