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Journal of Applied Mathematics
Volume 2013, Article ID 841690, 13 pages
Research Article

Application of the Characteristic Time Expansion Method for Estimating Nonlinear Restoring Forces

Department of Marine Engineering, National Taiwan Ocean University, No. 2, Pei-Ning Road, Keelung 20224, Taiwan

Received 17 May 2013; Revised 29 September 2013; Accepted 30 September 2013

Academic Editor: Magdy A. Ezzat

Copyright © 2013 Yung-Wei Chen. 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 proposes a characteristic time expansion method (CTEM) for estimating nonlinear restoring forces. Because noisy data and numerical instability are the main causes of numerical developing problems in an inverse field, a polynomial to identify restoring forces is usually adopted to eliminate these problems. However, results of the way doing are undesirable for a high order of polynomial. To overcome this difficulty, the characteristic length (CL) is introduced into the power series, and a natural regularization technique is applied to ensure numerical stability and determine the existence of a solution. As compared to previous solutions presented in other researches, the proposed method is a desirable and accurate solver for the problem of restoring the force in the inverse vibration problems.