Analytical, experimental and computational models have historically been heavily simplified, linearized, and otherwise reduced. This paper shows how such model reductions eliminate the fundamental geometric changes that determine real behavior in cables, strings, moorings, guys, pipelines, riser, plates, skins, subsea hulls, and other such slender and thin structures. The paper details each physical quantity that we must add back into our overly reduced models to improve the basic nature, evolution, and accuracy of the resulting motions and vibrations.

For example, even slight changes in local rotation anywhere along a cable can create large nonlinear changes in the dynamic nature of its behavior. The evolved complexity of the resulting global motions and vibrations in space and time often defy what we normally expect from such a simple structure.

Although this paper focuses on the modeling of deep-water moorings and risers of an ocean platform, the same geometric effect is fundamental to most science and engineering models. Understanding how small changes in geometry can nonlinearly affect any structured behavior will help demystify much of the poorly-understood motions and vibrations in a large diversity of applications, including induced vibrations, sound, structural acoustics, aero-elasticity, sound, light and atomic radiation.

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