Vibration Analysis of Circular Magneto-electro-elastic Nano-plates based on Eringen’s Nonlocal Theory

The present work mainly studies the free vibration of circular magneto-electro-elastic (MEE) nanoplates based on Kirchhoff’s plate theory within the framework of nonlocal elasticity theory to account for the small scale effect. The MEE nano-plate studied here is considered to be fully clamped and subjected to the external magnetic and electric potentials. Using nonlocal constitutive relations of MEE materials, the governing equations are derived by applying Maxwell’s equation and Hamilton’s principle. By employing Galerkin method, the eigen matrix form of the governing equation is obtained. The effect of magneto-electric potential on instability of the system is investigated and consequently critical values of applied potentials are calculated. A detailed numerical study is conducted to study the influences of the small scale effect, thickness and radius of the nano-plate and piezoelectric volume fraction of the MEE material on the natural frequencies of nano-plate. Furthermore, the effects of the applied magnetic and electric potentials on the size-dependent natural frequencies are investigated numerically.