Stability Analysis of Pantograph–Catenary System Under Dual-Frequency Parametric Excitation

Abstract Dual-frequency parametric excitation widely exists in coupled systems. The action of the contact wire on the pantograph in the pantograph–catenary coupled system can be simplified as a typical dual-frequency parametric excitation. The two disproportionate parametric excitation frequencies cause the stiffness of the nonlinear springs to change in quasi-periodic, which make the dynamic characteristics of the pantograph–catenary system more complicated and affect collect currents steadily of the train. In this paper, the dynamics model of pantograph–catenary under dual-frequency parametric excitation is established, and the analytical results of the system stability boundary are obtained by the harmonic balance method. The accuracy of the results with the harmonic balance method in this paper is verified by comparing with the numerical iteration results. Finally, the stability boundary of the pantograph–catenary with different frequency ratios is determined according to the stiffness variation coefficient of the contact wire and the train speed, and the influence of the frequency ratio on the stability boundary of the pantograph–catenary system is analyzed. The influence of the dual-frequency parametric excitation on the stability of the pantograph–catenary system caused by the joint effect of the stiffness fluctuation between the support poles and the vertical droppers during the train running is investigated. The influence of dual-frequency parametric excitation on the stability of the pantograph–catenary system is revealed, which provides guidance for the parameter design and vibration suppression of the pantograph–catenary system.