T. S. Jang/S. H. Kwon/S. L. Han
The Journal of Mechanical Science and Technology, vol. 23, no. 11, pp.2938-2947, 2009

Abstract : A novel procedure is proposed to identify the functional form of nonlinear restoring forces in the nonlinear oscillatory motion of a conservative system. Although the problem of identification has a unique solution, formulation results in a Volterra-type of integral equation of the “first” kind: the solution lacks stability because the integral equation is the “first” kind. Thus, the new problem at hand is ill-posed. Inevitable small errors during the identification procedure can make the prediction of nonlinear restoring forces useless. We overcome the difficulty by using a stabilization technique of Landweber’s regularization in this study. The capability of the proposed procedure is investigated through numerical examples.

Keyword : Identification; Nonlinear restoring forces; Volterra nonlinear integral equation; numerical instability; Regularization