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

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Page 73

Nonlinear. Elastic. Waves. I. Theory The past decade has witnessed a

tremendous amount of work devoted to the area of

propagation in solid materials. Nonlinear effects in elastic wave propagation may

arise from several different causes. First, the amplitude of the elastic wave may

be sufficiently large so that finite strains arise. Second, a material which in its

undeformed state behaves in a linear fashion may behave in a nonlinear fashion

when infinitesimal ...

Nonlinear. Elastic. Waves. I. Theory The past decade has witnessed a

tremendous amount of work devoted to the area of

**nonlinear elastic wave**propagation in solid materials. Nonlinear effects in elastic wave propagation may

arise from several different causes. First, the amplitude of the elastic wave may

be sufficiently large so that finite strains arise. Second, a material which in its

undeformed state behaves in a linear fashion may behave in a nonlinear fashion

when infinitesimal ...

Page 113

In 1961, Goldberg (139) derived the equation of motion for finite amplitude

forth by Landau and Lifshitz (138). He considered the special case of plane

waves propagating along a single axis and derived the three component

equations of motion which we have reproduced as Eqs. (194). He showed that

when

cannot exist without ...

In 1961, Goldberg (139) derived the equation of motion for finite amplitude

**elastic****wave**propagation in an isotropic solid following the method and terminology setforth by Landau and Lifshitz (138). He considered the special case of plane

waves propagating along a single axis and derived the three component

equations of motion which we have reproduced as Eqs. (194). He showed that

when

**nonlinear**terms are taken into account, a pure mode transverse wavecannot exist without ...

Page 144

been obtained from measurements of wave velocity variations under conditions

of hydrostatic pressure and uniaxial stress ; from measurements of the

amplitudes of the fundamental, second, and third harmonic of an initially

sinusoidal longitudinal

conversion efficiency of two

wave ; and from measurement of the asymmetry of the diffraction pattern

produced by light propagation ...

been obtained from measurements of wave velocity variations under conditions

of hydrostatic pressure and uniaxial stress ; from measurements of the

amplitudes of the fundamental, second, and third harmonic of an initially

sinusoidal longitudinal

**nonlinear elastic wave**; from measurement of theconversion efficiency of two

**nonlinear elastic waves**interacting to produce a thirdwave ; and from measurement of the asymmetry of the diffraction pattern

produced by light propagation ...

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