Mode ling of Vortex-Excited Vibration of Underwater Cable System
Authors: Tsai N.T. 
Published: October 2008

A methodology is developed to analyze the vortex-induced vibration of moored or towed cable systems. The fluctuating forces are considered as sources of energy which generate waves propagating through the cable-body system with dissipation and scattering in the process. Because of its emphasis on energy flow, this method facilitates the incorporation of various vortex models into dynamic cable analysis.

INTRODUCTION
Cables exposed to current in deep-ocean moors or used for towing bodies or arrays for ocean survey are subject to transverse oscillations from vortex-induced forces. This phenomenon, called strumming, has been under investigation for many years because it affects the fatigue life of the structure and the noise of any attached sensors. Experiments conducted in water channels indicate that the vortex-induced vibration can be substantially reduced by introducing hydrodynamic disturbances to the flow near the structure. For example, mechanical devices, such as splitter vanes, trailing ribbons and fairings, have been used to disturb the formation of the vortex flow, while spiral wrappings have been used to disturb their spanwise coherence.
Other investigations have been made concerning the nature of the vortex flow and to model the vortex-induced cable vibrations. Wind tunnel and water channel experiments were carried out to measure the characteristics of vortex formation and cable responses. However, due to limitations of the experimental equipment, the motion of a full-scale system cannot easily be modeled experimentally. Thus, numerical modeling is probably the best way to analyze the dynamic motion of a cable system under strumming excitation. To this end, empirical models have been developed recently in which the fluid oscillation near the cable is represented by a non-linear, self-excited oscillator that is dynamically coupled to the structural member. These models can reproduce the synchronization effect as the shedding frequency approaches the natural frequencies of the structure. The models have been used to simulate the motion of an elastically mounted circular cylinder. The results are in good agreement with experimental data of the maximum amplitude in the resonant or entrained state when the vortex shedding frequency is equal to the natural frequencies of the vibrating cylinder. Studies are underway to couple the models to the equations of motion of a flexible cable to simulate the motion of a cable under vortex excitation.
The purpose of this paper is to present the bond graph method as a modeling technique that can incorporate a dynamic model of vortex-induced forces in models of cable systems. Using this method, the response of a complete cable system under various environmental conditions is simulated. In the next section this modeling technique is compared with other cable dynamic modeling techniques. A review of oscillator models then is presented with some examples given to demonstrate the feasibility of the bond graph method as a modeling technique for vortex-induced cable system vibrations.

DYNAMIC ANALYSIS OF CABLE-BODY SYSTEMS
Since cable-body systems are being used in more and more ocean facilities, there is a strong interest in valid analytical tools which require development of analytical approaches supported by experimental validation. Mathematical modeling and numerical techniques have been used by l 2 3 many investigations.