Mathematical Techniques for Wave Interaction with Flexible Structures: 1st Edition (Hardback) book cover

Mathematical Techniques for Wave Interaction with Flexible Structures

1st Edition

By Trilochan Sahoo

CRC Press

242 pages | 34 B/W Illus.

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Hardback: 9781466506046
pub: 2012-10-24
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Description

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

About the Series

IIT Kharagpur Research Monograph Series

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied
TEC009070
TECHNOLOGY & ENGINEERING / Mechanical
TEC063000
TECHNOLOGY & ENGINEERING / Structural