Nonlinear planar secondary resonance analyses of suspended cables with thermal effects

Abstract

This paper deals with a geometrically nonlinear model of suspended cables in thermal environments. In particular, the secondary resonant behaviors with thermal effects are investigated and discussed analytically and numerically. First, considering the influence of temperature changes, a dimensionless coefficient is generated. The nonlinear dynamic equations of motion in thermal environments are established, and the governing PDEs are reduced to a set of ODEs by using the Galerkin procedure. Four super and sub-harmonic resonant cases are studied, and frequency responses equations and steady-state solutions for each case are obtained. Extensive numerical results show that the hardening/softening behaviors, the response amplitudes, the number of nontrivial solutions, the range of resonant responses, the jump points, and the peak values are all closely connected to temperature. In some specific warming/cooling conditions, the nonlinear system just shows linear vibration behaviors or even just opposite spring characteristics. The time–displacement curves and phase portraits are extremely sensitive to temperature changes, but the number of cluster points in Poincaré sections seem to be independent of temperature changes.

Keywords:

• Suspended cable
• thermal effect
• secondary resonance
• perturbation analysis
• numerical integration
• vibration characteristic

Additional information

Funding

The authors gratefully acknowledge the support of the National Natural Science Foundation of China (11602089), Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University (ZQN-YX505), and Open Research Fund Program of Hunan Provincial Key Laboratory of Structures for Wind Resistance and Vibration Control.