Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/9585
Title: Superposed standing waves in a Timoshenko beam
Authors: Chan, KT
Wang, XQ
So, RMC
Reid, SR
Keywords: Anomalous dispersion
Evanescent wave
Normal dispersion
Second spectrum
Standing wave
Wave mechanics approach
Issue Date: 2002
Publisher: Royal Soc London
Source: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2002, v. 458, no. 2017, p. 83-108 How to cite?
Journal: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 
Abstract: A wave mechanics approach is used to solve the Timoshenko beam equation, revealing that two waves exist. One is called the s a-wave and the other the s b-wave. These two waves are found to be the basic constituent components of the mode shapes of the beam. An experiment was carried out and the measured mode shapes of a free-free beam are shown to consist of one s a-wave and one s b-wave in superposition for each of the modes. The measured s a-wave and s b-wave exhibit the Rayleigh-Lamb first (with anomalous dispersion) and Rayleigh-Lamb second (with normal dispersion) flexural modes, respectively. The issue of the second spectrum is addressed and it is shown that, within the measurable frequency range, Rayleigh-Lamb second flexural modes are present in the free-free beam. The s b-wave is identified as the second-spectrum mode. The role of shear deformation is also investigated in explaining the basic difference in the behaviour of the s a- and s b-waves. This paper also contributes to a physical interpretation of the hyperbolic functions in the classical solution of beam vibration problems.
URI: http://hdl.handle.net/10397/9585
ISSN: 1364-5021
DOI: 10.1098/rspa.2001.0855
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