Analysis of the vibration of flexible structures

Abstract

Research on vibrations of flexible structures is ongoing in engineering and applied mathematics fields. Flexible structures in practice can be considered as systems of interconnected rod-like components. This dissertation consists largely of a literature study on some mathematical models for flexible structures and structural components, and includes existence theory and finite element analysis of these models and their solutions. These models include beam models such as the Timoshenko theory, Euler-Bernoulli theory, as well as recently published work on a so-called locally linear Timoshenko rod. The multi-dimensional wave equation is also used to illustrate the application of some of the theory in this dissertation.