Identification of Restoring Force Surfaces in Nonlinear MDOF Systems from FRF Data Using Nonlinearity Matrix

Abstract

The sensitivity of the response characteristics of a nonlinear structure to load level may prevent us to predict the linear behavior of a nonlinear system. The nonlinear identification method recently proposed by the authors is based on the measured linear and nonlinear Frequency Response Functions (FRFs). The method is easy to implement and requires standard testing methods. The data required is limited with measured linear and nonlinear FRFs. In order to obtain the linear FRFs in a nonlinear system, it is the general practice to use low level forcing, unless the nonlinearity is due to dry friction. However, depending on the level of nonlinearity it may not be possible to lower the harmonic forcing amplitude beyond a practical limit, and this may not be sufficient to obtain linear FRFs. The approach presented in this study aims to perform the nonlinear identification directly from a series of measured nonlinear FRFs. It is shown that Restoring Force Surfaces (RFS) can be identified more accurately by employing this approach. The verification of the method is demonstrated with simulated and experimental case studies.