Dynamics of Fixed Marine Structures, Third Edition proves guidance on the dynamic design of fixed structures subject to wave and current action. The text is an update of the ""UR8"" design guide ""Dynamics of Marine Structures"" with discussion of foundations, wind turbulence, offshore installations, earthquakes, and strength and fatigue.
The book employs analytical methods of static and dynamic structural analysis techniques, particularly the statistical and spectral methods when applied to loading and in the calculating dynamic responses. The statistical methods are explained when used to wave, wind, and earthquake calculations, together with the problems encountered in actual applications. Of importance to fixed offshore platforms are the soil properties and foundation covering soil behavior, site investigation, testing, seabed stability, gravity structures, and the use of single piles. Methods of forecasting, measuring, and modeling of waves and currents are also presented in offshore structure construction. Basic hydrodynamics is explained in understanding wave theory, and some description is given to forecasting of environmental conditions that will affect the structures. The effects of vortex-induced vibrations on the structure are explained, and the three methods that can prevent vortex-induced oscillations are given. Wind turbulence or wind loads are analyzed against short natural period or long natural periods of structures. The transportation of offshore platforms, installation, and pile driving, including examples of the applications found in the book, are given as well.
The guide is helpful for offshore engineers, designers of inshore jetties, clients needing design and analysis work, specialists related to offshore structural engineering, and students in offshore engineering.

Foreword
Preface

1 Introduction

1.1 Outline of the contents

1.2 Layout

1.3 Sections which help with the selection of analysis strategy

1.4 Use of the book as a technical reference

1.5 Use of the book as an introductory text

2 Dynamics with deterministic loading

2.1 Linear single degree of freedom systems: SDOF

2.1.1 Units

2.2 Oscillation of an SDOF with neither forcing nor damping

2.3 Steady state oscillation of an SDOF with forcing and viscous damping

2.3.1 Steady state solution using real algebra

2.3.2 Dynamic amplification factor

2.3.3 Significance of forcing and natural frequencies

2.3.4 Steady state solution using complex algebra

2.3.5 Complex number representation of response

2.3.6 Steady state response of a non-linear SDOF

2.4 Damped decay and build-up of oscillation

2.4.1 Viscous, damped decay of oscillation

2.4.2 Damping ratio and logarithmic decrement

2.4.3 Response to an impulse

2.4.4 Viscous damped build-up of natural frequency oscillation

2.5 Damping

2.5.1 Hysteretic damping

2.5.2 Friction damping

2.5.3 Typical structural damping

2.6 Modeling multidegree of freedom structures: MDOFs

2.6.1 Natural frequencies of a 2 degree of freedom system

2.6.2 Modeling frame structures

2.6.3 Beam element stiffness

2.6.4 Global axes

2.6.5 Axis transformation

2.6.6 Assembly of global stiffness matrix

2.6.7 Damping

2.6.8 Mass

2.6.9 Supports

2.6.10 Forces applied at nodes

2.6.11 Forces applied to members

2.6.12 Constraints

2.6.13 Joints

2.6.14 Geometric stiffness

2.6.15 Hydrostatic stiffness and effective tension

2.6.16 Modeling continuous structures using plate, shell and brick elements

2.6.17 Substructures

2.7 Static analysis of MDOF structures

2.7.1 Quasi-static analysis

2.8 Steady state solution using complex matrix algebra

2.9 Natural frequencies of MDOFs

2.9.1 Eigenvalue form

2.9.2 Jacobi method

2.9.3 Householder QR/QL method

2.9.4 Polynomial solution

2.9.5 Vector iteration methods

2.9.6 More complicated methods

2.9.7 Selection of frequency/mode shape calculation method

2.9.8 Some frequencies of commonly used structural elements

2.10 Normal mode (or principal or generalized) coordinates

2.10.1 Forced vibration of MDOF systems

2.10.2 Other uses of principal/generalized coordinates

2.11 Time history solution methods

2.11.1 Convolution integral

2.11.2 Time stepping methods

2.11.3 Central difference (explicit) method

2.11.4 Runge-Kutta (explicit) method

2.11.5 Newmark ß (implicit) method

2.12 Economic solution of large dynamic problems

2.12.1 Separate, simpler model

2.12.2 Guyan reduction or static condensation

2.12.3 Static improvement

Notation

Bibliography

References

3 Statistical and spectral description of random loading and response

3.1 Short term, frequency and sequence independent properties of y(t)

3.1.1 Measures of location

3.1.2 Measures of spread

3.1.3 Probability density function (PDF)

3.1.4 Cumulative distribution function (CDF)

3.1.5 Moments of a PDF

3.1.6 Gaussian (normal distribution)

3.1.7 Non-Gaussian distributions

3.2 Sequence dependent properties of a time history y(t)

3.2.1 Autocovariance

3.2.2 Autocorrelation function Ryy(x)

3.2.3 Autocorrelation coefficient or normalised autocovariance

3.2.4 Time scale

3.3 Fourier analysis and spectra of y(t)

3.3.1 Fourier series

3.3.2 Fourier transform representation of a random time history

3.3.3 Alternative forms of the Fourier transform

3.3.4 The discrete Fourier transform

3.3.5 The Fourier transform pair

3.3.6 Integral form of the Fourier transform pair

3.3.7 Spectral density

3.3.8 Spectral analysis of a dynamic system subject to loading defined by one variable

3.4 Relationship between autocovariance and the energy spectrum

3.5 Short term frequency and sequence independent statistics of simultaneous samples from several time histories: y^t), y2(t) ...

3.5.1 Covariance of yx(t) and y2(t)

3.5.2 Correlation coefficient or normalised covariance

3.5.3 Statistical properties of a + byt(t) + cy2(t)

3.5.4 Statistical properties of y^t) x y2(t)

3.5.5 Joint probability of n random variables

3.5.6 Gaussian multivariate distribution

3.6 Sequence dependent properties of samples from several time histories

3.6.1 Cross-covariance

3.6.2 Cross-correlation coefficient or normalised cross-covariance

3.6.3 Cross-correlation function

3.6.4 Nomenclature

3.7 Cross spectral density and coherence

3.7.1 Cross spectral density

3.7.2 Single-sided cross spectral density

3.7.3 Co- and quad-spectral density

3.7.4 Coherence

3.7.5 Spectral analysis of the response to a summation of random signals

3.8 Relationship between the cross-covariance and the cross-spectrum

3.9 Some further derivations based on spectral properties

3.9.1 Velocity and acceleration spectra

3.9.2 Spectral moments

3.9.3 Bandwidth

3.9.4 Crossing periods and peak distributions

3.9.5 Level crossing periods and the zero crossing period Tz

3.9.6 The crest frequency fc and period Tc

3.9.7 Distribution of amplitudes in a narrow band…