Theoretical and Experimental Analysis of the Forced Response of Sagged Cable/Mass Suspensions

Abstract

This study examines the forced response of a sagged elastic cable supporting an array of discrete masses. Such systems arise, for instance, in ocean engineering applications employing cable hydrophone arrays. The excitation considered is harmonic and normal to the cable and may, for instance, approximate prescribed environmental loading. An asymptotic model is presented that describes the linear forced response of a cable/mass suspension having small equilibrium curvature. Closed-form expressions for the Green’s function to an associated boundary value problem are obtained using a transfer matrix formulation. The derived Green’s function is utilized to construct integral representations for steady-state response under boundary and/or domain excitation. Solutions obtained for a variety of domain loading distributions demonstrate the utility and efficiency of this solution strategy. The theoretical response predictions are verified through experimental measurements of the natural frequency spectrum and frequency response of laboratory cable/mass suspensions.