Flexural transient response of elastically supported elliptical plates under in-plane loads using Mathieu functions

The elaborated method of eigenfunction expansion in elliptic coordinates is employed to obtain an exact time-domain series solution, involving products of angular and radial Mathieu functions, for the forced flexural vibrations of a thin elastic plate of elliptical planform. The plate is supported by a constant moduli two-parameter foundation, while elastically restrained against translation and rotation at its edge, and subjected to the combined action of uniform in-plane static edge forces and general arbitrary time-dependent transverse loads with arbitrary initial conditions. Numerical calculations are carried out for the displacement response of clamped or simply supported elliptical plates of selected aspect ratios in various practical loading configurations (i.e., an impulsive point load, a point force in circular motion, a uniformly distributed harmonic load, and a blast load), with or without an elastic foundation, while taking the effects of initial tension or compression below the buckling load into consideration. Limiting cases are considered and good agreements with available results as well as with the computations made by using a commercial finite element package are obtained.