Characterization of Beam Vibration

Abstract

A beam is one of the most fundamental elements in structural engineering, mechanical engineering, and aerospace engineering. Moreover, complex structures like large flexible solar arrays, airplane wings, high-rise buildings, and long-span bridges can be often modeled as beam-like members. Therefore, it is important to study the static and dynamic behavior of this element under various loading conditions. In the analysis and design of beam or beam-like elements, it is sometimes necessary to determine the eigenparameters (natural frequency, mode shape, and modal damping) of the element under axial force (for example pre-stressed elements). The eigenparameters are also important in the application of nondestructive health monitoring of structural elements as a cost-effective way to detect the existence of damage and its extent. However, most of the research has focused on how cracking affects natural frequencies of the element. Very little research has been done in terms of how natural frequency changes within the yielding and strain hardening region (specifically for steel structures). In this thesis, the relationship between natural frequency and axial force within the linear elastic region, buckling region, and yielding and strain hardening region is investigated using an analytical model, numerical model, and experiments. The effect of plastic deformation on the natural frequency of beams was investigated. Cyclic loading experiments were conducted to study how re-loading stiffness changes within both the elastic and plastic region. Finally, large amplitude vibration (geometric nonlinearity) was investigated both experimentally and numerically. It is hoped that this thesis will provide a summary of the critical behavior of beams, particularly from the linear versus nonlinear, elastic versus plastic, and static versus dynamic points of view.