This paper presents a novel, general method that is aimed at identifying both the harmonic excitations and nonlinear damping of forced nonlinear oscillation systems. An inverse formalism is developed for the identification method, which is shown to be well posed. That is, the inverse formalism has a unique solution and it depends continuously on the data. The unique solution is derived in the closed form. In addition to the mathematical analysis, a numerical example involving a highly nonlinear system is examined for demonstrating the workability of the proposed method for simultaneously identifying both the two aforementioned excitations and nonlinear damping.
T. S. Jang. "A New Simultaneous Identification of the Harmonic Excitations and Nonlinear Damping of Forced Damped Nonlinear Oscillations: A Parametric Approach." J. Appl. Math. 2013 1 - 7, 2013. https://doi.org/10.1155/2013/754576