Simultaneous detection of the nonlinear restoring and excitation of a forced nonlinear oscillation: an integral approach

Abstract

We address in this article, how to calculate the restoring characteristic and the excitation of a nonlinear forced oscillating system. Under the assumption that the forced nonlinear oscillator has a periodic solution with period T = 2π/ω, we constructed a system of linear equations by introducing time-dependent multipliers. The periodicity assumption helps to simplify the system of linear equations. The stability and uniqueness are also presented for the inverse problem. Numerical testing is conducted to show the effectiveness of our presented methodology.