Dynamic lateral torsional post-buckling of a beam–mass system: Theory

Abstract

In this paper, the theory of a Cosserat point is used as a numerical model of a nonlinear elastic beam–mass system and simulations of dynamic lateral torsional buckling are compared with results of experiments. The Cosserat equations are solved using the Newmark time-integration scheme and an analytical expression for the tangent stiffness of the resulting Newton–Raphson iteration procedure is developed. Also, the effects of material damping, aerodynamic drag and gravity have been included. The simulations reproduce the experimental result that two different nonlinear modes of vibration occur at the same excitation amplitude and frequency. One mode: Torsion I is a post-buckling mode associated with out-of-plane motion of the beam–mass system, which is dominated by oscillating torsion of the beam. The second mode: Bending II is dominated by a nonlinear second bending mode in the weak bending plane. The simulations of Torsion I and Bending II and another mode Torsion II are in reasonably good quantitative agreement with the experimental results. However, the model is not able to accurately simulate the response of Torsion III (which was similar to Torsion I and II but with a larger amplitude of vibration). Comparison is also made with the commercial code ANSYS.