This paper analyses the dynamical response of taut strings subjected to systems of travelling forces provided with constant velocity. A new solution for the problem of the single force is proposed, based on a change of variable accounting for the quasi-static response. Then, the effect of trains of forces having a step equal to the string length is dealt with. The response is formulated in terms of a linear map, whose reiteration furnishes the discrete-time response, and enables the investigation of the asymptotic behavior of the system. The analytical solution highlights the presence of many critical velocities, for which an instability phenomenon by response accretion may occur.
Dynamic analysis of taut strings subjected to trains of moving forces
PICCARDO, GIUSEPPE
2011-01-01
Abstract
This paper analyses the dynamical response of taut strings subjected to systems of travelling forces provided with constant velocity. A new solution for the problem of the single force is proposed, based on a change of variable accounting for the quasi-static response. Then, the effect of trains of forces having a step equal to the string length is dealt with. The response is formulated in terms of a linear map, whose reiteration furnishes the discrete-time response, and enables the investigation of the asymptotic behavior of the system. The analytical solution highlights the presence of many critical velocities, for which an instability phenomenon by response accretion may occur.
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