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.
Table of Contents
List of Symbols
NONLINEAR WAVES IN ELASTIC SOLIDS
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
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
"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