Nonlinear Vibrations of Metallic and Composite Structures

Abstract

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, pseudo-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.