Variational approach of Timoshenko beams with internal elastic restraints

Abstract

An exact approach for free transverse vibrations of a Timoshenko beam with ends elastically restrained against rotation and translation and arbitrarily located internal restraints is presented. The calculus of variations is used to obtain the equations of motion, the boundary conditions and the transitions conditions which correspond to the described mechanical system. The derived differential equations are solved individually for each segment of the beam with the corresponding boundary and transitions conditions. The derived mathematical formulation generates as particular cases, and several mathematical models are used to simulate the presence of cracks. Some cases available in the literature and the presence of some errors are discussed. New results are presented for different end conditions and restraint conditions in the intermediate elastic constraints with their corresponding modal shapes.

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Keywords

UTN, FRD, Calculus of variations, Timoshenko beams, elastically restrained ends, exact result

Citation

Raffo, J. L. and Grossi, R. O. “Variational approach of Timoshenko beams with internal elastic restraints”, ISSN 2159-5275 (Print), ISSN 2159-5283 (Online), Journal of Mechanics Engineering and Automation, 3, 491-498, 2013. http://www.davidpublishing.org/DownLoad/?id=13898

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Except where otherwised noted, this item's license is described as info:eu-repo/semantics/openAccess