A layered model for vibration analysis of piezoelectric–piezomagnetic bimorph nanobeams with nonlocal small-scale effect

Based on the nonlocal theory, a layered theoretical model is presented for vibration analysis of piezoelectric–piezomagnetic bimorph nanobeams. The layer-wise expressions of displacement and potential fields across the thickness are provided through ensuring the continuity of displacements and shear stresses at the interface as well as the shear stress free at the surface, and then the nonlocal governing equations and consistent boundary conditions are derived from the Hamilton’s principle. For typical support conditions at beam ends, the differential quadrature method is developed to obtain the numerical results which is verified by comparing with analytical solutions for the simply-supported beam. A detailed parametric study is conducted to analyze the influence of nonlocal parameter, structure size, external load and boundary condition on the natural frequency and mode shape. It indicates the nonlocal small-scale effect should be considered to accurately predict the vibration properties of magnetoelectric laminated nanostructures.