| This dissertation is concerned with two challenging areas of vibrations research: (1) inverse modeling for vibration-based structural damage detection, and (2) high-dimensional dynamic response of nonlinear and time-varying distributed structures.; In the first area, we address structural damage detection using changes of natural frequencies, treatment of non-uniqueness of solutions, and treatment of ill-conditioned systems. A robust iterative algorithm is developed and applied to identify the locations and extent of damage in slender structures using only the changes in their first several natural frequencies. The algorithm, which combines a first-order, multiple-parameter perturbation method and the generalized inverse method, is tested extensively through experimental and numerical means on cantilever beams with different damage scenarios. A new method is developed to enrich the measurement information by modifying the structure in a controlled manner. A new method using singular value decomposition is developed to handle the ill-conditioned system equations when they occur.; In the second area, we consider the high-dimensional, nonlinear and time-varying dynamic response of distributed systems with small bending stiffness, such as elevator cables and memory tapes. The effects of bending stiffness, different trial functions, number of trial functions used, and boundary conditions on the dynamics characteristics of cables with small bending stiffness are investigated. Furthermore, a nonlinear model of a friction-guided translating beam with a stationary load system, a boundary excitation, and a periodically varying transport speed is developed. The Incremental Harmonic Balance (IHB) method is extended for the first time on high-dimensional models of a distributed structural system. It is demonstrated that this method can successfully handle a variety of problems, including linear and nonlinear frequency response analyses, system optimization, determination of parametric instability region boundaries, determination of periodic responses for parametrically-excited nonlinear systems, and determination of periodic responses of linear and nonlinear systems under combined parametric and forced excitations. For the distributed system considered here, results show that a large number of trial functions in the spatial discretization are often required to yield the converged solutions; in addition to quantitative inaccuracy, low-dimensional models of the distributed system can lead to qualitatively misleading predictions. |
