A Non-Linear Non-Planar Coupling Mechanism of Suspended Cables in Thermal Conditions

Abstract

Slight variations induced by thermal effects may bring unexpected discrepancies in both the system’s linear and non-linear responses. The present study investigates the temperature effects on the non-linear coupled motions of suspended cables subject to one-to-one internal resonances between the in-plane and out-of-plane modes. The classical non-linear flexible system is excited by a uniform distributed harmonic excitation with the primary resonance. Introducing a two-mode expansion and applying the multiple scale method, the polar and Cartesian forms of modulation equations are obtained. Several parametric investigations have highlighted the qualitative and quantitative discrepancies induced by temperature through the curves of force/frequency-response amplitude, time history diagrams, phase portraits, frequency spectrum, and Poincaré sections. Based on the bifurcation and stability analyses, temperature effects on the multiple steady-state solutions, as well as static and dynamic bifurcations, it is observed that the periodic motions may be bifurcated into the chaotic motions in thermal environments. The saddle-node, pitch-fork, and Hopf bifurcations are sensitive to temperature changes. Finally, our perturbation solutions are confirmed by directly integrating the governing differential equations, which yield excellent agreement with our results and validate our approach.