Journal of Applied Mathematics
Volume 2013 (2013), Article ID 754576, 7 pages
Research Article

A New Simultaneous Identification of the Harmonic Excitations and Nonlinear Damping of Forced Damped Nonlinear Oscillations: A Parametric Approach

Department of Naval Architecture and Ocean Engineering, Pusan National University, Busan 609-735, Republic of Korea

Received 27 September 2012; Revised 21 December 2012; Accepted 23 December 2012

Academic Editor: George Jaiani

Copyright © 2013 T. S. Jang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.