A Probabilistic Approach to the Wave-Structure Interaction Problem

Abstract

ABSTRACT The analysis of the interaction of wave forces and structural response is a typical case of a random process. In the dynamic analysis of the platform only random excitations are of major concern, while the other parameters of the system can be reasonably considered to be deterministic. In this paper, a mathematical model for the deterministic analysis of wave-structure interaction developed by the author in a previous investigation 1, is modified and presented as a stochastic model. Maximum response of a platform using a random excitation is compared with the results obtained from the deterministic model. The nature of the wave-structure interaction is, such that the maximum response can be obtained with a few passes of the most critical wave. INTRODUCTION The reliable prediction of the response of offshore platform to random wave action requires knowledge about the interaction of the wave and the structure during motion. With the structural system defined in a deterministic way for its topological and mechanical properties, and with the wave known or estimated as a random excitation, random response follows from application of the proper theory. The forces exerted by waves on circular piles, plates, ships, and walls have been predicted by analytical methods and measured in the laboratory. Investigators agree in considering that water particle velocity and acceleration are the governing parameters of the hydrodynamic forces exerted by waves on structures. The velocities and accelerations should be relative values with respect to the body in motion and not the values with respect to ground. This fact is often overlooked because most structures designed in the past were fairly rigid; but for some flexible offshore platforms having velocities and accelerations in the same order of magnitude as the water velocities and accelerations computation of forces using velocities and accelerations, with respect to ground, yields completely unrealistic results. 1 DETERMINISTIC MODEL The author developed a mathematical model for the deterministic study of wave-structure interaction with basis on the following principles1:The force exerted by the wave on a body can be computed by the formula proposed by Morison, O?Brien, Johnson, and Schaaf2(available in full paper)where V and A are the ater particle velocity and acceleration, respectively; Cl and C2 are constants defined by the geometry of the body.For a structural system composed of lumped masses, the equation of motion for each one of the masses can be written as:(available in full paper)where YI (tn) is the acceleration of Mass I and time tn; FI (tn) is the hydrodynamic force of Mass I and is a function of time; M I is the lumped mass at point I; and R I (Yn) is a function of the configuration of the structure at that instant. The value of RI (Yn) can be computed from the expression available in full paper)