Nonlinear Effects in Elastic Flexural-Torsional Vibrations of Beams of Arbitrary Cross Section

Abstract

In this paper a boundary element method is developed for the nonlinear flexural-torsional dynamic analysis of beams of arbitrary, simply or multiply connected, constant cross section, undergoing moderate large deflections and rotations under general boundary conditions, taking into account the effects of rotary and torsional warping inertia. Four boundary value problems are formulated with respect to the transverse displacements, to the axial displacement and to the angle of twist and solved using the Analog Equation Method, a BEM based method. The geometric, inertia, torsion and warping constants are evaluated employing the Boundary Element Method. The proposed model takes into account, both the Wagner's coefficients and the shortening effect. Numerical examples are worked out to illustrate the efficiency, wherever possible the accuracy, the range of applications of the developed method as well as the influence of the nonlinear effects to the response of the beam.