Islamic Azad University Arak BranchJournal of Solid Mechanics2008-35053220110630Free Vibration of Thick Isotropic Plates Using Trigonometric Shear Deformation Theory172182514411ENY.M GhugalDepartment of Applied Mechanics, Government Engineering College, Aurangabad-431005 (Maharashtra State)A.S SayyadDepartment of Applied Mechanics, Government Engineering College, Aurangabad-431005 (Maharashtra State)Journal Article20110509In this paper a variationally consistent trigonometric shear deformation theory is presented for the free vibration of thick isotropic square and rectangular plate. In this displacement based theory, the in-plane displacement field uses sinusoidal function in terms of thickness coordinate to include the shear deformation effect. The cosine function in terms of thickness coordinate is used in transverse displacement to include the effect of transverse normal strain. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. Results of frequency of bending mode, thickness-shear mode and thickness-stretch mode are obtained from free vibration of simply supported isotropic square and rectangular plates and compared with those of other refined theories and frequencies from exact theory. Present theory yields exact dynamic shear correction factor π<sup>2</sup>/12 from thickness shear motion of the plate.http://jsm.iau-arak.ac.ir/article_514411_9cd976687f1a4475ff1c9da88145a2bf.pdf