Timoshenko Beam-Column with Generalized End Conditions and Nonclassical Modes of Vibration of Shear Beams
Publication: Journal of Engineering Mechanics
Volume 130, Issue 10
Abstract
The main objective of this publication is to derive, in a classic manner, the characteristic equations for the undamped natural frequencies and the corresponding modes of vibration of a two-dimensional (2D) Timoshenko beam–column with generalized support conditions (i.e., with semirigid flexural restraints and lateral bracings as well as lumped masses at both ends) and subjected to a constant axial load along its span. The model includes the simultaneous effects (or couplings) of bending and shear deformations, translational and rotational inertias of all masses considered. The proposed model is general, showing that the natural frequencies and the corresponding modes of vibration of 2D beam–columns are highly sensitive to the coupling effects just mentioned. This is particularly true in members with low shear stiffness and with the end flexural restraints and lateral bracing approaching those of free–free and pinned–free conditions. A second objective of this paper is to show that the obtained solution reproduce, as a special case, the nonclassical modes of shearbeams, including the inversion of modes of vibration (i.e., higher modes crossing lower modes) in shear beams with pinned–free and free–free end conditions, and the phenomena of double frequencies at certain values of beam slenderness .
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Published In
Journal of Engineering Mechanics
Volume 130 • Issue 10 • October 2004
Pages: 1151 - 1159
Copyright
Copyright © 2004 ASCE.
History
Published online: Oct 1, 2004
Published in print: Oct 2004
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