Free vibration and dynamic response of a fluid-coupled double elliptical plate system using Mathieu functions

A three-dimensional analytic model involving products of angular and radial Mathieu functions is developed for the exact free vibration analysis and transient acousto–structural response of two parallel elliptical plates, coupled with an internal bounded inviscid and compressible fluid medium, and under general external transverse loads of arbitrary temporal and spatial variations. Extensive numerical data are presented in an orderly fashion for the first ten symmetric/anti-symmetric system natural frequencies as a function of fluid layer thickness parameter for selected plate aspect ratios. Also, the occurrences of frequency veering phenomena between various modes of the same symmetry group and the interchange of associated mode shapes in the veering region are noted and discussed. Moreover, selected fluid-coupled structural deformation mode shapes are presented in vivid graphical form and the issue of mode localization is examined. The Laplace transform with respect to the time variable is subsequently invoked and a linear system of coupled algebraic equations is ultimately obtained, which is truncated and then solved by implementing Durbinʹs Laplace inversion algorithm accompanied with special solution convergence enhancement techniques for eradication of spurious oscillations (Gibbsʹ phenomenon). Numerical simulations are conducted for the displacement time histories of water-coupled double aluminum plates of selected aspect ratios and fluid depths, subjected to external loads of practical interest (i.e., an impulsive point load, a concentrated pulse load, and a uniformly distributed blast load). Validity of the results is established through computations made by using a commercial finite element package as well as by comparison with the data available in literature.