Free vibration and biaxial buckling analysis of double magneto-electro-elastic nanoplate-systems coupled by a visco- Pasternak medium via nonlocal elasticity theory

Abstract

Abstract This paper deals with the analysis of free vibration and biaxial buckling of double-magneto-electro-elastic nanoplate-systems (DMEENPS) subjected to initial external electric and magnetic potentials, using nonlocal plate theory. It is supposed that the two nanoplates are bonded with each other using a visco-Pasternak medium, and are also limited to the external elastic substrate. Hamilton's variational principle is applied to acquire the partial differential equations of motion and corresponding boundary conditions for three modes (out-of-phase, in-phase and one nanoplate fixed) and solved analytically to determine clear closed-form phrase for complex natural frequencies natural frequencies and buckling loads. Numerical examples are performed to demonstrate the changes of the vibration frequency and buckling load ratio ( N L L ) of DMEENP against to different values of the nonlocal parameters, initial external electric and magnetic potentials, aspect ratio, damping and transverse stiffness coefficients of the viscoelastic foundation, shear stiffness coefficient of Pasternak medium, length to thickness ratio, nanoplate thickness and higher modes. Also, the effect of biaxial compression ratio on the buckling load is investigated. Results of this study show that considering the interaction between two Magneto-electro-elastic nanoplates lead to achieving greater frequencies and biaxial buckling loads. Moreover, the influences of the nonlocal parameter become more pronounced when the half wave number, initial external electric potential and aspect ratio increase, while the effect of the length to thickness ratio and initial external magnetic potential has the opposite trend.