Nonlinear dynamic modeling of geometrically imperfect magneto-electro-elastic nanobeam made of functionally graded material

Smart magneto-electro-elastic (MEE) structures with high performance are highly valuable across a vast range of aerospace and industrial applications like smart sensing, space robotics, energy harvesting and biomedical research. This work focuses on the nonlinear dynamic response of a functionally graded MEE nanobeam. Initial geometric imperfection including global and localized imperfection modes is considered to reflect the effect of undesired error during nanofabrication process. Such geometric imperfection is involved by the product of hyperbolic and trigonometric functions. The nonlinear dynamic model for the FG-MEE nanobeam is established according to Hamilton's principle and nonlocal constitutive relation to derive its governing equations of motion. The interaction between the imperfect FG nanobeam and its multi-physical stimulus is numerically solved via differential quadrature method. After validating the proposed model with existing works, the parametric study is conducted to fully reveal the coupling effect of geometric imperfection and numerous parameters including imperfection mode and amplitude, external electric and magnetic potentials, functionally graded index, boundary constraint and size-dependent parameter on nonlinear dynamic response of the FG-MEE nanobeam. Simulation results have demonstrated the significance of the MEE coupling effect, which can be used as a guide to design smart and advanced devices for aerospace and industrial applications.