Abstract
AbstractThis paper presents a method for solving vibration problems of a plate with irregular shape lying on an elastic foundation in consideration of effects of masses of foundation. For the foundation, the equation of motion of longitudinal vibrations of a solid is utilized, and the solutions of both the foundation and the plate are joined together by use of the conditions of continuity between the plate and the foundation. The analysis uses the Fourier expansion collocation method given by Nagaya to satisfy the irregular boundary conditions. Numerical calculations have been carried out for general polygonal plates on elastic foundations. The results for the plate on Winkler's foundation are also given to compare both results. It is clarified that there are some discrepancies between the present result which includes foundation inertias and that of Winkler's foundation.
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