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

The present work mainly studies the free vibration of circular magneto-electro-elastic (MEE) nanoplatesbased on Kirchhoff’s plate theory within the framework of nonlocal elasticity theory to accountfor the small scale effect. The MEE nano-plate studied here is considered to be fully clamped andsubjected to the external magnetic and electric potentials. Using nonlocal constitutive relations of MEEmaterials, the governing equations are derived by applying Maxwell’s equation and Hamilton’sprinciple. 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 consequentlycritical values of applied potentials are calculated. A detailed numerical study is conducted to study theinfluences of the small scale effect, thickness and radius of the nano-plate and piezoelectric volumefraction of the MEE material on the natural frequencies of nano-plate. Furthermore, the effects of theapplied magnetic and electric potentials on the size-dependent natural frequencies are investigatednumerically.