Abstract
Simplified non-linear, uncoupled differential equations for the dynamic case of an elastic plate resting on an elastic foundation, vibrating with large amplitudes are presented by making the assumption, due to Berger [5], that the strain energy corresponding to the second invariant of the middle surface strains can be neglected. A modified Galerkin method is used to derive a non-linear differential equation of which the solution is given in terms of elliptic functions. Numerical results are presented for a simply supported rectangular plate and simply supported and clamped circular plates performing large amplitude vibrations.
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