Vibration response of a two-dimensional magneto-electro-elastic plate is investigated in this paper. The considered multi-phase plate is rectangular and simply-supported resting on an elastic foundation. The plate is under aerodynamic pressure and subjected to temperature change. It is also assumed that the magneto-electro-elastic body is poled along the z direction and subjected to electric and magnetic potentials between the upper and lower surfaces. The nonlinear vibrational analysis of the described plate is considered as an innovation of the present paper,which had not been done before. To model this problem, third-order shear deformation theory along with Gauss’s laws for electrostatics and magnetostatics, first-order piston theory, and Galerkin and multiple times scale methods are used. After validating the presented method, effects of several parameters on the natural frequency, time history, backbone curve, and phase plane diagram of this smart composite plate are obtained. It is found that for plates with constant a/h ratio, electric and magnetic potentials have noticeable effects on the time histories, phase plane diagrams and backbone curves of the plates with smaller thicknesses. In addition, the numerical results of this research indicate that some parameters have considerable effect on the vibration behavior of presented plate. Elastic parameters of the foundation, applied electric and magnetic potentials, and environment temperature are important parameters in this analysis. تفاصيل المقالة

Free vibration of a simply-supported magneto-electro-elastic doubly-curved nano-shell is studied based on the first-order shear deformation theory in the presence of the rotary inertia effect. To model the electric and magnetic behaviors of the nano-shell, Gauss’s laws for electrostatics and magneto statics are used. By using Navier’s method, the partial differential equations of motion are reduced to a single ordinary differential equation. Then, an analytical relation is obtained for the natural frequency of magneto-electro-elastic doubly-curved nano-shell. Some examples are presented to validate the proposed model. Moreover, the effects of the electric and magnetic potentials, temperature rise, nonlocal parameter, parameters of Pasternak foundation, and the geometry of the nano-shell on the natural frequencies of magneto-electro-elastic doubly-curved nano-shells are investigated. It is found that natural frequency of magneto-electro-elastic doubly-curved nano-shell decreases with increasing the temperature, increasing the electric potential, or decreasing the magnetic potential. تفاصيل المقالة