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Study of nonlinear dynamic behaviour of plates resting on two parameters foundation under various environmental conditions has been an area of increasing research interests in industrial and engineering applications. In this work, the dynamic behaviour of functionally graded plates resting on Winkler and Pasternak foundation is investigated. The inherent singularities in the governing equation are analyzed using differential transform method. Good relationship is established when the results of the semi - approximate analytical methods are compared with the already established research based on experimental. To assess the effect of nonlinear Pasternak foundation introduced, the governing differential equation is converted using Galerkin one-parameter approach into Duffing equation. Thereafter, the domain issue peculiar to semi analytical solutions is treated using cosine after treatment method. Analytical Solutions obtained are used to examine the material properties variation, linear Winkler, nonlinear Winkler and Pasternak foundation effects on plate vibration. It is established that natural frequency decrease with decrease in thickness of the plate, Natural frequency increases with increase in the value of Winkler and Pasternak foundation coefficients. The modal shape obtained satisfy the classical theory of the plate vibration. It is expected that the findings of this work will be relevant in tackling problems related to plate vibration in the industries.

Nonlinear dynamic behaviour of functionally graded circular plates resting on two-parameters foundation using differential transform method