FREE AND FORCED RESPONSE OF AN AXIALLY MOVING STRING TRANSPORTING A DAMPED LINEAR-OSCILLATOR

The transverse response of a cable transport system, which is modelled as an ideal, constant tension string travelling at constant speed bet ween two supports with a damped linear oscillator attached to it, is p redicted for arbitrary initial conditions, external forces and boundar y excitations. The exact formulation of the coupled system reduces to a single integral equation of Volterra type governing the interaction force between the string and the payload oscillator. The time history of the interaction force is discontinuous for non-vanishing damping of the oscillator. These discontinuities occur at the instants when tran sverse wavefronts propagating along the string interact with the oscil lator. The discontinuities are treated using the theory of distributio ns. Numerical algorithms for computing the integrals involving general ized functions and for solution of the delay-integro-differential equa tion are developed. The response analysis shows a discontinuous veloci ty history of the payload attachment point. Special conditions leading to absence of the above discontinuities are given.