On the response at the excitation frequency of a two degrees of freedom nonlinear oscillator

Abstract

This paper presents an overview of the main theoretical advances and experimental analyses, achieved by the authors in recent years of collaborative research in the field of nonlinear dynamics of coupled oscillators. The initial motivation came from some experimental phenomena observed in the dynamics of a two degrees-of-freedom test-rig consisting of a shaker with an attached nonlinear oscillator. An analytical solution for the system response in terms of the frequency response curve was derived, and some insight into the effect of the system parameters on its shape was obtained. For specific combinations of the system parameters, interesting features and shapes of the frequency response curve were theoretically uncovered. Some assumptions were adopted to derive simple closed-form solutions for the amplitude-frequency equation, which allowed for experimental validation.