Development of a new and effective modal identification method - mathematical formulations and numerical simulations

Abstract

A new effective and efficient time domain modal analysis is presented in this paper. Based on the theoretical expansion of free decay response functions of damped structures, the method is formulated to utilize measured free-decay response data to efficiently form an equivalent derived eigensystem. Rigorous mathematical derivation will show that modal parameters (natural frequencies, damping ratios and mode shapes) of a damped test structure can be determined from the eigenvalues and eigenvectors of the derived equivalent eigensystem. Scaling of the resulting mode shapes so that they become so called A-normalized will be explored. General guidelines for selection of user-selectable algorithm parameters are also discussed to maximize the benefit of the proposed method. Another important theoretical development associated with the new method is a new concept of modal confidence factor (MCF) for the examination of identification results. The practical applicability and validity of the proposed method and the new MCF will be demonstrated through various numerical case studies. The concepts of equivalent derived eigensystem and MCF associated with the proposed method are new and have been demonstrated to be very effective. The identification results obtained are very accurate as compared with their exact counterparts and the method is very efficient in computational implementations.