Lateral-torsional dynamic instability of uniform and double-tapered rectangular beams under harmonic shear deformation

Abstract

Abstract This paper analyzes lateral-torsional dynamic instability of elastic beams with rectangular cross section having constant thickness, with the depth symmetric with respect to the midpoint and either uniform or tapered linearly in each half. Free vibrations are also investigated. The ends of the beam are prevented from twisting and are pinned with respect to bending in the weak direction. In the strong direction, one end of the beam is fixed and the other is subjected to transverse harmonic motion. This problem was motivated by “butterfly-shaped links” proposed for use in seismic mitigation. Uniform torsion is assumed. Frequencies of free vibration are computed, critical excitation frequencies for lateral-torsional instability are determined, and critical combinations of excitation amplitude and frequency are obtained. The effects of geometric parameters of double-tapered beams on instability are presented. Lateral-torsional instability may occur for very small amplitudes of the moving end of the beam, as is typical for such problems involving parametric resonance.