关键词: singular perturbation problem, first-order ordinary differential equation, two-point boundary-value problem, precise integration method, reduction method

Abstract: The reflection and radiation of a wave system at the open end of a submerged semi-infinite elastic pipe are studied. This wave system consists of a flexural wave in the pipe, an acoustic surface wave in the fluid exterior to the pipe and an acoustic wave in the pipe’s interior. Fourier transform techniques are used to formulate this semi-infinite geometry problem rigorously as a Wiener-Hopf type equation. An approximate solution is obtained by using a perturbation method in which the ratio of the massdensities of the fluid and the pipe material is regarded as a small parameter. The calculation of the reflection coefficient is emphasized, and the polar plots of the radiation coefficient are also presented.

Key words: singular perturbation problem, first-order ordinary differential equation, two-point boundary-value problem, precise integration method, reduction method