Timoshenko beam theory: A perspective based on the wave-mechanics approach |
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| Affiliation: | 1. Faculties of Mechanical and Aerospace Engineering, School for Energy, Material, and Transport Engineering, Arizona State University, Tempe, AZ 85287, USA;2. Mechanical Engineering Department, Hong Kong Polytechnic University, HK, HKSAR, People’s Republic of China;3. Building Services Engineering Department, Hong Kong Polytechnic University, HK, HKSAR, People’s Republic of China;1. Department of Mechanics and Engineering Science, Sichuan University, Chengdu 610065, China;2. Division of Dynamics and Control, School of Astronautics, Harbin Institute of Technology, Harbin 150001, China;3. Department of Mechanical Engineering, University of Maryland, Baltimore County, Baltimore, MD, 21250, USA;1. School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, PR China;2. School of Mechanical Engineering, Chongqing University of Technology, Chongqing 400054, PR China;1. NTIS – New Technologies for Information Society, University of West Bohemia, Univerzitní 22, 306 14 Pilsen, Czech Republic;2. Institute of Thermomechanics, Academy of Sciences of the Czech Republic, Veleslavínova 11, 301 14 Pilsen, Czech Republic |
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| 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. |
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| Keywords: | Timoshenko theory Wave propagation Wave approaches |
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