Stability analysis of taut strings carrying a moving mass

Oscillations induced by a moving mass on a taut string are studied. A linear continuum model is formulated, and both a standard Galerkin technique and a perturbation method are used to tackle the problem. This appear in the form of a parametrically excited system, in which the excitation frequency is related to the velocity of the travelling mass. The perturbation analysis permits to detect all the existing parametric excitation conditions of the mass-string system, potentially leading to instability phenomena in which single modes are involved, or several modes interact. In particular, the occurrence of summed or difference combination resonance, which lead to unstable or stable responses, respectively, has been identified. Preliminary analyses, devoted to a specific instability domain, present the accuracy of the perturbation solution compared to direct numerical integrations of the discrete equations of motion.