Vibration analysis of a beam with partially distributed internal viscous damping |
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| Authors: | Ting-Chiang Tsai Jia-Hau Tsau Chun-Sheng Chen |
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| Affiliation: | 1. Department of Mechanical Engineering, National Taipei University of Technology, No. 1, Sec. 3, Chung Hsiao E. Rd., Taipei 10608, Taiwan, ROC;2. Department of Mechanical Engineering, Lunghwa University of Science and Technology, Taoyuan 33306, Taiwan, ROC;1. College of Aerospace and Material Engineering, National University of Defence Technology, Changsha, Hunan 410073, PR China;2. College of Engineering, Swansea University, Singleton Park, Swansea SA2 8PP, UK;1. College of Civil Engineering and Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China;2. Department of Automotive Engineering, Guangxi University of Technology, Liuzhou 545006, China;1. School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, PR China;2. Changjiang Institute of Survey Planning Design and Research, Wuhan 430010, PR China;3. Sichuan Provincial Transport Department Highway Planning, Survey, Design and Research Institute, Chengdu 610041, PR China |
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| Abstract: | In this paper, governing equations of vibration for a beam with distributed internal viscous damping are established by using Timoshenko beam theory and Hamilton's principle. Then, the transfer matrix method is applied to obtain the frequency equations for the beam. The results reveal, when the internal viscous damping fully distributes along the beam, that the natural frequency decreases with the increasing damping and drops to a zero value at a certain critical damping. While the damping is locally distributed, damped frequency, mode shape and transient response time are affected most significantly by locating the damped segment at the position with maximum bending moment. The flexural amplitudes and phase angles of a beam excited by the resonant harmonic load can be effectively predominated by tuning the damping value. |
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