To study the interactive behavior of long vertical tensioned cylinders in close proximity, a combined numerical and experimental analysis program was carried out. An overview of many numerical investigations into the response behavior of a single riser is provided in a paper by Chakrabarti and Frampton (1982). In their paper they distinguish between static and dynamic solutions and between two and three dimensional solutions. Numerical examples are summarized and various riser end conditions and wave theories are described. In most of the discussed formulations the stiffness of the riser is assumed to be linear, through some of the numerical models implemented a non-linear riser stiffness and thus can be used when large riser deflections are expected. Nordgren (1974) developed a formulation which yields the equation of motion for a slender rod which can be applied to describe either a riser or tendon. While Nordgren used a finite difference method to solve the equations, Garrett (1982) expanded on this formulation and applied a finite element approach to obtain response estimates for vertical and curved systems. Paulling and Webster (1986) further contributed to this formulation by addressing the hydrodynamic loading and coupled tendon displacements with platform motions. The advantage of the rod type formulation over many other methods is that it requires fewer steps to obtain a global system of equations and provides the flexibility of explicitly specifying all parameters including the finite element specific shape functions. Therefore, this formulation was selected for the development of a numerical model which describes the motions of clustered cylinders and was further developed to assess the uncertainty related to the numerical modeling of risers and tendons by introducing a compatible probabilistic analysis procedure (e.g. Sundararajan, 1994). A study which evaluated the uncertainty of some marine riser designs was performed by Leder and Niedzwecki (1990).
The experimental portion of this research study focused on measuring response and interactive behavior in regular and random seas. Duggal (1993) performed an experimental study where the displacements were computed from strain gauge measurements along the inside of hollow cylinders. To avoid the complex computational issues which were encountered by Duggal and Niedzwecki (1995) direct displacements measurements were obtained by utilizing underwater optical tracking techniques. The algorithm used to resolve the displacements of multiple submerged objects from multiple cameras is described in a recent paper by Rijken and Niedzwecki (1997). Initial experiments performed in this study were designed to investigate the response behavior of a single cylinder with the purpose of developing reference configurations and examining some of the basic phenomena like pretension effects on tendon or riser displacements. The effect of the configuration on the response was systematically analyzed in the subsequent experiments. The experimental plan was concluded by investigation two interesting practical design aspects. The first examined the likelihood of modal excitation were a peak of a wave elevation spectrum was selected to coincide with a natural frequency of the cylinder. The second was more exploratory in nature and here one of three cylinders in a TLP-like configuration disconnected.
This research strategy of combining large scale experiments with advanced numerical methods provides the opportunity to investigate the basic phenomenon of cylinder interaction. This approach allows one to determine the ability of current hydrodynamic models to predict the observed behavior and to evaluate the need for new modeling capabilities. In the sections which follow the development of a numerical formulation describing the response of a cluster of cylinders I given and assessment of the uncertainty related to numerical modeling is made. The experimental setup is described and numerical and experimental findings are presented.
Related Publications: Niedzwecki, J.M., Rijken, O.R. and Soemantri, D.S., “Dynamic Behavior of Tendons in Random Seas,” Proceedings of the 14th International Conference on Offshore Mechanics and Arctic Engineering, Copenhagen, June, 1995, Vol. I, Part B, pp. 383-392.
Niedzwecki, J.M. and Rijken, O.R., “Collision of Cylinders in Random Seas,” Proceedings, 10th ASCE Eng. Mech. Specialty Conference, Boulder, Colorado, May, 1995.
Niedzwecki, J.M., van de Lindt, J. and Rijken, O.R. “Behavior of Tendon Models in Random Seas,” Proceedings of the 24th American Towing Tank Conference, November 1995.
Niedzwecki, J.M., Rijken, O.R., and Soemantri, D.S. “Wave Induced Reaction Force and Tension in Deepwater TLP Tendons,” Proceedings of the ASCE EMD/STD Specialty Conference, August 1996.
Niedzwecki, J.M. and Rijken, O.R., “Complex Flow Induced Response of Slender Structures in Random Seas,” COSU’96, Buenos Aires, Argentina, December 3-6, 1996.