Boundary Element Method For Wide Band Noise Analysis

With the improvement of science and technology in China,the prediction and analysis of noise radiation has become the primary problem of intelligent manufacturing and green manufacturing.The high-precision prediction and analysis of multi-frequency noise field depends on the high-precision analysis algorithm.At present,the boundary element method is a typical representative of the noise field calculation and analysis methods.However,the BEM has some problems such as low computational efficiency and difficult inverse transformation when it is applied to the analysis of multi-frequency noise,especially broadband noise.This paper focuses on the BEM method of broadband noise,aiming to explore and solve the numerical inverse transformation problem of BEM analysis in frequency domain and research and popularize a time-domain BEM to analyze multi-frequency noise.The main contents are as follows:(1)Transform the controlling wave equation of sound source propagation in time domain into Helmholtz equation described in frequency domain by Fourier transform.According to the step size requirement of time domain calculation,several frequency points with equal intervals were selected as sampling frequencies in the frequency domain,and the Helmholtz equation of each characteristic frequency was solved by using the boundary element method to obtain the sound pressure in the frequency domain at each sampling frequency.Discrete inverse Fourier transform is used to transform frequency domain sound pressure into time domain sound pressure,and the time domain transient sound pressure is obtained.Numerical examples are given to verify the correctness of the proposed method.(2)A double reciprocity precise integration method is developed for direct analysis of acoustic radiation problems in time domain.First,the basic solution of Laplace problem is used to transform the wave equation into the boundary integral equation.Then,the boundary integral of the domain integral with time derivative term is transformed by using the double reciprocity method.After boundary discretization,the second order ordinary differential equations with respect to time are obtained.Secondly,by introducing a new variable,the rate of change of sound pressure and the boundary unknown vector,the second order ordinary differential equations are extended to the first order ordinary differential equations,and the general expression of the exact solution of the first order ordinary differential equations is obtained by using Euler’s formula.Finally,the exact integration method is used to calculate the state transition matrix in the exact solution expression.The numerical example shows that the method has high precision and good numerical stability...