Shear deformation effect in flexural–torsional vibrations of beams by BEM
 E. J. Sapountzakis,
 J. A. Dourakopoulos
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Abstract
In this paper, a boundary element method is developed for the general flexural–torsional vibration problem of Timoshenko beams of arbitrarily shaped cross section taking into account the effects of warping stiffness, warping and rotary inertia and shear deformation. The beam is subjected to arbitrarily transverse and/or torsional distributed or concentrated loading, while its edges are restrained by the most general linear boundary conditions. The resulting initial boundary value problem, described by three coupled partial differential equations, is solved employing a boundary integral equation approach. Besides the effectiveness and accuracy of the developed method, a significant advantage is that the displacements as well as the stress resultants are computed at any crosssection of the beam using the respective integral representations as mathematical formulae. All basic equations are formulated with respect to the principal shear axes coordinate system, which does not coincide with the principal bending one in a nonsymmetric cross section. To account for shear deformations, the concept of shear deformation coefficients is used. Six boundary value problems are formulated with respect to the transverse displacements, to the angle of twist, to the primary warping function and to two stress functions and solved using the Analog Equation Method, a BEM based method. Both free and forced vibrations are examined. Several beams are analysed to illustrate the method and demonstrate its efficiency and wherever possible its accuracy.
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 Title
 Shear deformation effect in flexural–torsional vibrations of beams by BEM
 Journal

Acta Mechanica
Volume 203, Issue 34 , pp 197221
 Cover Date
 20090301
 DOI
 10.1007/s0070700800417
 Print ISSN
 00015970
 Online ISSN
 16196937
 Publisher
 Springer Vienna
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 Authors

 E. J. Sapountzakis ^{(1)}
 J. A. Dourakopoulos ^{(1)}
 Author Affiliations

 1. Institute of Structural Analysis, School of Civil Engineering, National Technical University of Athens, Zografou Campus, 157 80, Athens, Greece