Selected Topics in Nonlinear Wave Mechanics (eBook, PDF)

Redaktion: Christov, C. I.; Guran, Arde

• Format: PDF

Produktbeschreibung

Comprehensive reference text giving an overview of the current state of nonlinear wave mechanics in both elastic and fluid media. Consists of self-contained, interdisciplinary chapters covering new aspects on strong discontinuities (shock waves) and localized self-preserving shapes (solitary waves and solitons). Special attention is devoted to the influence of dissipative forces on the balance between nonlinearity and dispersion. Useful for applied mathematicians, physicists, mechanical, civil and aerospace engineers, as well as graduate students in those fields.

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Produktdetails

• Verlag: Birkhäuser Boston
• Seitenzahl: 263
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781461200956
• Artikelnr.: 44209708

Inhaltsangabe

1 Elastic Surface Waves, Resonances, and Inverse Acoustic Scattering.- 1.1 Introduction.- 1.2 Waves on elastic plates: Lamb-type and Scholte-Stoneley waves.- 1.3 Acoustic Interactions Wich Ocean-Floor Sediments.- 1.4 Conclusions.- 2 Amplitude Equation Models for the Interaction of Shocks with Nonlinear Dispersive Wave Envelopes.- 2.1 Introduction.- 2.2 The Weak Coupling Limit.- 2.3 The Riemann Problem.- 2.4 The Zero Diffusion Limit.- 2.5 Dynamics Prior to Shock Onset.- 2.6 The Incompressible Limit.- 2.7 Exact Solutions.- 2.8 The ? = 0 Problem.- 2.9 The Multi-Scale Expansions.- 2.10 Modulation Equations for the Dispersive Wave.- 2.11 Analysis of the Effective Shock Equation for the Nonlinear Limit.- 2.12 Analysis of the Effective Shock Equation in the Linear Limit.- 2.13 Numerical Experiments.- 3 Some Aspects of One-Dimensional Finite Amplitude Elastic Wave Propagation.- 3.1 First Order Equations.- 3.2 Systems of First Order Equations.- 3.3 Elastic Strings.- 3.4 Problems for membranes.- 3.5 Some problems for three dimensional elastic bodies.- 3.6 Thermodynamic considerations.- 4 Nonlinear Duality Between Elastic Waves and Quasi-particles.- 4.1 Introduction.- 4.2 Hyperbolicity and Conservation Laws.- 4.3 Elasticity as a field theory.- 4.4 Solitonic systems.- 4.5 Nearly integrable systems.- 4.6 Examples from Continuum Mechanics.- 4.7 Conclusions.- 5 Time-Harmonic Waves in Pre-Stressed Dissipative Materials.- 5.1 Introduction.- 5.2 Linearized Equations in Solids.- 5.3 Constitutive Equation for Solids.- 5.4 Linearized Equations and Restrictions for Fluids.- 5.5 Propagation Condition for Inhomogeneous Waves.- 5.6 Dissipation and Wave Decay.- 5.7 A New Approach to Wave Propagation.- 5.8 Rays in Pre-Stressed Solids.- 6 Dissipative Effects on the Evolution of Internal SolitaryWaves in a t Sheared, Stably Stratified Fluid Layer.- 6.1 Introduction.- 6.2 Model system.- 6.3 Discussion.- 6.4 Conclusions.- 7 Dissipative Nonlinear Strain Waves in Solids.- 7.1 Introduction.- 7.2 Modelling of nonlinear waves in an elastic rod.- 7.3 Mathematical tools for analysis of the governing equations.- 7.4 Amplification of a strain solitary wave in a narrowing rod.- 7.5 Selection of nonlinear strain waves in an elastic rod due to the influence of an external medium.- 7.6 Influence of macro- and micro-dissipation on the formation of dissipative solitary waves.- 7.7 Concluding remarks.