Ultrasonic Investigation of Mechanical Properties |
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Page 92
... obtain PoV2a = ( 2μ + λ ) + a ( 5λ + 10μ + 21 + 4m ) + 2ẞ ( 2 + 21 ) , ( 253 ) where again we have neglected terms of order a2 or greater , and where we have set VLa = w / k . ( 254 ) The subscripts L and a denote longitudinal wave ...
... obtain PoV2a = ( 2μ + λ ) + a ( 5λ + 10μ + 21 + 4m ) + 2ẞ ( 2 + 21 ) , ( 253 ) where again we have neglected terms of order a2 or greater , and where we have set VLa = w / k . ( 254 ) The subscripts L and a denote longitudinal wave ...
Page 127
... obtain C11 = - C11 [ P / ( C11 + 2c12 ) ] [ 2c11 + 2c12 + 6c111 + 4c112 ] , ( 362 ) which demonstrates the linear pressure dependence . A similar expression can be obtained for c12 if we use Eq . ( 343 ) , namely , pV2 = 2 — ( C11 — C12 ) ...
... obtain C11 = - C11 [ P / ( C11 + 2c12 ) ] [ 2c11 + 2c12 + 6c111 + 4c112 ] , ( 362 ) which demonstrates the linear pressure dependence . A similar expression can be obtained for c12 if we use Eq . ( 343 ) , namely , pV2 = 2 — ( C11 — C12 ) ...
Page 132
... obtain the correct expression for the amplitude of the second harmonic for nonlinear elastic wave propagation in an isotropic solid from Eq . ( 207 ) , namely , A2 = ( kA1 ) 2B 2 8poco 2 a = A1 k2a B 8 α 2 ( 383 ) where we have used the ...
... obtain the correct expression for the amplitude of the second harmonic for nonlinear elastic wave propagation in an isotropic solid from Eq . ( 207 ) , namely , A2 = ( kA1 ) 2B 2 8poco 2 a = A1 k2a B 8 α 2 ( 383 ) where we have used the ...
Contents
Introduction | 1 |
Nonlinear Elastic Waves | 73 |
On the Energetics Kinetics and Topography of Interfaces | 78 |
Copyright | |
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Common terms and phrases
Alers aluminum Andreatch anisotropic Appl axis Breazeale calculated compressive stress crystallographic orientation cubic crystals determine direction cosines displacement gradients displacements along 001 displacements along 110 elastic moduli elastic wave propagation energy-flux vector equation of motion experimental germanium given by Eq hydrostatic pressure hydrostatic pressure transverse ideal orientation interaction isotropic solid linear elastic wave longitudinal wave longitudinal wave propagating materials mode transverse wave nonlinear elastic wave obtain Papadakis particle displacements phonons Phys Physical Acoustics plane wave pressure transverse wave pure mode longitudinal pure mode transverse pv² quasilongitudinal quasitransverse wave rolling direction second harmonic second-order elastic constants shear wave single crystals six third-order elastic stress along 001 symmetry test specimen texture third-order elastic constants Thurston and Brugger transducer transverse wave ultrasonic beam ultrasonic pulse uniaxial stress v₁ v₂ values wave along 100 wave normal wave speeds wave velocity Young's modulus