PLANAR NONLINEAR FORCED VIBRATIONS OF A SUSPENDED CABLE

This paper discusses planar nonlinear forced vibrations of a suspended cable with initial sag. By means of the Hamilton's principle, the non linear partial differential motion equations of the suspended cable ar e derived. The planar motion is described by a differential equation i n the transverse displacement component through neglecting the longitu dinal inertia. The partial differential equation of planar motion is r educed to one ordinary differential equation via the Galerkin procedur e by assuming a modal deflection shape. Furthermore, by applying the m ethod of multiple scales, this paper studies the approximate solution of nonlinear vibration of the suspended cable under the planar harmoni c force and the influence of initial sag on the responses, and discuss es the stability of steady-date solutions. It is shown that the vibrat ion of the suspended cable is governed by a unique parameter collectin g its geometrical and mechanical properties. The nonlinearities may pr oduce a considerable change of frequency, and the frequency-amplitude relationship of a suspended cable exhibits both hardening and softenin g behaviour.