Free vibration analysis of magneto-electro-elastic nanobeams in flexural and thickness modes

Abstract In this study, a novel formulation is developed for the free vibration analysis of magneto-electro-elastic (MEE) nanobeams resting on an elastic foundation. A key feature of the proposed displacement-based approach is the adoption of a general (non-predefined) form for the displacement field, in-plane and out-of-plane strain components, and the electric and magnetic potential distributions across the nanobeam thickness. The nanobeam is subjected to externally electric and magnetic potentials. The governing equations of the MEE nanobeam are derived using Hamilton’s principle. The nonlocal elasticity theory is employed to account for the small-size effects in the model. An analytical solution is presented to obtain the natural frequencies of the nanobeam for various boundary conditions. The proposed formulation is capable of capturing both thickness and flexural vibration modes and natural frequency. The numerical predictions are compared to those of shear deformation beam modes of MEE nanobeams available in the literature. The natural frequencies related to various flexural and thickness modes are presented in numerical results. Numerical results are presented to investigate the effects of electric and magnetic potentials, foundation stiffness, nonlocal parameter, length-to-thickness ratio and boundary conditions on the free vibration behavior of MEE nanobeams. Numerical results demonstrate that the present model accurately predicts natural frequencies and mode shapes, including thickness modes, which are neglected by conventional shear deformation theories.