Ultrasonic Investigation of Mechanical Properties |
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Page 88
... displacement gradients . Finally , we substitute Eqs . ( 239 ) into Eq . ( 236 ) to obtain the first component of the general equations of motion for an isotropic solid , to terms quadratic in the displacement gradients , as Poü = ( 2μ ...
... displacement gradients . Finally , we substitute Eqs . ( 239 ) into Eq . ( 236 ) to obtain the first component of the general equations of motion for an isotropic solid , to terms quadratic in the displacement gradients , as Poü = ( 2μ ...
Page 92
Robert Edward Green. Again in this case the only nonvanishing displacement gradients are ua , uaa v , and w , and therefore we may use the reduced equation of motion given by Eq . ( 245 ) as in the previous case . If we substitute the ...
Robert Edward Green. Again in this case the only nonvanishing displacement gradients are ua , uaa v , and w , and therefore we may use the reduced equation of motion given by Eq . ( 245 ) as in the previous case . If we substitute the ...
Page 107
... displacement gradients . Finally , we substitute Eqs . ( 320 ) into Eq . ( 318 ) to obtain the first com- ponent of the general equations of motion for a cubic crystal , to terms quadratic in the displacement gradients , as Poü = C11Uaa ...
... displacement gradients . Finally , we substitute Eqs . ( 320 ) into Eq . ( 318 ) to obtain the first com- ponent of the general equations of motion for a cubic crystal , to terms quadratic in the displacement gradients , as Poü = C11Uaa ...
Contents
Introduction | 1 |
Nonlinear Elastic Waves | 73 |
On the Energetics Kinetics and Topography of Interfaces | 78 |
Copyright | |
4 other sections not shown
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