Identification of nonlinear multi-degree-of freedom structures based on Hilbert transformation

Abstract

The modeling method and identified method adapted to multi-degree-of-freedom structures with strucrural nonlinearities are established. The component mode synthesis method is used to establish the nonlinear governing equations by extending the connected relationships. Based on the modeling method, the Hilbert transform method is applied to identify the nonlinear stiffness of multi-degree-of-freedom structures. Nonlinear analysis and identification of a typical folding wing configuration with three freeplay hinges are investigated. The nonlinear governing equation is established based on present methods and the computing results of different stiffness are checked by finite element programming. In order to illustrate the influence of the nonlinearities, the frequency response characteristics of the structure are analyzed and Hilbert transform is performed. The Hilbert transform identification method is utilized to identify the nonlinear stiffness of nonlinear hinges in the time domain and several parametric studies are performed. In addition, the comparison of response is made to illustrate the feasibility of the methods. The results show that the extending component mode synthesis method in the present work can be used to establish the governing equation with structural nonlinearities. Based on the modeling method, the Hilbert transform identified method can be extended to multi-degree-of-freedom structures accurately.