Boundary Element Method For Multifrequency Noise Radiation Problems

Nowadays,noise problem has become an inevitable factor in modern society,and the corresponding research gradually deepened.Boundary element method(BEM)has natural advantages in dealing with infinite field problems such as real sound field.The advantage of only discretizing the boundary makes this method easier to implement than other numerical methods such as finite element method(FEM),and the computational accuracy of the results obtained by bem is higher.The boundary element method(BEM)in frequency domain needs to be optimized to meet the requirements of modern computing efficiency in large scale multi-frequency acoustic radiation problems,and there will be error accumulation in numerical inverse transformation.The boundary element method(BEM)in the time domain can avoid the extra inverse numerical transformation in the frequency domain,but the time term processing will be unstable.This paper focuses on the boundary element method(BEM)under the noise radiation problem,aiming to explore and solve the above problems.The specific research contents are as follows:(1)Compared with the common frequency-domain boundary element method,the frequency domain boundary element method combined with the inverse Fast Fourier transform is applied to solve the sound pressure value in the multi-frequency acoustic field,which greatly improves the computational efficiency and effectively reduces the error accumulation in the calculation process.(2)Double reciprocal boundary element method(DRM)combined with precise integration method(PIM)is applied to solve complex sound pressure in acoustic radiation field.In the double reciprocity method,the pure boundary integral is obtained by the discrete control point fitting based on the radial basis function(RBF)of radiated sound field.The precise integration method is used to calculate the state transition matrix,and the error of the calculated results is small,which can meet the requirements well,and the numerical results do not appear unstable phenomenon.(3)The double reciprocal boundary element method combined with Runge-Kutta methods is applied to solve the complex sound pressure of acoustic radiation field.The runge-Kutta method can avoid the introduction of complex differential equation solving process in the calculation,and the numerical results obtained by iterative calculation also have a small error.(4)Compare the application of double reciprocal fine integration method and double reciprocal Runge-Kutta method.The calculation of the two methods has high accuracy and stability.Under the condition of considering the computational efficiency,the double-reciprocal RungeKutta method can get the numerical results faster under the condition of satisfying the error requirement.Considering the calculation accuracy,the double reciprocity precise integration method can get the numerical results with lower error when the step size is smaller.