36 Fluid-Induced Vibration Seon M. Han

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Texas Tech University

36.1 Description of the Ocean Environment ............................ 36-1

Spectral Density † Ocean Wave Spectral Densities †

Approximation of Spectral Density from Time Series †

Generation of Time Series from a Spectral Density †

Short-Term Statistics † Long-Term Statistics † Summary

36.2 Fluid Forces ......................................................................... 36-16

Wave Force Regime † Wave Forces on Small Structures —

Morison Equation † Vortex-Induced Vibration † Summary

36.3 Examples .............................................................................. 36-23

Static Configuration of a Towing Cable † Fluid Forces on an

Articulated Tower † Distribution of Significant Wave

Heights — Weibull and Gumbel Distributions †

Reconstructing Time Series for a Given Significant Wave

Height † Available Numerical Codes

Summary

This chapter gives an overview on the subject of fluid-induced vibration in an ocean environment. The main

objective is to show how the fluid forces on an offshore structure due to current and random waves are

modeled. The chapter is divided into three sections. The first section describes the ocean environment,

especially the currents and random waves. The second section is dedicated to obtaining fluid forces utilizing

the results from the first section and the third section gives some examples to show how the results from

the first two sections can be used in practice. In the first section, the concept of spectral density is introduced.

For a given spectrum, methods to obtain a sample time series are given. In the second section, the forces that

the fluid can exert on a body are discussed. The regimes in which inertia, drag, or diffraction forces are

dominant are shown in terms of the ratio of the wave height to the structural diameter and the ratio of the

structural diameter to the wavelength. The Morison equation is extended to the case of a moving inclined

cylinder. The Morison equation requires the use of experimentally determined fluid coefficients such as added

mass, inertia, and drag coefficients. Plots of these fluid coefficients for various values of the fluid parameters

are reproduced here. The vortex shedding force is discussed briefly. In the third section, four examples are

given to show how fluid forces affect the static and dynamics of ocean structures, how the significant wave

height can be chosen to represent the condition in a certain area for a long time, and how the time series can

be constructed from a given spectrum. Finally, the available numerical codes for modeling slender flexible

bodies in fluids are listed.

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