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 response localization could occur more easily even when the disorder is small. Suitable measurements of localization for practice, i.e., the modified degree of mode localization and the degree of response localization were proposed.
The effects of the disorder to the dynamic characteristics, to the mode localization, to the responses and to the response localization are figured out. It is shown that, in dynamic problem, the maximum responses and the response localization vary in a complex way, depending on dynamic characteristics of structure as well as the frequency contents of the loading. Thus in a good structural design, one has to tune the disorder parameters to effectively reduce the responses of the structure. An application of vibration localization was proposed. By using cantilevers attached to the outer-span substructure with properly tuned parameters, the responses of main structure could be reduced.
In the structural analysis problems, one often bases on the assumption that full knowledge of mass, damping and stiffness of the structure is available. This assumption is reasonable in the phase of structural design. However, after being constructed, structures degrade, deteriorate, and/or have damages. As a result, its characteristics (mass, damping, and stiffness) change and they are often subjected to be identified. System identification is dealt in Chapter 4. This chapter proposes improved methods of the well-known least-squares methods and extended Kalman filter method. The improved methods are then applied into a time domain SI procedure to estimate the system parameters when the input is just partially known. The improved least-squares methods are based on the rearrangement of the system parameters into matrix form rather than in a column vector as traditional arrangement did. Likewise, the improved extended Kalman filter method rearranges the augmented state into matrix form before linearizing and discretizing the dynamic and observation equations. The improvement of the proposed methods is the smaller size of the coefficient matrix thus the requirements of storage and computing time are reduced, especially in the case of large-scale structures. Generally, the least-squares methods and the extended Kalman filter method apply when the input excitation information is known or can be measured exactly. However, in real situations, the time-history of input excitation is difficult and often costly to obtain. Commonly, the available information of the input is the locations of the excitation. To deal with this situation, simple SI procedures based on the improved least-squares methods and on the improved Kalman filter method are suggested.
