Dynamic Stiffness Formulation for Torsional Vibrations of Generally Restrained Thin-Walled Beams of Open Section Resting on Continuous Elastic Foundation

This paper deals with the dynamic stiffness matrix formulation for the problem of torsional vibrations and stability of generally restrained doubly symmetric thinwalled beams of open section, resting on Winkler type continuous elastic foundation. An analytical method is developed, including the effects of warping and neglecting the effects of longitudinal inertia and shear deformation. The resulting transcendental frequency equation can be solved for various values of linear and rotational end restraint parameters. A computer program is developed, based on the dynamic stiffness matrix approach. The software consists of a master program to set up the dynamic stiffness matrix and to call specific subroutines to perform various system calculations. To demonstrate the influence of end restraints and warping on the torsional natural frequency, numerical results are obtained for the case of cantilever thinwalled beam of open section partially restrained against warping for various values of restraint parameter and warping parameter and the same are presented in suitable form.