magneto-electro-mechanical size-dependent vibration analysis of three-layered nanobeam with initial curvature considering thickness stretching

Thickness stretching effect based on shear and normal deformation theory is used in this paper for magnetoelectro- elastic vibration analysis of a three-layered curved nanobeam including a nano core and two piezo-magnetic layers. size-dependency is included in derivation of governing equations of motion based eringen's nonlocal elasticity theory. the initial curvature is accounted in calculation of external works due to pre-mechanical, electrical and magnetic loads. the analytical method is presented to study the effect of significant parameters on the vibration characteristics. the numerical results are presented in terms of initial electro-magneto-mechanical loads, size-dependency parameter, opening angle, two parameters of pasternak's foundation and core thickness to face-sheet thickness ratio.