(Ebook) Strain Solitons in Solids and How to Construct Them Monographs and Surveys in Pure and Applied Mathematics 117 1st Edition by Alexander Samsonov ISBN 978-0367455408 0367455404

(Ebook) Strain Solitons in Solids and How to Construct Them Monographs and Surveys in Pure and Applied Mathematics 117 1st Edition by Alexander Samsonov ISBN 978-0367455408 0367455404

(Ebook) Strain Solitons in Solids and How to Construct Them (Monographs and Surveys in Pure and Applied Mathematics 117) 1st Edition by Alexander M. Samsonov - Ebook PDF Instant Download/Delivery: 978-0367455408, 0367455404
Full download (Ebook) Strain Solitons in Solids and How to Construct Them (Monographs and Surveys in Pure and Applied Mathematics 117) 1st Edition  after payment

Product details: 

ISBN 10:0367455404

ISBN 13:  978-0367455408

Author:  Alexander M. Samsonov

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: 

1 Nonlinear waves in elastic solids

1.1 Basic definitions

1.1.1 Wave terminology

1.1.2 Deformation and strains

1.1.3 Stresses

1.2 Physical and geometrical sources of nonlinearity

1.2.1 Elastic potentials and moduli

1.3 Compressibility, dispersion and dissipation in wave guides.

2 A mathematical description of the general deformation wave prob-lem

2.1 Action functional and the Lagrange formalism

2.2 Coupled equations of long wave propagation

2.3 One-dimensional quasi-hyperbolic equation

2.3.1 Derivation of the Doubly Dispersive Equation (DDE)

2.3.2 Refinement of the derivation of the DDE

2.3.3 Equations for wave in non-uniform highly nonlinear wave guide

2.4 Main assumptions and 2-D coupled equations

2.5 Waves in a wave guide embedded in an external medium

3 Direct methods and formal solutions

3.1 Nonlinear hyperbolic and evolution equations

3.1.1 Travelling wave solutions to the KdV and the DDE equations

3.2 Conservation laws

3.2.1 The Hamiltonian structure.

3.3 Some notices in critical points analysis for an o.d.e.

3.4 New approach to a solution for an autonomous dissipative nonlinear equation

3.5 A general theorem of reduction

3.6 Dissipative equations with polynomial nonlinearity

3.6.1 Square and cubic polynomial nonlinearities

3.6.2 Physical interpretation of additional conditions for the travel-ling wave existence

3.7 Elliptic function solutions to higher order problems

3.8 Example of a nonlinear reaction-diffusion problem

3.8.1 Discontinuous solutions

3.8.2 Bounded periodical and solitary wave solutions

3.8.3 Autosoliton solution

3.8.4 Periodic bounded solutions in case A>0.

4 Nonlinear strain waves in elastic wave guides

4.1 Features of longitudinal waves in a rod

4.2 Experiments in nonlinear waves in solids

4.2.1 Strain soliton observation

4.2.2 Why is it a soliton?.

4.2.3 Reflection of a strain soliton

4.3 Solitons in inhomogeneous rods

4.3.1 Solitons in the non-uniform rod

4.3.2 Solitons in the inhomogeneous rod

4.4 Experiments in soliton propagation in the non-uniform rod

5 Nonlinear waves in complex wave guides

5.1 Longitudinal nonlinear waves in an elastic plate

5.1.1 Generation and observation of the strain soliton in a plate

5.2 Longitudinal waves in rods embedded in a surrounding medium

5.2.1 Kinks in a rod in full contact with a surrounding medium.

5.2.2 Waves in a rod in sliding contact with a surrounding medium

5.2.3 Statement and the solution to the problem

5.2.4 External stresses on the rod lateral surface

5.2.5 Derivation of strain-displacement relationships inside the rod.

5.2.6 A nonlinear evolution equation for longitudinal strain waves along the rod and its solution

5.2.7 The influence of the external medium on the propagation of the strain soliton along the rod

5.2.8 A numerical simulation of unsteady strain wave propagation

5.2.9 Applications of the theory

5.2.10 Conclusions

5.3 Nonlinear waves in the layer upon the elastic half space

5.3.1 Physical background

5.3.2 Basic equations

5.3.3 The layer and the half-space contact with slippage.

5.3.4 The full contact of the layer and the half-space.

5.3.5 On various mathematical models of nonlinesar waves in a layered medium

5.3.6 On physical experiments in waves in a layered medium

6 Numerical simulation of the solitary waves in solids

6.1 Numerical simulation of non-stationary deformation waves

6.1.1 Parametrisation of the strain solitary wave

6.2 Solitary waves in a homogeneous rod

6.3 Solitary waves in a nomuniform rod

6.4 Solitary waves in complex rods.

6.4.1 Strain solitons in a rod with the periodically varied cross section

6.4.2 An example of classification using soliton transformation

Conclusive remarks and tentative applications

Bibliography

Appendix

Index

People also search for:

    
strain in solids
    
solid b
    
strain solution meaning
    
c starr solid
    
crystalline solids chemistry

Tags: Alexander Samsonov, Strain Solitons, How to Construct, Monographs and Surveys