Strain Solitons in Solids and How to Construct Them: 1st Edition (Hardback) book cover

Strain Solitons in Solids and How to Construct Them

1st Edition

By Alexander M. Samsonov

Chapman and Hall/CRC

248 pages

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Hardback: 9780849306846
pub: 2001-01-18
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Description

Although the theory behind solitary waves of strain shows that they hold significant promise in nondestructive testing and a variety of other applications, an enigma has long persisted-the absence of observable elastic solitary waves in practice. Inspired by this apparent contradiction, Strain Solitons in Solids and How to Construct Them refines the existing theory, explores how to construct a powerful deformation pulse in a waveguide without plastic flow or fracture, and proposes a direct method of strain soliton generation, detection, and observation.

The author focuses on the theory, simulation, generation, and propagation of strain solitary waves in a nonlinearly elastic, straight cylindrical rod under finite deformations. He introduces the general theory of wave propagation in nonlinearly elastic solids and shows, from first principles, how its main ideas can lead to successful experiments. In doing so, he develops a new approach to solving the corresponding doubly dispersive equation (DDE) with dissipative terms, leading to new explicit and exact solutions. He also shows that the method is applicable to a variety of nonlinear problems.

First discovered in virtual reality, nonlinear waves and solitons in solids are finally moving into the genuine reality of physics, mechanics, and engineering. Strain Solitons in Solids and How to Construct Them shows how to balance the mathematics of the problem with the application of the results to experiments and ultimately to generating and observing solitons in solids.

Reviews

"Samsonov's book, Strain Solitons in Solids and How to Construct Them is an original one. It clearly deserves to be on the shelves of all researchers interested in the nonlinear dynamical elasticity of structures."

- Applied Mechanics Reviews, Vol. 54, No. 4, July 2001

"The author is known for his own contributions to nonlinear waves and solutions in elastic solids…This book is written to stimulate further study and research in this growing and important field…it could be used in graduate-level seminar courses…well-written…an excellent addition to the literature on solutions in elastic solids."

- Zentralbatt für Mathematik

Table of Contents

Preface

Introduction

List of Symbols

NONLINEAR WAVES IN ELASTIC SOLIDS

Basic Definitions

Physical and Geometrical Nonlinearity

Compressibility, Dispersion, and Disipation in Wave Guides

MATHEMATICAL DESCRIPTION OF GENERAL DEFORMATION WAVE PROBLEM

Action Functional and the Lagrange Formalism

Coupled Equations of Long Wave Propagation

One-Dimensional Quasi Hyperbolic Equation

Main Assumptions and 2-D Coupled Equations

Waves in a Wave Guide Embedded in External Medium

DIRECT METHODS AND FORMAL SOLUTIONS

Nonlinear Hyperbolic and Evolution Equations

Conservation Laws

Some Notices in Critical Points Analysis for an O.D.E.

New Approach to a Solution for an Autonomous Dissipative Nonlinear Equation

A General Theorem of Reduction

Dissipative Equations with Polynomial Nonlinearity

Elliptic Function Solutions to Higher Order Problems

Example for a Nonlinear Reaction-Diffusion Problem

NONLINEAR STRAIN WAVES IN ELASTIC WAVE GUIDES

Features of Longitudinal Waves in a Rod

Experiments in Nonlinear Waves in Solids

Solitons in Inhomogeneous Rods

Experiments in Soliton Propagation in the Non-Uniform Rod

NONLINEAR WAVES IN COMPLEX WAVE GUIDES

Longitudinal Nonlinear Waves in Elastic Plate

Longitudinal Waves in Rods Embedded in Surrounding Medium

Nonlinear Waves in Layers on the Elastic Half Space

NUMERICAL SIMULATION OF SOLITARY WAVES IN SOLIDS

Numerical Simulation of Non-Stationary Deformation Waves

Solitary Waves in a Homogenous Rod

Solitary Waves in a Nonuniform Rod

Solitary Waves in Complex Rods

CONCLUSIVE REMARKS AND TENTATIVE APPLICATIONS

APPENDIX

INDEX

About the Series

Chapman & Hall/CRC Monographs and Research Notes in Mathematics

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied
MAT037000
MATHEMATICS / Functional Analysis