In this work, several studies into the dynamic response of structures are made.
In all the studies there is an interaction between the theoretical and experimental work
that lead to important results. In the first study, previous theoretical results for the
single-mode response of a parametrically excited cantilever beam are validated. Of
special interest is that the often ignored nonlinear curvature is stronger than the
nonlinear inertia for the first mode. Also, the addition of quadratic damping to the
model improves the agreement between the theoretical and experimental results. In
the second study, multi-mode responses of a slender cantilever beam are observed and
characterized. Here, frequency spectra, psuedo-phase planes, Poincare sections, and
dimension values are used to distinguish among periodic, quasi-periodic, and chaotic
motions. Also, physical interpretations of the modal interactions are made. In the
third study, a theoretical investigation into a previously unreported modal interaction
between high-frequency and low-frequency modes that is observed in some
experiments is conducted. This modal interaction involves the complete response of
the first mode and modulations associated with the third and fourth modes of the
beam. A model that captures this type of modal interaction is developed. In the
fourth study, the natural frequencies and mode shapes of several composite plates are
experimentally determined and compared with a linear finite-element analysis. The
objective of the work is to provide accurate experimental natural frequencies of
several composite plates that can be used to validate future theoretical developments.
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