Size-dependent nonlinear vibration analysis of nonlocal magneto-electro-elastic sandwich nanobeam based on Reddy’s third-order shear deformation theory

The size-dependent nonlinear vibration model of the magneto-electro-elastic (MEE) sandwich nanobeam on Winkler-Pasternak foundation is built based on nonlocal elasticity theory and Reddy's third-order shear deformation theory. Employing the Hamilton variational principle and von Karman's geometrically nonlinear theory, the nonlinear governing equation system of MEE sandwich nanobeam is deduced. The expressions of nonlinear frequency ratio and critical external electric and magnetic potential are derived with the perturbation method. Several cases are studied in order to show the influence of nonlocal parameter, Winkler and Pasternak elastic foundation, stacking sequence, external electric and magnetic potential on size-dependent nonlinear vibration behaviors of MEE simply supported sandwich nanobeam.