Free vibration of complex cable/mass systems: theory and experiment

Abstract A theoretical model is presented that describes the non-linear, three-dimensional response of a suspended cable supporting an array of discrete masses. The equations of motion for the cable/mass suspension are linearized about a generally sagged and supported equilibrium state and the eigensolutions governing free response are determined. A hybrid analytical/numerical method is developed that permits the efficient evaluation of low and higher order eigensolutions for arbitrarily complex and sagged cable/mass suspensions. The method utilizes a numerical implementation of a transfer matrix solution to an asymptotic form of the equations of motion. Experimental modal tests, performed on laboratory cables, provide corroborating measurements of system natural frequencies. This investigation contributes an important extension to previous investigations of cable/mass suspensions which are limited by mode order, array complexity or suspension sag.