中文摘要：

为了研究一维管道Webster方程的适用范围,介绍了采用有限差分策略和通过求解线性方程组获得一维Webster方程数值解的方法。通过比较直管、圆锥管道、指数型管道和悬链线管道的数值解和解析解,分析了该数值方法的求解精度。同时,在三维LMS Virtual Lab有限元分析软件平台上,对圆锥管道、指数管道、悬链线管道等三种典型喇叭管道中的声波进行了三维仿真分析。通过比较其基于一维Webster方程的解析解和三维仿真解,讨论了它们基于一维Webster方程的解析解的适用范围。最后,应用三次样条插值方法,设计了一种样条曲线管道,其入口端和出口端的声波更接近平面波。与三种典型喇叭管道相比,采用一维Webster方程数值解能更准确地预测其三维实际管道传声问题。

英文摘要：

In order to research the applied scope of the one dimensional Webster equation for analyzing acoustical properties of pipes, a numerical method for solving the Webster equation is introduced by combining the finite difference method and the algorithm solving linear matrix equations. Compared with the existing analytical solutions of the one dimensional Webster equation for straight pipes, conical pipes, index pipes and catenary pipes, the feasibility and computational accuracy of the numerical method is verified. Meanwhile, the three dimensional finite element analysis of acoustical fields for the three above- mentioned pipes with gradual change cross sections are implemented by using the LMS Virtual Lab software, and the three dimensional simulating results are compared with the analytical solution of the three kinds of pipes. As a result, the applied scope of the one dimensional Webster equation is analyzed and discussed for describing the three kinds of pipes. Finally, a curved pipe is designed by means of the cubic B-Spline functions, its main characteristic is that the acoustical waves at its inlet and outlet are closer to plane waves than those at the inlet and outlet of the three above-mentioned pipes, that is, the description of the curved pipe with the one-dimensional Webster equation is more accurate.