Helmholtz, Duffing and Helmholtz-Duffing Oscillators: Exact Steady-State Solutions

Abstract

This work presents an analytic technique aimed at designing the external excitation of linear and nonlinear oscillators so that a prescribed form of their steady-state response can be achieved. The technique exploits the exact analytic solutions of the oscillator response having quadratic and/or cubic nonlinearities. Both single-frequency and multi-frequency responses are considered. Examples of possible applications are provided in terms of virtual experiments.