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Strain Solitons in Solids and How to Construct Them : Chapman & Hall/CRC Monographs and Research Notes in Mathemat - Alexander M. Samsonov

Strain Solitons in Solids and How to Construct Them

Chapman & Hall/CRC Monographs and Research Notes in Mathemat

Hardcover Published: 18th January 2001
ISBN: 9780849306846
Number Of Pages: 248

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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.

Industry 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 solidsThis book is written to stimulate further study and research in this growing and important fieldit could be used in graduate-level seminar courseswell-writtenan excellent addition to the literature on solutions in elastic solids." - Zentralbatt f]r Mathematik

Nonlinear waves in elastic solidsp. 1
Basic definitionsp. 1
Wave terminologyp. 3
Deformation and strainsp. 7
Stressesp. 10
Physical and geometrical sources of nonlinearityp. 12
Elastic potentials and modulip. 16
Compressibility, dispersion and dissipation in wave guidesp. 19
A mathematical description of the general deformation wave problemp. 23
Action functional and the Lagrange formalismp. 23
Coupled equations of long wave propagationp. 26
One-dimensional quasi-hyperbolic equationp. 27
Derivation of the Doubly Dispersive Equation (DDE)p. 28
Refinement of the derivation of the DDEp. 31
Equations for wave in non-uniform highly nonlinear wave guidep. 36
Main assumptions and 2-D coupled equationsp. 37
Waves in a wave guide embedded in an external mediump. 44
Direct methods and formal solutionsp. 49
Nonlinear hyperbolic and evolution equationsp. 49
Travelling wave solutions to the KdV and the DDE equationsp. 52
Conservation lawsp. 53
The Hamiltonian structurep. 54
Some notices in critical points analysis for an o.d.e.p. 56
New approach to a solution for an autonomous dissipative nonlinear equationp. 60
A general theorem of reductionp. 62
Dissipative equations with polynomial nonlinearityp. 64
Square and cubic polynomial nonlinearitiesp. 66
Physical interpretation of additional conditions for the travelling wave existencep. 70
Elliptic function solutions to higher order problemsp. 71
Example of a nonlinear reaction-diffusion problemp. 74
Discontinuous solutionsp. 75
Bounded periodical and solitary wave solutionsp. 76
Autosoliton solutionp. 76
Periodic bounded solutions in case [Delta] ] 0p. 77
Nonlinear strain waves in elastic wave guidesp. 79
Features of longitudinal waves in a rodp. 79
Experiments in nonlinear waves in solidsp. 84
Strain soliton observationp. 93
Why is it a soliton?p. 97
Reflection of a strain solitonp. 98
Solitons in inhomogeneous rodsp. 103
Solitons in the non-uniform rodp. 105
Solitons in the inhomogeneous rodp. 108
Experiments in soliton propagation in the non-uniform rodp. 111
Nonlinear waves in complex wave guidesp. 121
Longitudinal nonlinear waves in an elastic platep. 121
Generation and observation of the strain soliton in a platep. 124
Longitudinal waves in rods embedded in a surrounding mediump. 128
Kinks in a rod in full contact with a surrounding mediump. 129
Waves in a rod in sliding contact with a surrounding mediump. 131
Statement and the solution to the problemp. 132
External stresses on the rod lateral surfacep. 133
Derivation of strain-displacement relationships inside the rodp. 135
A nonlinear evolution equation for longitudinal strain waves along the rod and its solutionp. 136
The influence of the external medium on the propagation of the strain soliton along the rodp. 138
A numerical simulation of unsteady strain wave propagationp. 140
Applications of the theoryp. 144
Conclusionsp. 149
Nonlinear waves in the layer upon the elastic half spacep. 150
Physical backgroundp. 150
Basic equationsp. 152
The layer and the half-space contact with slippagep. 154
The full contact of the layer and the half-spacep. 161
On various mathematical models of nonlinear waves in a layered mediump. 167
On physical experiments in waves in a layered mediump. 171
Numerical simulation of the solitary waves in solidsp. 173
Numerical simulation of non-stationary deformation wavesp. 174
Parametrisation of the strain solitary wavep. 178
Solitary waves in a homogeneous rodp. 180
Solitary waves in a nonuniform rodp. 186
Solitary waves in complex rodsp. 189
Strain solitions in a rod with the periodically varied cross sectionp. 194
An example of classification using soliton transformationp. 198
Conclusive remarks and tentative applicationsp. 205
Bibliographyp. 209
Appendixp. 223
Indexp. 229
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780849306846
ISBN-10: 0849306841
Series: Chapman & Hall/CRC Monographs and Research Notes in Mathemat
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 248
Published: 18th January 2001
Country of Publication: US
Dimensions (cm): 24.28 x 17.42  x 2.97
Weight (kg): 0.47
Edition Number: 1

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