FREE AND FORCED VIBRATION OF REISSNER–MINDLIN PLATES WITH FREE EDGES RESTING ON ELASTIC FOUNDATIONS

Abstract

Free and forced vibration analysis is presented for Reissner–Mindlin plates with four free edges resting on a Pasternak-type elastic foundation. The formulations are based on the Reissner–Mindlin plate theory, considering the first order shear deformation effect and including the plate–foundation interaction and thermal effects. A new set of admissible functions, which satisfy both geometrical and natural boundary conditions, are developed for the free vibration analysis of moderately thick plates with four free edges. The Rayleigh–Ritz Method is employed in conjunction with this set of admissible functions to determine the vibration behaviors. Then on this basis, the modal superposition approach is used in conjunction with Mindlin–Goodman procedure to determine the dynamic response of free edge Reissner–Mindlin plates exposed to thermomechanical loading. The mechanical loads consist of transverse partially distributed impulsive loads and in-plane edge loads while the temperature field is assumed to exhibit a linear variation through the thickness of the plate. The numerical illustrations concern moderately thick plates with four free edges resting on Pasternak-type elastic foundations with the Winkler elastic foundations being a limiting case. Effects of foundation stiffness, transverse shear deformation, plate aspect ratio, shape and duration of impulsive load, loaded area, and initial membrane stress as well as thermal bending stress on the dynamic response of Reissner–Mindlin plates are studied.