Closed-form solution for the free axial-bending vibration problem of structures composed of rigid bodies and elastic beam segments |
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| Institution: | 1. Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, Belgrade 35 11120, Serbia;2. Faculty of Mechanical and Civil Engineering in Kraljevo, University of Kragujevac, Dositejeva 19, 36000 Kraljevo, Serbia;1. School of Science, University of New South Wales, Canberra, Australia;2. I.E. Tamm Theory Department, P.N. Lebedev Physical Institute of the Russian Academy Sciences, 53 Leninsky Prospect, 119991 Moscow, Russia;1. Laboratory of Nano- and Microfluidics and Microsystems - LabMEMS, Mechanical Engineering Department and Nanoengineering Department, POLI & COPPE and Interdisciplinary Nucleus for Social Development - NIDES/CT, Universidade Federal do Rio de Janeiro, Cidade Universitária, Cx. Postal 68503, Rio de Janeiro, RJ CEP 21945-970, Brazil;2. General Directorate of Nuclear and Technological Development - DGDNTM, Brazilian Navy, Rio de Janeiro, RJ, Brazil;1. School of Naval Architecture, Ocean and Civil Engineering (State Key Laboratory of Ocean Engineering), Shanghai Jiaotong University, Shanghai 200240, China;2. Departments of Civil and Environmental Engineering, Mechanical Engineering, and Materials Science and Engineering, Northwestern University, Evanston, IL 60208, USA;3. AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China;1. College of Electronic and Optical Engineering & College of Microelectronic, Nanjing University of Posts and Telecommunications, Nanjing 210003, China;2. National and local Joint Engineering Laboratory of RF Integration and Micro-Assembly Technology, Nanjing University of Posts and Telecommunications, Nanjing 210003, China;3. School of Mechanical Engineering, Southeast University, Nanjing 211189, China;1. Key Laboratory of Electronic Equipment Structure Design, Ministry of Education, Xidian University, P.O. Box 187, Xi''an 710071, PR China;2. Xi''an Microelectronics Technology Institute, The Ninth Academy of China Aerospace Science and Technology Corporation, P.O. Box 187, Xi''an 710119, PR China;3. Institute of Continuum Mechanics, Leibniz Universität Hannover, 30167 Hannover, Germany;4. Centre for Infrastructure Engineering and Safety, School of Civil and Environmental Engineering, The University of New South Wales, Sydney, NSW 2052, Australia |
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| Abstract: | In this paper, the coupled axial-bending vibration of planar serial frame structures composed of rigid bodies and Euler-Bernoulli beam segments is considered. The corresponding mode orthogonality conditions for this kind of structures are derived. It is assumed that the mass centers of rigid bodies have both the transverse and the axial eccentricity with respect to beam neutral axes and that the mass centers are located in the plane in which the rigid bodies perform planar motion. The system responses to initial excitation in the case of distinct as well as repeated natural frequencies are considered. Theoretical considerations are accompanied by four numerical examples. |
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