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

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Results 1-3 of 26

Page 51

Finally, in order to remain in the linear elastic regime the electrical power applied

to the transducer should not be increased beyond the level required to establish

an acceptable pulse train in the test specimen. If we rearrange Eqs. (60) we may

write them in the form k + 2fi = pvl2, n = pv22, (159) where p is the density and, as

was shown in Chapter II, Section III, vl and v2 are the wave speeds associated

with

...

Finally, in order to remain in the linear elastic regime the electrical power applied

to the transducer should not be increased beyond the level required to establish

an acceptable pulse train in the test specimen. If we rearrange Eqs. (60) we may

write them in the form k + 2fi = pvl2, n = pv22, (159) where p is the density and, as

was shown in Chapter II, Section III, vl and v2 are the wave speeds associated

with

**pure mode longitudinal**and pure mode transverse wave propagation along...

Page 82

Longitudinal Wave Harmonic Generation If we attempt to propagate a

equations of motion Eqs. (194) reduce to p0u-au^ = Puauaa. (196) Hence we see

that a

However, such a wave cannot propagate without distortion and the generation of

higher harmonics. Let us assume that /? <^ a and calculate a perturbation

solution ...

Longitudinal Wave Harmonic Generation If we attempt to propagate a

**pure mode****longitudinal**wave only, then we have u = u(a,t), v = w = 0 (195) and the threeequations of motion Eqs. (194) reduce to p0u-au^ = Puauaa. (196) Hence we see

that a

**pure mode longitudinal**wave may propagate in a nonlinear isotropic solid.However, such a wave cannot propagate without distortion and the generation of

higher harmonics. Let us assume that /? <^ a and calculate a perturbation

solution ...

Page 97

Breazeale and Ford (150) have applied the results of finite amplitude wave

analysis, as worked out for fluids, to

waves in cubic single crystals. They write the equation of motion equivalent to Eq.

(281) in the form p0 £/„ = K2 (U„ + 3 U. UJ + K3 Ua U„ (283) where for the [100]

direction K2 = cll, K3 = clll (284) using Bruggers' notation for the third-order

elastic constants and subscript t to denote time differentiation. Comparison shows

that Eq. (281) is ...

Breazeale and Ford (150) have applied the results of finite amplitude wave

analysis, as worked out for fluids, to

**pure mode longitudinal**nonlinear elasticwaves in cubic single crystals. They write the equation of motion equivalent to Eq.

(281) in the form p0 £/„ = K2 (U„ + 3 U. UJ + K3 Ua U„ (283) where for the [100]

direction K2 = cll, K3 = clll (284) using Bruggers' notation for the third-order

elastic constants and subscript t to denote time differentiation. Comparison shows

that Eq. (281) is ...

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