Ebook: Nonlinear and Stochastic Dynamics of Compliant Offshore Structures

The purpose of this monograph is to show how a compliant offshore structure in an ocean environment can be modeled in two and three di­ mensions. The monograph is divided into five parts. Chapter 1 provides the engineering motivation for this work, that is, offshore structures. These are very complex structures used for a variety of applications. It is possible to use beam models to initially study their dynamics. Chapter 2 is a review of variational methods, and thus includes the topics: princi­ ple of virtual work, D'Alembert's principle, Lagrange's equation, Hamil­ ton's principle, and the extended Hamilton's principle. These methods are used to derive the equations of motion throughout this monograph. Chapter 3 is a review of existing transverse beam models. They are the Euler-Bernoulli, Rayleigh, shear and Timoshenko models. The equa­ tions of motion are derived and solved analytically using the extended Hamilton's principle, as outlined in Chapter 2. For engineering purposes, the natural frequencies of the beam models are presented graphically as functions of normalized wave number and geometrical and physical pa­ rameters. Beam models are useful as representations of complex struc­ tures. In Chapter 4, a fluid force that is representative of those that act on offshore structures is formulated. The environmental load due to ocean current and random waves is obtained using Morison's equa­ tion. The random waves are formulated using the Pierson-Moskowitz spectrum with the Airy linear wave theory.

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The purpose of this monograph is to show how to model a compliant offshore structure in an ocean environment. Such structures are of increasing importance because of the desire to access the deep ocean. A brief history and an extensive review of the four existing transverse beam models are presented. The four beam models are Euler-Bernoulli, Rayleigh, shear and Timoshenko models. These are the fundamental models for the preliminary studies of offshore structures. The complete analytical solutions are given for each model. This review is followed by a chapter on the stochastic modelling of environmental forces. The waves are assumed to be random, and the fluid force is modelled using the Morison Equation. In subsequent chapters, the models are expanded to include the axial motion as well as the transverse motion in two and three dimensions.
Numerical results are obtained using both deterministic and random forces. A detailed description of the numerical methods is provided so that the reader can adapt these methods to his or her particular problem. Researchers in the fields of structural mechanics and ocean engineering, especially those with an interest in nonlinear hybrid beam/cable models, will find this a useful book.

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The purpose of this monograph is to show how to model a compliant offshore structure in an ocean environment. Such structures are of increasing importance because of the desire to access the deep ocean. A brief history and an extensive review of the four existing transverse beam models are presented. The four beam models are Euler-Bernoulli, Rayleigh, shear and Timoshenko models. These are the fundamental models for the preliminary studies of offshore structures. The complete analytical solutions are given for each model. This review is followed by a chapter on the stochastic modelling of environmental forces. The waves are assumed to be random, and the fluid force is modelled using the Morison Equation. In subsequent chapters, the models are expanded to include the axial motion as well as the transverse motion in two and three dimensions.
Numerical results are obtained using both deterministic and random forces. A detailed description of the numerical methods is provided so that the reader can adapt these methods to his or her particular problem. Researchers in the fields of structural mechanics and ocean engineering, especially those with an interest in nonlinear hybrid beam/cable models, will find this a useful book.
Content:
Front Matter....Pages i-xiii
Introduction....Pages 1-12
Principle of Virtual Work, Lagrange’s Equation and Hamilton’s Principle....Pages 13-28
Overview of Transverse Beam Models....Pages 29-93
Environmental Loading-Waves and Currents....Pages 95-110
Coupled Axial and Transverse Vibration in Two Dimensions....Pages 111-186
Three-Dimensional Vibration....Pages 187-228
Summary....Pages 229-231
Back Matter....Pages 233-274

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The purpose of this monograph is to show how to model a compliant offshore structure in an ocean environment. Such structures are of increasing importance because of the desire to access the deep ocean. A brief history and an extensive review of the four existing transverse beam models are presented. The four beam models are Euler-Bernoulli, Rayleigh, shear and Timoshenko models. These are the fundamental models for the preliminary studies of offshore structures. The complete analytical solutions are given for each model. This review is followed by a chapter on the stochastic modelling of environmental forces. The waves are assumed to be random, and the fluid force is modelled using the Morison Equation. In subsequent chapters, the models are expanded to include the axial motion as well as the transverse motion in two and three dimensions.
Numerical results are obtained using both deterministic and random forces. A detailed description of the numerical methods is provided so that the reader can adapt these methods to his or her particular problem. Researchers in the fields of structural mechanics and ocean engineering, especially those with an interest in nonlinear hybrid beam/cable models, will find this a useful book.
Content:
Front Matter....Pages i-xiii
Introduction....Pages 1-12
Principle of Virtual Work, Lagrange’s Equation and Hamilton’s Principle....Pages 13-28
Overview of Transverse Beam Models....Pages 29-93
Environmental Loading-Waves and Currents....Pages 95-110
Coupled Axial and Transverse Vibration in Two Dimensions....Pages 111-186
Three-Dimensional Vibration....Pages 187-228
Summary....Pages 229-231
Back Matter....Pages 233-274
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