Non-linear Free Vibrations of a Hanging Cable with Small Sag

Abstract

This paper presents a method for evaluating non-linear modes and the corresponding natural frequencies of hanging cables with small sag. The use of a Galerkin temporal scheme on the governing equations of motion associated with a fictitious normal force accounting for the effects of the resulting non-linear terms leads to a closed-form solution for the non-linear free vibration problem. The influence of amplitude on the modal shapes and frequencies are presented.