MODELLING OF WARPING EIGENVIBRATION BY NON-UNIFORM TORSION

Abstract eng:
This contribution contains a novel investigation of the influence of warping of the cross-section of twisted beams on their eigenvibrations. The investigation is based on the analogy of the bending beam theory and the non-uniform torsion theory of thin-walled open and closed cross-sections. Based on them, the differential equations for dynamic loads, considered as equivalent static loads, are presented. The effect of the secondary torsion moment deformation is taken into account. A part of the first derivative of the twist angle is taken as a warping degree of freedom. The solution of this differential equation is then used for setting up the transfer matrix. The numerical investigation contains the analysis of the natural frequencies and mode shapes of straight cantilever beams with and without consideration of the influence of warping of the cross-section. Beams with open and closed cross-sections are considered. Obtained results are compared with the ones calculated by standard solid and warping beam finite elements.

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