The lumped-mass-and-spring model is employed to predict the snap loading of marine cables operating in alternating taut-slack conditions. The governing equations are integrated m the time domain by using the modified Euler method. Stability analysis is performed and the necessary stability conditions are given for the numerical integration. Numerical examples show various effects of nonlinearities and Illustrate the emergence of period doubling as a consequence of loss of stability of motion. Comparisons of the numerical results and the available experimental results are made which demonstrate the validity of the present method.
Snap loading of marine cables operating in alternating taut-slack conditions has been studied by several investigator. Niedzwecki and Thampi (1991) studied a one-dimensional case. A single-degree. of-freedom model was used for preliminary, assessment of snap loading occurrence, and a more complex multi-degree-of-freedom model for predicting the snap loading qualitatively for a two-dimensional case. Milgram et al (1988) and Shin (1991) formulated the problem mathematically, the cable being modelled as a distributed system. A spectral method was then employed for a numerical solution. The time-domain solution of marine cable dynamics often involves an integration of second order ordinary differential equations. Newmark's method is extensively used for this purpose (Hughes and Belytschko, 1983). For a nonlinear problem such as one involving marine cables, the application of Newmark's method is not convenient as additional computation effort is needed for determining iteratively the response-dependent forces such as tension and fluid drag (Peyrot, 1981). Furthermore, although Newmark's method is stable and the time increment can be reasonably large, the method is only effective when the system properties remain constant during the total length of time increment. This is not the case for snap loading as the cable is characterized by a discontinuity in the axial stiffness.
