Nonlinear piezoelectric surface waves

Parker, D. F.; David, E.A.

doi:10.1016/0020-7225(89)90008-6

Cited by 25 publications

(10 citation statements)

References 6 publications

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“…1 In these instances, it is possible for nonlinear coupling ͑and therefore energy exchange͒ between the surface acoustic wave and quasitransverse bulk wave to occur. Several theoretical models for the nonlinear propagation of SAWs in anisotropic media [2][3][4] do not account for this coupling, an observation also made previously in the context of nonlinear Scholte waves. 5 To properly use these theories it is important to quantitatively determine their regions of applicability, a topic that does not appear to have been explored.…”

Section: Introductionmentioning

confidence: 85%

Nonlinear coupling of surface and quasitransverse bulk modes in cubic crystals

Kumon

Hamilton

2003

The Journal of the Acoustical Society of America

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In crystals the speed of the surface acoustic wave mode may approach that of the lowest-speed quasitransverse bulk mode in some directions of propagation. Under these circumstances, it is possible for energy to be transferred from the surface mode to the bulk mode by nonlinear coupling. In the present paper we investigate the possibilities for mode coupling in the (001), (110), and (111) planes of cubic crystals. A condition is given for determining the range of propagation directions with significant coupling, and numerical results are provided for eight different crystals with a range of anisotropy ratios. It is shown that even for significant excitation amplitudes the coupling is negligible for most propagation directions in the aforementioned surface cuts.

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Section: Introductionmentioning

confidence: 85%

Nonlinear coupling of surface and quasitransverse bulk modes in cubic crystals

Kumon

Hamilton

2003

The Journal of the Acoustical Society of America

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“…All involve linear partial differential equations and scaleinvariant boundary-value problems in one half-space or two adjacent half-spaces. The eigenvalue problems determining the wave speed and deformation field of piezo-electric surface waves were computed in [13,14] in the context of nonlinear evolution effects. The cases both of an electrically earthed boundary and of free space adjoining the material were studied.…”

Section: Concluding Commentsmentioning

confidence: 99%

The Stroh formalism for elastic surface waves of general profile

Parker

2013

Proc. R. Soc. A.

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The Stroh formalism is widely used in the study of surface waves on anisotropic elastic half-spaces, to analyse existence and for calculating the resultant wave speed. Normally, the formalism treats complex exponential solutions. However, since waves are non-dispersive, a generalization to waves having general waveform exists and is here found by various techniques. Fourier superposition yields a description in which displacements are expressed in terms of three copies of a single pair of conjugate harmonic functions. An equivalent representation involving just one analytic function also is deduced. Both these show that at the traction-free boundary just one component (typically the normal component) of displacement may be specified arbitrarily, the others then being specific combinations of it and its Hilbert transform. The algebra is closely related to that used for complex exponential waves, although the surface impedance matrix is replaced by a transfer matrix, which better embodies the scale invariance properties of the waves. Using the scale-invariance property of the boundary-value problem, a further derivation is presented in terms of real quantities.

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“…Note that F͑X͒ is proportional to the function J −1 K͑X͒, 0 Ͻ X Ͻ 1, which was introduced by Parker [15] and by Parker and David [31]. In the latter work piezoelectricity has also been taken into account.…”

Section: ͑221b͒mentioning

confidence: 99%

Solitary surface acoustic waves

et al. 2004

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Solitary acoustic pulses can propagate along the surface of a coated homogeneous and inhomogeneous medium. It is shown how these nonlinear surface acoustic waves evolve out of initial pulselike conditions generated by pulsed laser excitation and how they can be monitored by optical detection. The solitary pulse shapes at the surface are computed on the basis of an evolution equation with nonlocal nonlinearity. They depend on the anisotropy of the substrate. Various approaches for the derivation of the evolution equation from nonlinear elasticity theory are critically compared. The behavior of the solitary pulses in collisions is investigated and is found to strongly depend on the linear dispersion law. The nontrivial depth dependence of these solitary pulses is also analyzed.

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Nonlinear piezoelectric surface waves

Cited by 25 publications

References 6 publications

Nonlinear coupling of surface and quasitransverse bulk modes in cubic crystals

Nonlinear coupling of surface and quasitransverse bulk modes in cubic crystals

The Stroh formalism for elastic surface waves of general profile

Solitary surface acoustic waves

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