Vibration localization and its application and improved methods in system identification with partially known input

Abstract

This dissertation investigates the vibration localization phenomena in real civil structures, their application to reduce the responses of structures, and propose improved methods in the fields of eigenproblem and system identification. A basic problem in structural dynamics is the eigenproblem and is addressed first in Chapter 2 of this dissertation. In realistic situations, non-proportionally damped systems are often met than the proportionally damped ones. The traditional eigensolution methods are not efficient in the view of stability, accuracy and convergence. Other recent eigensolution methods may require a great deal of complex arithmetic operations or may be subjected to a serious breakdown. The proposed method is obtained by applying the accelerated Newton-Raphson technique and the orthonormal condition of the eigenvectors to the linearized form of the quadratic eigenproblem. In the Newton-Raphson scheme, a step length and a selective scheme are introduced to increase the convergence of the solution. The step length can be evaluated by minimizing the norm of the residual vector using the least-squares method. While the singularity may occur during factorizing process in other iteration methods such as the inverse iteration method and the subspace iteration method if the shift value is close to an exact eigenvalue, the proposed method guarantees the nonsingularity by the orthonormal condition of eigenvectors, which can be proved analytically. Chapter 3 deals with the two important phenomena related to disordered structures, i.e., the mode localization and response localization, one occurs in the modal model and the other occurs in the spatial model of the structure. By parametric study, as one of the contributions, this dissertation showed that in civil engineering structure, even with the presence of strong coupling between substructures, the disorder of the structure can still cause mode localization, given the disorder large enough, meanwhile the ...