Timoshenko beam theory: A perspective based on the wave-mechanics approach

Abstract

This paper reviews Timoshenko beam theory from the point of view of wave mechanics. Vibration of beam structures can be studied in terms of either normal modes or propagating waves. The latter wave approach has two distinct features: first, it gives rise to clear physical understanding of beam vibration; second, it leads to exact methods for vibration analysis of beam structures, especially in the mid-frequency range. In this paper, the work on wave solutions of an infinite Timoshenko beam is first discussed. The work on the splitting effect of spinning on wave solutions is also reviewed. The wave is treated as constitutive components of standing waves (i.e. normal modes), and a discussion on how the wave components formulate various standing waves is presented. Finally, several numerical examples are presented to illustrate the pros and cons of using different wave approaches to tackle vibration analysis of finite-length Timoshenko beams.