No abstract

The vibration analysis of an annular plate made up of functionally graded magneto-electro-elastic materials subjected to multi physical loads is presented. The plate is in thermal environment and temperature is distributed non-uniformly in its thickness direction. In addition, the plate is assumed moderately thick, the material properties vary through the thickness, and the exact neutral surface position is determined and took into account. According to Hamilton’s principle and the first-order shear deformation theory, the governing motion equations are extracted. Numerical results for various boundary conditions are obtained via the generalized differential quadrature method and are validated in simpler states with those of the literature. The effects of different parameters such as material property gradient index, multi physical loads, temperature variations, boundary conditions and geometric specifications of the plate on the natural frequencies and mode shapes are investigated. Temperature changes have little effect on the natural frequencies and the effect of electric potential on them is opposite of magnetic one. In other words, by increasing the magnetic potential, the rigidity of the plate increases too, and the frequency increases. The results of this study are useful to design more efficient sensors and actuators used in the smart or intelligent structures.

The current study aims to analyze the asymmetric free vibration behavior of shear deformable functionally graded magneto-electro-thermo-elastic circular plates. The plate’s displacements are described by employing the first-order shear deformation theory and based on the von Karman assumptions, the strains and displacements are related together. Using Hamilton’s principle and variational formulation, the governing motion equations and also the associated boundary conditions have been derived. The generalized differential quadrature method is applied to discretize and solve them. The effects of the most important parameters such as material gradient index, electromagnetic loads, boundary conditions, and also aspect ratio of the plate on the natural frequencies and mode shapes of the plate are considered and discussed in details. The results show that the effect of electric potential on the natural frequency is the opposite of the magnetic one. In other words as the magnetic potential increases, the rigidity of the plate increases too and the frequency enhances. The results are compared and verified with the simpler states in literature. The findings of this study are useful for designing more efficient sensors and actuators used in smart or intelligent structures.

In the present article, according to the nonlocal elasticity theory within the framework of the third-order shear deformable plate assumption, the theoretical analysis of thermomechanical vibration response of magneto-electro-thermo-elastic nanoplate made of functionally graded materials resting on the visco-Pasternak medium is carried out. The simply supported magneto-electro-thermo-elastic nanoplate is supposed to subject to initial external electric, magnetic potentials, and temperature environment. The material characteristics of magneto-electro-thermo-elastic nanoplate are assumed to be variable continuously across the thickness direction based upon power law distribution. Hamilton’s principle is utilized to achieve the partial differential equations and corresponding boundary conditions. The equilibrium equations are solved analytically to determine the complex eigenfrequency using Navier’s approach which satisfies the simply supported boundary conditions. Numerical studies are performed to illustrate the dependency of the natural frequency of the system on the damping coefficient of the visco-Pasternak medium, nonlocal parameter, aspect ratio, temperature change, volume fraction index of functionally graded material, initial external electric voltage, initial external magnetic potential, and plate thickness. It is clearly indicated that these factors have highly significant impacts on the dynamic behavior of the proposed system.

No abstract