Investigation of Super-harmonic Resonance Response of Suspended Cables Considering Temperature Variation Effects

Abstract

 By introducing two non-dimensional parameters related to the cable tension force and sag, in-plane nonlinear equations for motion of the suspended cable considering the temperature effect were derived. Firstly, the nonlinear partial differential equation was discretized by the Galerkin method. Then, the approximate solutions of the second and third order single mode super-harmonic resonances of the suspended cable were obtained by the multiple scales method, and the corresponding frequency response equations were also derived. Finally, the effect of temperature variations on the single mode super-harmonic resonances of the suspended cable with three different sag-to-span ratios was illustrated by the numerical calculations. The numerical results show that: in the case of small sag-to-span ratio, the nonlinear vibration characteristics would be changed by a certain degree of the temperature change quantitatively and qualitatively, the softening and hardening spring behaviors are changed, and it means that the degree and direction of the frequency response curves are changed. The single/multi-values of the excitation-response amplitude curves are also varied by the temperature variations. However, with the increase of the sag-to-span ratio, only some quantitative changes are found under the thermal effect. With the increase of the temperature change, the frequency response curves are bent to the left much more, and the softening spring characteristic is also increased. Moreover, due to the initial tension force of the suspended cable, the effects of warming and cooling conditions on the vibration characteristics of the suspended cable are not symmetric.

Keywords: suspended cable,  temperature variations,  multiple scales method,  vibration characteristics,  super-harmonic resonance,  frequency response curves