A numerical scheme for recovering the nonlinear characteristics of a single degree of freedom structure: Non-parametric system identification

Abstract

The aim of this paper is to present a numerical scheme for the identification of the nonlinear characteristics of a dynamically excited, single degree of freedom structure, using a non-parametric procedure, recently proposed by the second author; this involves the simultaneous identification of the nonlinear characteristics of both damping and restoring force in dynamic systems whose damping depends on velocity alone. According to this method, the response of the structure is first measured then an integral equation accounting for its unknown nonlinear characteristics is derived. This is an integral equation of the first kind, involving numerical instability in the Hadamard sense. To overcome this difficulty, the Landweber regularization, combined with the L-curve criterion, is applied to the integral equation. Adopting a dynamic model for a test structure, the corresponding nonlinear system identification is achieved through the proposed numerical solution of the governing integral equation. ？ 2014 WIT Press.