## Treatise on materials science and technology, Volume 3 |

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Page 16

Therefore, in summary of plane wave propagation in an unbounded linear elastic

homogeneous

longitudinal wave may propagate and the energy flux associated with this wave

is in the same direction as the wave normal. Also in any arbitrary direction a pure

mode transverse wave, with particle displacements anywhere in a plane

perpendicular to the wave normal, may propagate and the energy flux associated

with this ...

Therefore, in summary of plane wave propagation in an unbounded linear elastic

homogeneous

**isotropic solid**, we find that in any arbitrary direction a pure modelongitudinal wave may propagate and the energy flux associated with this wave

is in the same direction as the wave normal. Also in any arbitrary direction a pure

mode transverse wave, with particle displacements anywhere in a plane

perpendicular to the wave normal, may propagate and the energy flux associated

with this ...

Page 76

7l2 722 (178) Substituting Eqs. (178) into Eq. (177) we have the expression for

the elastic strain energy of an

+ X)/2-](yll+y22 + y33)2 -2/i(722 733 -723 732 +733 7ll-7l3 731+711 722 -7l272l)

+ [(/+2/w)/3](711+722 + 733)3 -2m(711 + )>22 + y33)(y22y33-y23)>32 + )<33711

-713731 (179) + 7ll722-7l272l) + «(7l 1 722 733 - 7l 1 723 732 - 72 1 7l2 733 +

72 1 7l 3 732 + 73l7l2723-73l7l3722)- S 5 * O I ^ - Here is a 76 III. NONLINEAR ...

7l2 722 (178) Substituting Eqs. (178) into Eq. (177) we have the expression for

the elastic strain energy of an

**isotropic solid**as a function of the strains 0 = {.(2/x+ X)/2-](yll+y22 + y33)2 -2/i(722 733 -723 732 +733 7ll-7l3 731+711 722 -7l272l)

+ [(/+2/w)/3](711+722 + 733)3 -2m(711 + )>22 + y33)(y22y33-y23)>32 + )<33711

-713731 (179) + 7ll722-7l272l) + «(7l 1 722 733 - 7l 1 723 732 - 72 1 7l2 733 +

72 1 7l 3 732 + 73l7l2723-73l7l3722)- S 5 * O I ^ - Here is a 76 III. NONLINEAR ...

Page 130

Benson and Raelson (194) employed the acoustoelastic effect, i.e., the

phenomenon of variation of ultrasonic transverse wave velocity with different

polarizations in stressed

aluminum bar such that the particle displacements associated with these

transducers were parallel to each other and at an angle of 45° to the axis of

compressive stress.

Benson and Raelson (194) employed the acoustoelastic effect, i.e., the

phenomenon of variation of ultrasonic transverse wave velocity with different

polarizations in stressed

**isotropic solids**, to study the stress state of an**isotropic****solid**. They placed transverse wave transducers on opposite parallel sides of analuminum bar such that the particle displacements associated with these

transducers were parallel to each other and at an angle of 45° to the axis of

compressive stress.

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### Common terms and phrases

Alers aluminum Andreatch anisotropic Appl axis calculated compressive stress copper crystallographic orientation cubic crystals determine direction cosines displacement gradients displacements along 001 elastic moduli elastic wave propagation energy-flux vector equation of motion experimental germanium given by Eq hydrostatic pressure hydrostatic pressure longitudinal 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 plane wave pressure longitudinal wave pressure transverse wave pure mode longitudinal pure mode transverse quasitransverse waves rolling direction rolling plane second harmonic second-order elastic constants shear wave single crystals six third-order elastic stress along 001 stress along 110 Substituting Eqs symmetry test specimen texture third-order elastic constants Thurston and Brugger transducer transverse wave ultrasonic beam ultrasonic pulse uniaxial stress values wave along 100 wave normal wave speeds wave velocity Young's modulus