Some benefits of using exact solutions of forced nonlinear oscillators: Theoretical and experimental investigations

This work first presents an analytical technique on how to exploit exact solutions for the response of certain oscillators to design specific external excitation and get a desired form of the exact steady-state response, both in the undamped and damped systems. Related benefits are then discussed, which include: (i) producing the response of free nonlinear oscillators by exciting a linear system in a particular way, (ii) determining the multi-term excitations of nonlinear oscillators to produce a single-term harmonic response, and (iii) tuning nonlinearities in a system excited by certain two-term excitation to produce a single-term harmonic response. Illustrations of these applications are presented in terms of physical and computer-aided experiments.