Free Vibration Analysis of Rectangular Plates using Two Variable Trigonometric Shear Deformation Theory

Abstract

In this paper, a two variable trigonometric shear deformation plate theory is developed for the free vibration analysis of thick isotropic square and rectangular plates. The theory involves only two unknowns, as against three in first order shear deformation theory and other higher order theories. 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 transverse displacement consists of bending and shear components. The theory satisfies the traction free conditions at top and bottom surfaces of the plate without using shear correction factor. Governing equations and boundary conditions of the theory are obtained using the dynamic version of principle of virtual work. Results of frequencies of bending and shear modes are obtained from free vibration analysis of simply supported isotropic square and rectangular plates and compared with those of other refined theories and exact theory.

Cite this Article

Sachin M. Gunjal, Atteshamuddin S. Sayyad, Rajesh B. Hajare et al. Free vibration analysis of rectangular plates using two variable trigonometric shear deformation theory. Journal of Experimental & Applied Mechanics. 2015; 6(3): 58–64p.