Dynamic responses of Reissner–Mindlin plates with free edges resting on tensionless elastic foundations

Dynamic response analysis is presented for a Reissner–Mindlin plate with four free edges resting on a tensionless elastic foundation of the Winkler-type and Pasternak-type. The mechanical loads consist of transverse partially distributed impulsive loads and in-plane static edge loads while the temperature field is assumed to exhibit a linear variation through the thickness of the plate. The material properties are assumed to be independent of temperature. The two cases of initially compressed plates and of initially heated plates are considered. The formulations are based on Reissner–Mindlin first-order shear deformation plate theory and include the plate–foundation interaction and thermal effects. A set of admissible functions is developed for the dynamic response analysis of moderately thick plates with four free edges. The Galerkin method, the Gauss–Legendre quadrature procedure and the Runge–Kutta technique are employed in conjunction with this set of admissible functions to determine the deflection-time and bending moment–time curves, as well as shape mode curves. An iterative scheme is developed to obtain numerical results without using any assumption on the shape of the contact region. The numerical illustrations concern moderately thick plates with four free edges resting on tensionless elastic foundations of the Winkler-type and Pasternak-type, from which results for conventional elastic foundations are obtained as comparators. The results confirm that the plate will have stronger dynamic behavior than its counterpart when it is supported by a tensionless elastic foundation.