Buckling and Free Vibrations of a Magneto-Electro-Elastic Sandwich Panel with Flexible Core

Abstract

This paper presents the buckling and out-of-plane free vibration response of a sandwich panel with flexible core for the different boundary condition. In the desired configuration of the sandwich panel, the top and bottom plates are made of magneto-electro-elastic (MEE) plates. Moreover, the in-plane electric and magnetic potential fields are neglected for the derivation of the required relations. The sandwich structure is subjected to axial force in both longitudinal and transverse directions; in addition, and the top and bottom plates are exposed to electric and magnetic fields. The governing equations of motion for MEE sandwich panel with a flexible core are derived based on the first-order shear deformation theory by neglecting the displacement of the mid-plate and using the Hamilton’s principle. Furthermore, the derived partial differential equations (PDEs) are solved. According to the obtained numerical results, the core thickness, variation of electric field, variation of magnetic field and plate length are introduced as the most influential parameters on the free vibration response of the panel as well as the critical force of buckling. As one of the results, the electric potential is inversely related to the natural frequency and buckling load, so that with increasing the electric potential, the natural frequency and critical load of the structure is also increased.Moreover, the magnetic potential is directly related to the natural frequency and buckling load of the system, and increasing trends of natural frequency and critical load are observed by increasing the magnetic potential.