An analytical theory for the response of finite elastic plates at low frequencies under heavy fluid loading

Abstract

The low-frequency response to concentrated excitation of a finite thin elastic plate under heavy fluid loading is examined using a generalized Wiener-Hopf approach. The plate size is assumed large in an appropriate sense, and it is shown how the solution can be derived from the exact solution for the structure-acoustic problem at the edge of a semi-infinite plate. In particular, it is shown that the reflection, with no more than a phase change dependent on the edge conditions, of a low-frequency structural wave at the edge leads to the phenomena of resonance and antiresonance very much as in the absence of fluid loading. It is then argued that exact results for infinite and semi-infinite geometries may be used to solve, approximately, a wide variety of problems in the heavy fluid loading limit which are not otherwise susceptible to analytical treatment, and also that this method in principle permits heavy fluid loading effects to be incorporated in large-scale finite element calculations for realistic structures. [Work supported by ONR, Code 222.]