Abstract
This paper discusses planar nonlinear forced vibrations of a suspended cable with initial sag. By means of the Hamilton’s principle, the nonlinear partial differential motion equations of the suspended cable are derived. The planar motion is described by a differential equation in the transverse displacement component through neglecting the longitudinal inertia. The partial differential equation of planar motion is reduced to one ordinary differential equation via the Galerkin procedure by assuming a modal deflection shape. Furthermore, by applying the method of multiple scales, this paper studies the approximate solution of nonlinear vibration of the suspended cable under the planar harmonic force and the influence of initial sag on the responses, and discusses the stability of steadydate solutions. It is shown that the vibration of the suspended cable is governed by a unique parameter collecting its geometrical and mechanical properties. The nonlinearities may produce a considerable change of frequency, and the frequency-amplitude relationship of a suspended cable exhibits both hardening and softening behaviour.
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