8(2011) 229 – 243 Free vibration of thick orthotropic plates using trigonometric shear deformation theory Abstract In this paper a trigonometric shear deformation theory is presented for the free vibration of thick orthotropic square and rectangular plates. In this displacement based theory the in-plane displacement field uses sinusoidal function in terms of thickness coordinate to include the shear deforma- tion effect. The cosine function in terms of thickness coordi- nate is used in transverse displacement to include the effect of transverse normal strain. The most important feature of the theory is that the transverse shear stress can be ob- tained directly from the constitutive relations satisfying the shear stress free surface conditions on the top and bottom surfaces of the plate. Hence the theory obviates the need of shear correction factor. Governing equations and bound- ary conditions of the theory are obtained using the principle of virtual work. Results obtained for frequency of bending mode, shear mode and thickness stretch mode of free vibra- tion of simply supported orthotropic square and rectangular plates are compared with those of other refined theories and exact solution from theory of elasticity wherever applicable. Keywords shear deformation, thick orthotropic plate, transverse nor- mal strain, free vibration, frequencies. Y. M. Ghugal * and A. S. Sayyad Department of Applied Mechanics, Govern- ment Engineering College, Aurangabad-431005, Maharashtra State, India Received 06 Nov 2010; In revised form 17 May 2011 * Author email: ghugal@rediffmail.com 1 INTRODUCTION The use of composite materials has increased steadily during last two decades, particularly in aerospace, underwater and automotive structures. This is largely because many compos- ite materials exhibit high strength-to-weight and stiffness-to-weight ratios, which make them ideally suited for use in weight-sensitive structures. The study of free vibration dates back to the 1800s. Kirchhoff [9, 10] developed classical plate theory (CPT) which is based on hypothesis that straight lines normal to the undeformed midplane remain straight and normal to the deformed midplane. Since the transverse shear deformation is neglected in Kirchhoff theory, it can not be adequate for the analysis of shear flexible thick plates wherein shear deformation effects are more significant. Thus, its suitability Latin American Journal of Solids and Structures 8(2011) 229 – 243