子波分析在声辐射和声散射中的应用

文章提出将子波分析用于求解声学中的边界积分方程,能提高现有边界元方法解决工程问题的能力。在子波分析于声辐射和声散射的应用研究中,提出了把积分核函数用级数展开,建立频率响应函数计算的频率迭代技术,大大提高了频率响应函数的计算效率。讨论了子波分析在声学工程数值计算中的研究前景。

Application of Wavelet Transform to Acoustic Radiation and Scattering

Traditional boundary element methods with a full matrix equation for acoustic problems, have been met by a challenge in large scale scientific computation and numerical simulation in engineering. In this paper, the new wavelet approaches have been presented for solving acoustic radiation and scattering, and structural acoustic coupling. The boundary quantities are expanded in terms of a basis of the orthogonal wavelets on the interval, and a wavelet spectral formulation for solving acoustic problems is derived. Then coupled wavelet spectral and finite element method is formulated for solving sound structure interaction. The advantages of the new approaches include a highly sparse matrix system which can be solved rapidly by sparse solvers and accurate modeling of curve surface. In the new technique, the iterative technique of frequencies is established for evaluating frequency response functions through expanding the integral kernel in Taylor series in integral equation. The new technique was employed to investigate the underwater acoustic radiation from a complicate structure which is composed of shells, stiffening ribs and plates. The comparisons of the results from the new technique with analytic solution show that it has high computational efficiency and good accuracy. At the end of the paper, the prospects of the application of wavelet analysis to numerical computation in acoustic engineering are discussed.