An MSPT of a parametrically excited cantilever beam

Abstract A system of nonlinear, coupled, second-order differential equations describing the oscillations of a cantilever beam has been considered and solved. The multiple-time scale perturbation technique (MSPT) has been applied to solve those differential equations up to the fourth approximation. The obtained solutions are presented as the response of the system's different modes. The theoretical resonance conditions of the system (three different modes) have been obtained from the third and fourth approximations. Some of these resonance conditions have been confirmed applying well-known numerical techniques.