In-plane antisymmetric response of cables through bifurcation under symmetric sinusoidally time-varying load

Analysis and results for in-plane non-linear antisymmetric responses of a cable, supported at the same level, through bifurcation under in-plane symmetric sinusoidally time-varying load are presented. The non-linear equation of the in-plane motion of the cable is solved by a Galerkin method and the harmonic balance method. From the computed results the frequency range, where the antisymmetric response occurs, varies with the sag-to-span ratio of the cable and is broad in the particular sag-to-span ratios. The second unstable region is important compared with the principal unstable region. Strong coupling between symmetric and antisymmetric modes is observed in the unstable regions for the particular sag-to-span ratios.