Subspace and Nonlinear-Normal-Modes-Based Identification of a Beam with Softening-Hardening Behaviour

Abstract

The capability to reproduce and predict with high accuracy the behaviour of a real system is a fundamental task of numerical models. In nonlinear structural dynamics, additional parameters compared to classical linear modelling, which include the nonlinear coefficient and the mathematical form of the nonlinearity, need to be identified to bring the numerical predictions in good agreement with the experimental observations. In this context, the present paper presents a method for the identification of an experimental cantilever beam with a geometrically nonlinear thin beam clamped with a prestress, hence giving rise to a softening-hardening nonlinearity. A novel nonlinear subspace identification method formulated in the frequency domain is first exploited to estimate the nonlinear parameters of the real structure together with the underlying linear system directly from the experimental tests. Then a finite element model, built from the estimated parameters, is used to compute the backbone of the first nonlinear normal mode motion. These numerical evaluations are compared to a nonlinear normal modes-based identification of the structure using system responses to stepped sine excitation at different forcing levels.