Multiple Resonances, Responses, and Parametric Instabilities in Offshore Structures

Abstract

Based on a functional analysis approach, time history effects are introduced into the representation of the fluid forces associated with offshore structures operating at shallow draft, shallow submergence and/or having a multihull construction, etc. A general linear theory is developed illustrating the pattern of behavior expected in the structure when performing a free decay motion or a forced motion excited by sinusoidal waves. It is shown that even in a simple one-degree-of-freedom mathematical model describing the behavior of an offshore structure, multiple natural frequencies and resonances may be exhibited in the responses. These features are examined and the investigation extended to assess the possibility of multiple parametric instabilities arising in the motions. For this purpose, the mathematical model is slightly modified to include a specific sinusoidal time-dependent term—as is common in a Mathieu type analysis—and conditions determined allowing motion instabilities to occur. This is confirmed by simple numerical examples.