Nonlinear Responses and Stability of an Elastic Suspended Cable System Subjected to Parametrical External Excitations

Abstract

This research investigates the nonlinear behavior and stability of an elastic suspended cable system under combined parametric and external excitations, with an approach of higher accuracy and reliability. Geometric nonlinearity of the cable and its in-plane and out-of-plane vibrations are considered. Multiple solutions of the system are found existing, corresponding to a single frequency of external excitation. The nonlinear stability of the cable system is investigated with focus on the influence of different system parameters. With the newly developed Periodicity-Ratio (P-R) method, the influences of different external excitations on the nonlinear vibrations of the cable system are examined, and a periodic-nonperiodic-chaotic region diagram is created for quantitatively and graphically identifying the stability and nonlinear behavior of the system.

Keywords

• elastic suspended cable
• external excitation
• parametrical excitation
• perturbation method
• nonlinear stability
• p-r method
• periodicity
• chaos
• nonlinear vibration