Mathematical Techniques for Wave Interaction with Flexible Structures
Features
- Introduces basic differential equations and the fundamentals of wave structure interaction problems
- Covers the application of Fourier analysis to deal with boundary value problems associated with Laplace equations satisfying higher order boundary conditions in single and double layer fluid
- Uses Green’s function techniques to derive alternate derivation of the expansion formulae
- Illustrates the role of wave interaction with vertical flexible structures in the cases of both single and double-layer fluids having a free surface
- Discusses and illustrates mathematical approaches to deal with initial boundary value problems associated with surface wave interactions with large floating structures
- Deals with wave structure interaction problems in case of long wave under the assumption of linear shallow water approximation
- Illustrates the use of the boundary integral equation method by analyzing the wave diffraction by a flexible floating membrane
Summary
Mathematical Techniques for Wave Interaction with Flexible Structures is a thoughtful compilation of the various mathematical techniques used to deal with wave structure interaction problems. The book emphasizes unique determination of the solution for a class of physical problems associated with Laplace- or Helmholtz-type equations satisfying higher order boundary conditions with the applications of the theory of ordinary and partial differential equations, Fourier analysis, and more.
Features:
- Provides a focused mathematical treatment for gravity wave interaction with floating and submerged flexible structures
- Highlights solution methods for a special class of boundary value problems in wave structure interaction
- Introduces and expands upon differential equations and the fundamentals of wave structure interaction problems
This is an ideal handbook for naval architects, ocean engineers, and geophysicists dealing with the design of floating and/or flexible marine structures. The book’s underlying mathematical tools can be easily extended to deal with physical problems in the area of acoustics, electromagnetic waves, wave propagation in elastic media, and solid-state physics.
Designed for both the classroom and independent study, Mathematical Techniques for Wave Interaction with Flexible Structures enables readers to appreciate and apply the mathematical tools of wave structure interaction research to their own work.
Table of Contents
General Introduction
Preamble
State of the art
Fundamentals of differential equations
Fundamentals of waves and flexible structures
Examples and exercises
Fourier Analysis
General introduction
Integral transforms
Expansion formulae in single layer fluid
Flexural gravity wave maker problem
Effect of compression on wave scattering by a crack
Expansion formulae in double layer fluid
Examples and exercises
Green’s Function Technique
Introduction
Green’s function technique for expansion formulae
Green’s theorem for expansion formulae
Scattering of surface waves by floating elastic plates
Examples and exercises
Wave Interaction with Vertical Flexible Porous Structures
Introduction
Eigenfunction expansion method
Method of least square approximation
Transform method
Method of wide spacing approximation
Conclusion
Examples and exercises
Time Domain Analysis of Wave Structure Interaction Problems
General introduction
Mathematical formulation
Unsteady wave structure interaction problems
Flexural gravity wave motion due to initial disturbances
Conclusion
Examples and exercises
Shallow Water Approximation
General introduction
Surface gravity wave interaction with floating elastic plates
Flexural gravity wave scattering by articulated floating plates
Conclusion
Examples and exercises
Boundary Integral Equation Method
General introduction
Wave diffraction by a floating membrane
Mathematical formulation
Conclusion
Examples and exercises
