Modeling, analysis, and experimental verification of a multi-mode vibro-impacting system

This thesis presents the model problem of a pinned-free beam impacting a linear spring due to sinusoidal base motion. The beam has been represented as both a single- and multi-degree-of-freedom (DOF) system and the results of these representations have been compared to each other as well as experimental data. It has been found that the multi-DOF model is required in order to capture higher frequency response. In addition, the effect of multiple impacts on the Fourier transform of the response has been examined and suggests a method by which experimentalists can estimate the number of impacts per cycle in a given motion by observation of its frequency response.; The analytical expressions for period-1,1 response (i.e., those solutions which repeat with every forcing cycle and undergo one-impact per period) were developed by matching the piecewise linear expressions at the loss- and regaining-of-contact times. The results of these solutions have been compared to experimental responses and are found to agree in qualitative character. Parameter studies show that increasing stiffness and decreasing contact damping reduce the existence of period-1,1 solutions. Both models exhibit behavior characteristic of potentially chaotic systems and the presence of strange attractors.; Finally, the system has been modeled using a unified set of modes prescribed by the Craig-Bampton method. This approximate model is found to agree reasonably well with the analytical models. Alternative one-mode models are discussed which could be used for further parameter studies. Modal convergence studies show that the inclusion of two modes in the multi-DOF model is sufficient for the parameter region presently discussed.