A general model is derived for the dynamics of suspended cables that support an array of offset bodies; e.g., cable/hydrophone arrays. The general model, which governs geometrically nonlinear, three-dimensional response, is used herein to analyze the linear out-of-plane response of suspensions with small equilibrium curvature. Closed-form solutions are derived for free response (natural frequencies and mode shapes) and for forced response under harmonic end excitation. Solutions for forced response reveal the existence of a "pass-band/stop-band" structure for frequency response. For excitation frequencies within the pass-band, vibration energy freely propagates from the source of excitation throughout the cable/body structure. By contrast, little vibration energy propagates from the excitation source for excitation frequencies in the stop-bands. Studies for free response highlight the key system parameters that have the greatest influence on the natural frequency spectrum.
Suspended marine cables are commonly used in applications that require long and easily deployable structural elements. Due to their flexibility, however, suspended cables are easily excited by a variety of sources which may produce undesirable dynamic response. For example, suspended cables submerged in cross-flows may experience vortex-induced oscillations (Griffen, 1985), commonly referred to as strumming, which, in addition to magnifying cable drag forces, may degrade the performance and positioning of instruments attached to the suspension. Wave loading (either directly or indirectly) on the cable can lead to similar degradations of instrument performance and positioning. The study of cable dynamics has enjoyed a long and rich history as detailed in (Irvine, 1981) and recent developments in this field are reviewed in (Triantafyllou, 1991). A significant understanding of the dynamics of suspended cables has been achieved through a series of analytical studies which date back to the 18-th Century.
