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E-raamat: Wave Momentum And Quasi-particles In Physical Acoustics

(Universite Pierre Et Marie Curie, France), (Univ Pierre Et Marie Curie, France)
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This unique volume presents an original approach to physical acoustics with additional emphasis on the most useful surface acoustic waves on solids. The study is based on foundational work of Léon Brillouin, and application of the celebrated invariance theorem of Emmy Noether to an element of volume that is representative of the wave motion.This approach provides an easy interpretation of typical wave motions of physical acoustics in bulk, at surfaces, and across interfaces, in the form of the motion of associated quasi-particles. This type of motion, Newtonian or not, depends on the wave motion considered, and on the original modeling of the continuum that supports it. After a thoughtful review of Brillouin's fundamental ideas related to radiative stresses, wave momentum and action, and the necessary reminder on modern nonlinear continuum thermomechanics, invariance theory and techniques of asymptotics, a variety of situations and models illustrates the power and richness of the approach and its strong potential in applications. Elasticity, piezoelectricity and new models of continua with nonlinearity, viscosity and some generalized features (microstructure, weak or strong nonlocality) or unusual situations (bounding surface with energy, elastic thin film glued on a surface waveguide), are considered, exhibiting thus the versatility of the approach.This original book offers an innovative vision and treatment of the problems of wave propagation in deformable solids. It opens up new horizons in the theoretical and applied facets of physical acoustics.
Preface v
1 Prolegomena: wave momentum and radiative stresses in 1D in the line of Brillouin 1(18)
1.1 Introduction
1(2)
1.2 One-dimensional motion in the Eulerian description
3(8)
1.2.1 Basic equations
3(2)
1.2.2 Method of perturbations
5(1)
1.2.3 First-order approximation
5(1)
1.2.4 Second-order approximation
6(1)
1.2.5 Example of momentum and radiative stress in a thin rod
7(4)
1.3 One-dimensional motion in the Lagrangian description
11(3)
1.3.1 Basic equations
11(1)
1.3.2 Perturbation analysis at the first-order of approximation
12(1)
1.3.3 Perturbation analysis at the second order of approximation
13(1)
1.4 Summary and concluding remarks
14(5)
2 Elements of continuum thermomechanics 19(18)
2.1 Material body
19(4)
2.2 Balance laws of the thermomechanics of continua
23(6)
2.2.1 Global balance laws in the Euler—Cauchy format
23(2)
2.2.2 Euler—Cauchy format of the local balance laws of thermomechanics
25(2)
2.2.3 Global balance laws in the Piola—Kirchhoff format
27(1)
2.2.4 Piola—Kirchhoff format of the local balance laws of thermomechanics
27(2)
2.3 General theorems of thermodynamics
29(1)
2.3.1 Thermodynamic hypotheses
29(1)
2.3.2 Local expression of the general theorems of thermomechanics
29(1)
2.4 Finite-strain elasticity
30(2)
2.4.1 Measures of finite strains
31(1)
2.4.2 Time rates of finite strains
31(1)
2.4.3 Rigid-body motions
32(1)
2.5 Strains in small-strain elasticity
32(1)
2.6 Constitutive equations for finite-strain elasticity
33(2)
2.7 Constitutive equations for small-strain elasticity
35(2)
3 Pseudomomentum and Eshelby stress 37(14)
3.1 Introduction
37(2)
3.2 Pseudomomentum in hyperelastic materials
39(2)
3.3 Field-theoretical formulation in the case of elasticity
41(4)
3.4 The case of small strains
45(1)
3.5 Peculiarity of a one-dimensional motion
46(2)
3.6 Small strains in the presence of dissipation
48(3)
4 Action, phonons and wave mechanics 51(16)
4.1 Wave-particle dualism and phonons
52(1)
4.2 Action in continuum mechanics
53(3)
4.3 Wave kinematics and wave action
56(3)
4.4 Evolution equation for the wave amplitude
59(1)
4.5 Hamiltonian formulation
60(1)
4.6 Further analytical mechanics
61(2)
4.7 The case of inhomogeneous waves
63(4)
5 Transmission-reflection problem 67(12)
5.1 Introduction
67(1)
5.2 Reminder on the wavelike picture
68(2)
5.2.1 One-dimensional case
68(1)
5.2.2 Transmission-reflection problem for a perfect interface
69(1)
5.2.3 Transmission-reflection problem for an interface with delamination
69(1)
5.3 Associated quasi-particle picture
70(4)
5.3.1 Basic equations
70(2)
5.3.2 Transmission-reflection problem (perfect interface)
72(2)
5.3.3 Case of an imperfect interface for an interface with delaminating
74(1)
5.4 Case of a sandwiched slab
74(2)
5.5 Conclusion
76(3)
6 Application to dynamic materials 79(20)
6.1 Reminder on the notion of dynamic materials
79(3)
6.2 General properties of linear wave propagation
82(2)
6.3 Case of a fixed material interface or transition layer
84(1)
6.4 Case of a time-line or thin time-like interface layer
85(1)
6.5 Quasi-particle re-interpretation at a time-like interface layer
86(3)
6.6 Waves along a rod of finite length
89(2)
6.7 Space-time homogenization of dynamic materials
91(4)
6.7.1 So-called "slow" time-like configuration
92(1)
6.7.2 So-called "fast" space-like configuration
93(1)
6.7.3 Space-time homogenization for a long time
94(1)
6.8 Generalization to moving interfaces
95(1)
6.9 Conclusion
96(3)
7 Elastic surface waves in terms of quasi-particles 99(36)
7.1 The notion of surface wave
99(3)
7.2 The Rayleigh surface wave in isotropic linear elasticity
102(13)
7.2.1 Definition of Rayleigh waves
102(2)
7.2.2 Conservation of wave momentum for Rayleigh surface waves
104(1)
7.2.3 Quasi-particles associated with Rayleigh surface waves
105(3)
7.2.4 The influence of surface energy
108(1)
7.2.5 The case of leaky surface waves
108(7)
7.3 The case of Love waves
115(8)
7.3.1 The Love SAW solution
115(2)
7.3.2 Conservation of wave momentum and energy
117(1)
7.3.3 Mass and energy of the associated quasi-particle
118(4)
7.3.4 Summary of this section
122(1)
7.4 The case of Murdoch waves
123(9)
7.4.1 Definition of Murdoch waves
123(2)
7.4.2 Murdoch SAW linear solution
125(1)
7.4.3 Canonical conservation laws for Murdoch linear SAWs
126(2)
7.4.4 Associated quasi-particle
128(2)
7.4.5 Consideration on the Lagrangian of the wave system
130(1)
7.4.6 Murdoch case as a limit of the Love case
131(1)
7.5 Conclusion
132(3)
8 Electroelastic surface waves in terms of quasi-particles 135(36)
8.1 The notion of electroelastic surface wave
135(2)
8.2 Basic equations of piezoelectricity
137(2)
8.3 Conservation laws of energy and wave momentum in electroelasticity
139(1)
8.4 The Bleustein—Gulyaev surface wave
140(10)
8.4.1 The general surface wave problem in piezoelectric materials
140(2)
8.4.2 The Bleustein—Gulyaev surface wave problem per se
142(2)
8.4.3 Dynamics of the associated quasi-particle
144(3)
8.4.4 Another case of electric boundary condition
147(3)
8.5 Perturbation by elastic nonlinearities
150(7)
8.5.1 Basic equations
150(1)
8.5.2 Surface wave solution
151(2)
8.5.3 Quasi-particle associated with the wave solution
153(4)
8.6 Perturbation by viscosity
157(14)
8.6.1 Some general words
157(1)
8.6.2 Reminder of the Bleustein—Gulyaev surface wave problem in presence of weak viscous losses
157(2)
8.6.3 Global equations of wave momentum and energy
159(12)
9 Waves in generalized elastic continua 171(16)
9.1 The notion of generalized continuum
171(2)
9.2 Weak nonlocality and gradient model of elasticity
173(2)
9.2.1 Summary of strain-gradient elasticity
173(1)
9.2.2 Wave solution for a simplified problem
174(1)
9.2.3 Wave momentum
174(1)
9.3 The case of Cosserat continua
175(4)
9.3.1 Summary of the general linear theory
175(2)
9.3.2 Wave solution for a simplified problem
177(1)
9.3.3 Wave momentum and quasi-particles
178(1)
9.4 The case of strong nonlocality
179(6)
9.4.1 Summary of nonlocal elasticity
179(1)
9.4.2 Wave solution for a simplified problem
180(2)
9.4.3 Wave momentum and quasi-particles
182(3)
9.5 Conclusion
185(2)
10 Examples of solitonic systems 187(24)
10.1 Introduction: The notion of soliton
187(1)
10.2 Reminder: Some standard cases
188(10)
10.2.1 The Bousginesq model in elastic crystals
188(2)
10.2.2 The Korteweg—De Vries equation
190(5)
10.2.3 The sine-Gordon equation
195(2)
10.2.4 The nonlinear Schrodinger model
197(1)
10.2.5 Comments
198(1)
10.3 The generalized Boussinesq model (gradient elasticity)
198(3)
10.4 Surface elastic solitons
201(10)
10.4.1 The basic equations
201(3)
10.4.2 Reminder: Linear harmonic approximation
204(1)
10.4.3 Solitary-wave solutions for envelope signals
205(6)
Appendix A Reminder on Noether's theorem 211(6)
Appendix B Justification of (4.33)—(4.34) by a two-timing method 217(4)
Bibliography 221(12)
Index 233