Alternative perturbation procedure of multiple scales for nonlinear dynamics systems

An alternative perturbation procedure of multiple scales is presented in this paper which is capable of treating various periodic and almost periodic steady-state vibrations including combination resonance of nonlinear systems with multiple degrees-of-freedom. This procedure is a generalization of the Lindstedt-Poincare method. To show its essential features a typical example of cubic nonlinear systems, the clamped-hinged beam, is analyzed. The numerical results for the almost periodic-free vibration are surprisingly close to that obtained by the incremental harmonic balance (IHB) method.link_to_subscribed_fulltex