Effect of Mechanical Impact and Electromagnetic Actuation on the Nonlinear Vibration of a Beam

This work is devoted to an investigation of the nonlinear vibration response of a simply-supported flexible beam under a mechanical impact in the presence of an electromagnetic actuator. The governing differential equation and the boundary conditions are modeled within the framework of a Euler-Bernoulli beam and using so-called Hamiltonian principle and Galerkin-Bubnov procedure. An explicit analytical solution is proposed for a complex problem by means of some auxiliary functions derived from the governing equation. The proposed procedure is proved to be very accurate, simple and easy to implement.