Nonlinear low-velocity impact response of magneto-electro-elastic beams with initial geometric imperfection

Previous studies on the dynamic problems of magneto-electro-elastic (MEE) beams mainly focused on the buckling and free vibration, no literature paid attention to the low-velocity impact response problem. More importantly, no one conducted the investigation on the nonlinear low-velocity impact of MEE beams with considering the effect of initial geometric imperfection. To fill this gap, this article aims to study the low-velocity impact problem of MEE beams with initial geometric imperfection. Firstly, the nonlinear Hertz contact law is used to describe the displacement and contact force of the MEE beam, and the initial conditions for the beam and impactor are given. Subsequently, considering the multiple coupling effect, the dynamic model is established through Hamilton’s principle. Taking the simply-supported boundary condition into account, the Galerkin principle is utilized to reduce the dimensionality, resulting in a nonlinear equation regarding contact time, lateral central displacement and contact force. Meanwhile, two comparative analyses are conducted to confirm the rationality of the present work. Finally, the Runge–Kutta method is employed to solve the low-velocity impact response, in which the effects of electric potential, magnetic potential, initial geometric imperfection, temperature rise, prestress, damping coefficient, the radius and velocity of the impactor as well as the geometric dimension of the beam are discussed.