Non-linear torsional vibration of lengthy thin-walled simply supported beam of open section resting on Winkler foundation

The aim of this paper is to study the non-linear torsional vibrations of lengthy thin-walled simply supported beam of open section resting on Winkler foundation. The governing differential equation of motion is derived. An effort has been made to obtain and solve the governing differential equation of large amplitude torsional vibrations of doubly symmetric thin-walled beams of open section with simply supported boundary. Approximate solutions are obtained for simply supported beams using the well-known Galerkin's method. Plots specifying the effect of large amplitudes on nonlinear frequency of torsional vibrations for various non-dimensional beam constants are furnished. From the present study, we observe, that for lower values of Winkler stiffness parameter lambda <= 0.1, the non-linear frequency increases drastically as beta increases. Also, it is noticed that as the value of Winkler stiffness parameter increases, the influence of beta decreases. For higher values of lambda >= 30, the effect of beta in the present range 0-0.1 on non-linear frequency seems to be negligible. (C) 2019 Elsevier Ltd. All rights reserved.