Asymmetric free vibration analysis of first-order shear deformable functionally graded magneto-electro-thermo-elastic circular plates

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.