Mode-like properties and identification of nonlinear vibrating systems

A study is made of mode-like properties and identification of nonlinear systems and their applications in structural seismic analysis. In the thesis, mode-like behavior of nonlinear systems is examined. The modal frequencies and mode shapes of nonlinear systems are found to be dependent on the response. Based on approximation, amplitude-dependent mode shape is defined and approximate methods for calculation of modal frequencies and mode shapes (instantaneous and amplitude-dependent) are presented. Based on amplitude-dependent modal relationship, amplitude-dependent models of modal equations which are valid in large range of response and suitable for unique identification are proposed and the corresponding modal identification procedures are developed. The applicability of the new models and identification algorithms is tested through the analysis of an ideal 3DOF nonlinear system. As applications, the seismic responses of a 47-story building and a 4-story building are investigated using the presented methods. The modal parameters and modal equations of the structures are identified.