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Free vibration analysis of a non-uniform cantilever Timoshenko beam with multiple concentrated masses using DQEM

In this paper, a differential quadrature element method (DQEM) is developed for free transverse vibration analysis of a non-uniform cantilever Timoshenko beam with multiple concentrated masses. | Free vibration analysis of a non-uniform cantilever Timoshenko beam with multiple concentrated masses using DQEM Engineering Solid Mechanics 1 2013 9-20 Contents lists available at GrowingScience Engineering Solid Mechanics homepage www.GrowingScience.com esm Free vibration analysis of a non-uniform cantilever Timoshenko beam with multiple concentrated masses using DQEM K. Torabi H. Afshari and M. Heidari-Rarani Faculty of Mechanical Engineering University of Kashan Kashan 87317-51167 Iran ARTICLE INFO ABSTRACT Article history In this paper a differential quadrature element method DQEM is developed for free Received January 15 2013 transverse vibration analysis of a non-uniform cantilever Timoshenko beam with multiple Received in Revised form concentrated masses. Governing equations compatibility and boundary conditions are March 26 2013 formulated according to the differential quadrature rules. The compatibility conditions at the Accepted 18 June 2013 Available online position of each concentrated mass are assumed as the continuity in the vertical displacement 25 June 2013 rotation and bending moment and discontinuity in the transverse force due to acceleration of the Keywords concentrated mass. The effects of number magnitude and position of the masses on the value of Transverse vibration the natural frequencies are investigated. The accuracy convergence and efficiency of the Non-uniform Timoshenko beam proposed method are confirmed by comparing the obtained numerical results with the analytical Concentrated masses solutions of other researchers. The two main advantages of the proposed method in comparison DQEM with the exact solutions available in the literature are 1 it is less time-consuming and subsequently moreefficient 2 it is able to analyze the free vibration of the beams whose section varies as an arbitrary function which is difficult or sometimes impossible to solve with analytical methods. 2012 Growing Science Ltd. All rights reserved. Nomenclature x