Effects of temperature variations on nonlinear planar free and forced oscillations at primary resonances of suspended cables

Abstract

This paper is concerned with the analysis of the free and forced nonlinear vibrations of the suspended cable with thermal effects. By introducing the new thermal stressed configuration, the effect of temperature variation on the nonlinear vibration equations of motion is reflected by a non-dimensional cable tension variation factor. The partial differential equations of the planar motion are discretized to the ordinary equations via the Galerkin method, and the single-mode discretization is investigated. The Lindstedt–Poincare method and multiple scales method are applied to obtain the higher-order approximate solutions of the nonlinear free vibrations and primary resonances, respectively. Parametric investigations of temperature effects on the linear and nonlinear vibration characteristics of the suspended cable with different sag-to-span ratios and excitation amplitudes are performed. The results of the perturbation analysis show that the nonlinear free and forced vibration characteristics would be changed by the temperature variations qualitatively and quantitatively, depending on the sag-to-span ratio and the excitation amplitude. The asymmetric phenomena between the effects of warming and cooling conditions on the vibration characteristics can be observed. The crossover points between next two mode frequencies are shifted under the temperature variation, and these would significantly influence the internal resonances of the suspended cable. Finally, temperature effects on the time-history diagram of the cable axial total tension force are investigated.