Free and forced vibration of reissner-mindlin plates with free edges resting on elastic foundations

Free and forced vibration analysis is presented for Reissner-Mindlin plates with four free edges resting on a Pasternak-type elastic foundation. The f ormulations are based on the Reissner-Mindlin plate theory, considering the first order shear deformation effect and including the plate-foundation in teraction and thermal effects. A new set of admissible functions, which sat isfy both geometrical and natural boundary conditions, are developed for th e free vibration analysis of moderately thick plates with four free edges. The Rayleigh-Ritz Method is employed in conjunction with this set of admiss ible functions to determine the vibration behaviors. Then on this basis, th e modal superposition approach is used in conjunction with Mindlin-Goodman procedure to determine the dynamic response of free edge Reissner-Mindlin p lates exposed to thermomechanical loading. The mechanical loads consist of transverse partially distributed impulsive loads and in-plane edge loads wh ile 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 foundat ions with the Winkler elastic foundations being a limiting case. Effects of foundation stiffness, transverse shear deformation, plate aspect ratio, sh ape and duration of impulsive load, loaded area, and initial membrane stres s as well as thermal bending stress on the dynamic response of Reissner-Min dlin plates are studied. (C) 2001 Academic Press.