Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 749309, 12 pages
http://dx.doi.org/10.1155/2011/749309
Research Article

A New Method for Detecting the Time-Varying Nonlinear Damping in Nonlinear Oscillation Systems: Nonparametric Identification

T. S. Jang,1 Hyoungsu Baek,2 M. C. Kim,1 and B. Y. Moon3

1Naval Architecture and Ocean Engineering, Pusan National University, Busan 609-735, Republic of Korea
2Department of Mathematics, Massachusetts Institute of Technology, 183 Memorial Drive, Cambridge, MA 02139, USA
3Department of Naval Architecture, Kunsan National University, Gunsan 573-701, Republic of Korea

Received 11 July 2011; Accepted 6 September 2011

Academic Editor: Anuar Ishak

Copyright © 2011 T. S. Jang et al. 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.

Abstract

This paper presents an original method that can be used for identifying time-varying nonlinear damping characteristics of a nonlinear oscillation system. The method developed involves the nonparametric identification, in which only the system responses, namely, displacement and velocity need to be known for the identification. However, the method is concerned with a Volterra-type integral equation of the first kind, which leads to an instability of numerical solutions. That is, the solutions identified lack stability properties. In order to overcome the difficulty, a stabilization technique is applied to the identification process. A numerical example comprising a highly nonlinear system is examined to demonstrate the workability of the proposed method for the time-varying damping identification.