In 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 p2/12 from thickness Shear motion of the plate.

In this study, the elastic buckling and static bending of a functionally graded porous plate based on Shear deformation theory have been investigated. The effect of the type and degree of porosity on the mechanical behavior of the plate using the principle of potential energy is the main goal of this research. The modulus of elasticity and mass density of the porous sheet are graded in terms of thickness according to two different distribution patterns. The system of partial differential equations governing the buckling and bending behavior of the plate is derived from Hamilton's principle. The Ritz method is used to calculate the critical buckling loads and transverse bending curvature. In order to validate the method and the results presented in this research, a comparison was made with the results presented in authoritative references and articles. In addition, the finite element modeling results have been compared with the present analysis. Also, a parametric study has been performed to investigate the effects of porosity coefficient and length to thickness ratio of plate on buckling and flexural properties of porous sheets with simply support boundaries. The effect of different porosity distributions on plate performance is discussed. In this research, by applying different porosity coefficients and changes in length to thickness ratio, buckling load and flexural behavior of a graded porous plate with a specific porosity distribution pattern has been investigated. According to parametric study of porous plate, the buckling load and the maximum transverse displacement on bending increase with increasing the porosity coefficient and the ratio of length to thickness. The results of this study are used to design of porous plate in various designs such as implants.

In this study, the dynamic buckling of the embedded laminated nanocomposite plates is investigated. Theplates are reinforced with the single-walled carbon nanotubes (SWCNTs), and the Mori-Tanaka model isapplied to obtain the equivalent material properties of them. Based on the sinusoidal Shear deformationtheory (SSDT), the motion equations are derived using the energy method and Hamilton's principle. TheNavier’ s method is used in conjunction with the Bolotin's method for obtaining the dynamic instabilityregion (DIR) of the structure. The effects of different parameters such as the volume percentage ofSWCNTs, the number and orientation angle of the layers, the elastic medium, and the geometricalparameters of the plates are shown on DIR of the structure. Results indicate that by increasing the volumepercentage of SWCNTs the resonance frequency increases, and DIR shifts to right. Moreover, it is foundthat the present results are in good agreement with the previous researches.

A Trigonometric Shear deformation theory (TSDT) for the analysis of isotropic plate, taking into account transverse Shear deformation effect as well as transverse normal strain effect, is presented. The theory presented herein is built upon the classical plate theory. In this displacement-based, trigonometric Shear deformation 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. It accounts for realistic variation of the transverse Shear stress through the thickness and satisfies the Shear stress free surface conditions at the top and bottom surfaces of the plate. The theory obviates the need of Shear correction factor like other higher order or equivalent Shear deformation theories. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. Results obtained for static flexural analysis of simply supported thick isotropic plates for various loading cases are compared with those of other refined theories and exact solution from theory of elasticity.

In this article fluid-structure interaction of vibrating composite piezoelectric plates is investigated. Since the plate is assumed to be moderately thick, rotary inertia effects and transverse Shear deformation effects are deliberated by applying exponential Shear deformation theory. Fluid velocity potential is acquired using the Laplace equation, and fluid boundary conditions and wet dynamic modal functions of the plate are expanded in terms of finite Fourier series to satisfy compatibility along with the interface between plate and fluid. The electric potential is assumed to have a cosine distribution along the thickness of the plate in order to satisfy the Maxwell equation. After deriving the governing equations applying Hamilton’ s principle, the natural frequencies of the fluid-structure system with simply supported boundary conditions are computed using the Galerkin method. The model is compared to the available results in the literature, and consequently the effects of different variables such as depth of fluid, the width of fluid, plate thickness, and aspect ratio on natural frequencies and mode shapes are displayed.

In this paper, free vibration of rectangular functionally graded material (FGM) plates with distributed patch mass is analyzed. Properties of these plates like Young’s modulus and density vary continuously throughout the thickness direction. The plate is defined by power-law, sigmoid or exponential function. The boundary condition of the plate is assumed to be simply supported and the equation of motion is obtained by using of Hamilton principle and third order Shear deformation theory. The effects of different parameters such as the plate and mass dimensions and mass ratio on the natural frequencies of the plate are analyzed. Compared to previous results, our results are very accurate in similar cases.