In the present paper, an exponential shear deformation theory is used to determine the natural frequencies and critical buckling loads of orthotropic plates. The theory accounts for a parabolic distribution of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The in-plane displacement field uses an exponential function in terms of thickness coordinate to include the effect of shear deformation and rotary inertia. Governing equations and boundary conditions are derived from the dynamic version of principle of virtual work. The Navier type solution is employed for solving the governing equations of simply supported square orthotropic plates. The results obtained using present higher order shear deformation theory are found to be agree well with those obtained by other several existing higher order theories for analyzing the buckling and free vibration behaviour of orthotropic plates.

In the present work, a layerwise trigonometric shear deformation theory is used for the analysis of two layered (90/0) cross ply laminated simply supported and fixed beams subjected to sinusoidal load. The displacement field of the present theory consists of trigonometric sine function in terms of thickness coordinate to take into account the effect of transverse shear deformation. Theory satisfies the trans-verse shear stress free boundary conditions at top and bottom surfaces of the beam. This model satisfies the constitutive relationship between shear stress and shear strain in both the layers and the axial displacement compatibility at the interface. Virtual work principle is employed to obtain governing equations and boundary conditions. Closed form solution technique has the limitation of simply supported boundary condition. In the present work general solution technique is developed, which can be used for any type of boundary and loading conditions. The transverse shear stresses are obtained using constitu-tive relation as well from the use of equilibrium equations. The results of displacements and stresses obtained by present theory are compared with the available results in the literature.

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 deformation effect. The cosine function in terms of thickness coordinate 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 obtained 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 boundary 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 vibration 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.