Nonlinear Dynamic Analysis Method of Underwater Line Structure and its Validation

Abstract

Three-dimensional nonlinear analysis method of underwater line structure is presented and its validity is discussed by direct comparison with experiments. This analysis method is formulated by finite element method and dynamic behavior of the structures are solved in time domain. The motion equation is integrated directly and the method can handle all nonlinearities involved in the dynamic motion of the line structures such as hydrodynamic nonlinearity, geometrical nonlinearity, nonlinear boundary condition and so on. This method is a combination of Newmark's time integration scheme, one of the most reliable scheme, and Newton's iteration scheme for solution of nonlinear equations.
Newmark's time integration scheme is an implicit scheme and its relatively complicated form produces a system of nonlinear algebraic equations which must be solved at each time step by iteration. Newton's iteration scheme is effective in solving the nonlinear equations and the analysis method is expected to be more robust against divergence. But direct application of the method requires large matrix of derivatives and time consuming calculation causes inefficiency. In the present method, the matrix of derivatives is decomposed into small band matrices and the nonlinear equations can be solved minimizing the inefficiency in the calculation. Thus the analysis method become robust and efficient by combining the Newmark's and Newton's schemes.
So far a number of methods have been published related to the dynamic analysis of underwater line structures. Because of the nonlinearities handled in the analysis methods, these methods should have been tested by comparing the solution with experiments, but the validity of the methods were not tested except some cases. Primary reason is that general purpose instruments to measure the dynamic behaviors of underwater line structures in towing tank model tests were not available or limited. In this paper, development of a general purpose ultrasonic sensor for towing tank tests is described and the validity of the analysis method is discussed by direct comparison with expemimental results obtained from towing tank test. In the ultrasonic instrumentation system, high accuracy is required due to the small size of models and high frequency is employed, and coordinates of maximum 16 points can be determined at accuracy of 1 mm.