000013192 001__ 13192
000013192 005__ 20161114160331.0
000013192 04107 $$aeng
000013192 046__ $$k2009-06-22
000013192 100__ $$aStoykov, S.
000013192 24500 $$aOn the influence of warping, shear and longitudinal displacements on the nonlinear vibrations of beams

000013192 24630 $$n2.$$pComputational Methods in Structural Dynamics and Earhquake Engineering
000013192 260__ $$bNational Technical University of Athens, 2009
000013192 506__ $$arestricted
000013192 520__ $$2eng$$aThe geometrically nonlinear vibrations of beams which may experience longitudinal, torsional and bending deformations in any plane are investigated by the p-version finite element method. Bernoulli-Euler or Timoshenko’s beam theories are considered for bending and Saint-Venants’s for torsion. A warping function is included in the model. The geometrical nonlinearity is taken into account by considering the Green’s strain tensor and the longitudinal displacements of quadratic order, which are most often neglected in the strain displacement relation, are considered here. Generalised Hooke’s law is used and the equation of motion is derived by the principle of virtual work. Comparisons of both models, Bernoulli-Euler and Timoshenko, and comparison of models including and neglecting the quadratic terms of longitudinal displacements are presented. It is shown that Timoshenko’s theory gives better results than Bernoulli-Euler’s when the bending and torsion motions are coupled and the nonlinear terms become important. This is explained by the fact that when bending and torsion are coupled, the rotations along the transverse axes of the beam cannot be approximated by the respective derivatives of the transverse displacement functions as is assumed in BernoulliEuler’s theory. The importance of warping is also analysed for different rectangular cross sections, and it is shown that its consideration can be fundamental to obtain correct results.

000013192 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000013192 653__ $$aBending-torsion coupling, nonlinear vibration, warping. Abstract. The geometrically nonlinear vibrations of beams which may experience longitudinal, torsional and bending deformations in any plane are investigated by the p-version finite element method. Bernoulli-Euler or Timoshenko’s beam theories are considered for bending and Saint-Venants’s for torsion. A warping function is included in the model. The geometrical nonlinearity is taken into account by considering the Green’s strain tensor and the longitudinal displacements of quadratic order, which are most often neglected in the strain displacement relation, are considered here. Generalised Hooke’s law is used and the equation of motion is derived by the principle of virtual work. Comparisons of both models, Bernoulli-Euler and Timoshenko, and comparison of models including and neglecting the quadratic terms of longitudinal displacements are presented. It is shown that Timoshenko’s theory gives better results than Bernoulli-Euler’s when the bending and torsion motions are coupled and the nonlinear terms become important. This is explained by the fact that when bending and torsion are coupled, the rotations along the transverse axes of the beam cannot be approximated by the respective derivatives of the transverse displacement functions as is assumed in BernoulliEuler’s theory. The importance of warping is also analysed for different rectangular cross sections, and it is shown that its consideration can be fundamental to obtain correct results.

000013192 7112_ $$aCOMPDYN 2009 - 2nd International Thematic Conference$$cIsland of Rhodes (GR)$$d2009-06-22 / 2009-06-24$$gCOMPDYN2009
000013192 720__ $$aStoykov, S.$$iRibeiro, P.
000013192 8560_ $$ffischerc@itam.cas.cz
000013192 8564_ $$s158055$$uhttps://invenio.itam.cas.cz/record/13192/files/CD258.pdf$$yOriginal version of the author's contribution as presented on CD, section: Nonlinear dynamics (MS).
000013192 962__ $$r13074
000013192 980__ $$aPAPER