Torsional vibrations and buckling of thin-walled beams on elastic foundation

Abstract

The problem of free torsional vibration and buckling of doubly symmetric thin-walled beams of open section, subjected to an axial compressive static load and resting on continuous elastic foundation, is discussed in this paper. An analytical method based on the dynamic stiffness matrix approach is developed, including the effects of warping. The resulting transcendental equation is solved for thin-walled beams clamped at one end and simply supported at the other. A computer program is developed, based on the dynamic stiffness matrix approach. The software consists of a master program to set up the dynamics stiffness matrix and to call specific subroutines to perform various system calculations. Numerical results for natural frequencies and buckling load for various values of warping and elastic foundation parameter are obtained and presented.