A high frequency impedance-based qualitative non-destructive evaluation (NDE) technique has been successfully applied for structural health monitoring at the Center for Intelligent Material Systems and Structures (CIMSS) [1-3]. This new technique uses piezoceramic (PZT) patches as actuator-sensors to provide a low-power driven constant voltage dynamic excitation, and to record the modulated current flow through the structure. Therefore, it relies on tracking the electrical point impedance to identify incipient level damage. The high frequency excitation provided by the PZT, ensures the detection of minor changes in the monitored structure. It also limits the sensing area to a region close to the PZT source, therefore only changes in the near field of the PZT are detected, enhancing the ability of this technique to localize incipient damage. The phenomena of the PZT's sensing region localization has been the driving motivation for this research. More fundamental analytical research should be performed before full application of this technique is possible. Thereby, a wave propagation continuum mechanics based approach has been applied to model the high frequency vibrations of one dimensional structures. Energy dissipation mechanisms, such as bolted connections and internal friction, are considered to have a major role in the attenuation of the PZT's induced wave, therefore these mechanisms has been extensively studied. To analyzed bolted connections, linear and nonlinear joint models have been used to describe the wave interaction with such nonconservative discontinuities. Also, with the use of an impedance based model, the electromechanical coupling of the PZT and the host structure is added into the formulation. The wave interaction and energy dissipated at the bolted discontinuity has been assessed with energy flux computations of the incident, transmitted, and reflected waves. The effect of loosening the bolted joint has been also analyzed by reducing the spring stiffness and increasing the damping in the dash pots for the linear joint model, and reducing the Coulomb stiffness and shearing force at the interface for the nonlinear case. A scheme based on the correspondence principle has been applied to calculate the specific damping capacity of a system, at any given frequency, as a quantification of the energy dissipated through the system. The material damping was added into the formulation assuming the modulus to have a complex representation, and therefore the corresponding loss factors were found with active measurement of the material properties of the specimen via a wave propagation method, that monitories the wave's speed at two locations. Once the bases of the analytical model have been set up and corroborated with experiments, a parametric study has been developed to account for the various factors that can affect the sensing range of the PZT’s induced wave, and therefore to have a “rule of thumb on how to go about” when bonding PZTs to structures to monitor them. Apart from the energy dissipation mechanisms, other parameters responsible for the reflection of the incoming wave, and its consequent attenuation, has also been reconstructed. With the extensive analysis of these parameters, an impedance damage metric, based on the undamaged and damaged impedance, has been developed for various factors that can be the source of incipient damage. An attenuation metric has also been introduced to identify the degree of transmission of the propagating wave at certain discontinuities. The analysis of the case scenarios reproduced in this parametric study will aid in the knowledge about the number of PZTs needed to be placed in the monitored structure, the most critical locations, and when a monitored member in a system need to be replaced. / Ph. D.