Parametric resonance in the pantograph-catenary system

In this paper, a theoretical study is presented of dynamic stability of the pantograph-catenary system. A one-level catenary is considered and modeled by an infinitely long taut string that is periodically supported by identical discrete visco-slastic supports. The pantograph is modeled by an oscillator with viscous damping that moves with a constant speed along the string. A new method is proposed for finding the boundaries of the instability zones in the space of the system parameters. Applying this method, a parametric analysis of the instability zones is accomplished showing that the liklehood of instability is increased by (i) increasing the mass of the pantograph, (ii) decreasing the stiffness and/or viscosity of the pantograph, (iii) increasing the stiffness and/or viscosity of the suspension rods of the catenary (the latter at relatively high speeds).