Reflection and radiation of a wave system at the open end of a submerged elastic pipe |
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Authors: | Song Jia-su |
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Institution: | Department of Applied Mechanics, Fudan University, Shanghai |
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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. |
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Keywords: | singular perturbation problem first-order ordinary differential equation two-point boundary-value problem precise integration method reduction method |
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