Nonlinear Forced Vibration of an Axially Functionally Graded Beam Under Combined Effects of an Electromagnetic Actuator and Mechanical Impact

The present paper deals with the nonlinear forced vibration of an axially functionally graded beam (FGB) subjected to a mechanical impact and an electromagnetic actuation. Material properties are expressed according to a power law function. The governing equation of motion is derived via Hamilton’s principle and Galerkin-Bubnov approach is implemented to reduce the nonlinear partial differential equation of the system to a nonlinear ordinary differential equation. The Optimal Homotopy Asymptotic Method (OHAM) is applied to obtain approximate analytical expressions for the nonlinear dynamic response and for the nonlinear frequency. This study shows a high accuracy of OHAM proved by comparison with numerical results.