Nonlinear surface acoustic waves on an elastic solid of general anisotropy

Lardner, R. W.

doi:10.1007/bf00041066

Cited by 39 publications

(23 citation statements)

References 7 publications

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“…Here, as in [8], the depth dependence within a disturbance having wavenumber k is where * denotes a complex conjugate, the vectors a} p) are eigenvectors corresponding to the three eigenvalues s <p) (p = 1, 2, 3) having negative imaginary part and arising from the 0(5) terms in system (6). The multipliers Bep) are determined by the boundary condition (7), for which the compatibility condition is the characteristic equation which determines the wavespeed c. then ensures that all displacements are real.…”

Section: Formulation and Leading-order Analysismentioning

confidence: 99%

The spreading of nonlinear elastic surface waves

1990

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Al~traet.A theory for the lateral spreading of a beam of nonlinear surface acoustic waves across the surface of an arbitrary, homogeneous, elastic half-space is developed. The resulting evolution equation generalizes that obtained for tmi-directional waves by replacing an ordinary derivative by a diffusion operator of Schr6dinger type. The coefficients arising in the evolution equation are related to partial derivatives of the dispersion relation for linearized surface waves on the half space. Details are given for isotropic materials and for two special cases of beams travelling along axes of high elastic symmetry.

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Section: Formulation and Leading-order Analysismentioning

confidence: 99%

The spreading of nonlinear elastic surface waves

1990

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“…Early work on nonlinear wave interaction was carried out by Göldberg [3], who investigated bulk wave interaction in elastic solids and harmonic generation. Nonlinear surface waves were studied by Kalyanasundaram [4,5], Lardner [6][7][8][9], Tupholme and Harvey [10], Harvey and Tupholme [11]. Also, Zabolotskaya [12] and Hamilton et al [13] used the averaging of the Hamiltonian to study nonlinear surface waves for isotropic and cubic materials.…”

Section: Introductionmentioning

confidence: 97%

Antisymmetric Waves in a Thin Plate with Geometric and Material Nonlinearities According to a Higher Order Theory

Al‐Qahtani

2011

Arab J Sci Eng

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This work investigates nonlinear antisymmetric waves in a plate. Both geometric and constitutive nonlinearities are accounted for in deriving the governing equations. The displacements are expanded in Legendre polynomials of the thickness coordinate instead of the thickness coordinate itself. The method of multiple scales has been employed to solve the nonlinear equations of motion. Evolution equations are derived and solved for small amplitude traveling antisymmetric elastic waves. Waveform distortion, amplitude amplification and harmonic amplification and harmonic generation are computed numerically.

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“…We refer to this as Method II. This method was followed by Lardner (1984Lardner ( , 1985Lardner ( , 1986), Lardner and Tupholme (1986), David (1985), , Tupholme (1991, 1992), Harvey (1988, 1992). The use of multiple scale η was also independently proposed by Planat (1985) but he assumed that the dependence on η and X was only through a linear combination of X and η with unspecified coefficients.…”

Section: Introduction -Background and Literature Reviewmentioning

confidence: 99%

Linear and Nonlinear Wave Propagation in Coated or Uncoated Elastic Half-spaces

Waves in Nonlinear Pre-Stressed Materials

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In these lectures, we discuss the following three closely related topics.(i) Unification of different methods for deriving evolution equations for surface acoustic waves. Early studies on nonlinear surface acoustic waves were thwarted by very complicated derivation of evolution equations. Worse still, different methods seemed to have given different evolution equations. Later on, it became known that all these methods except one yield the same evolution equation, but even at the time when we started to prepare the current lecture notes, there still existed a method that does not agree with the other methods. Such a situation is unsatisfatory since each method has some following. The purpose of the lectures on this topic is three-fold. Firstly, we aim to show that derviation of the evolution eqution for nonlinear surface waves can be carried out in one A4 page even in the most general case. Secondly, we show that the odd method that used to give a different evolution equation can in fact be used to obtain the same evolution equation if it is properly executed. Thus, we set the record straight: all known methods should and do give the same evolution equation! Thirdly, we express our evolution equation in terms of results from the linear surface-wave theory built on the Stroh formulation, and we explain how the coefficients in the evolution equation can be evaluated efficiently.(ii) Linear wave propagation in a coated elastic half-space. This is partly in preparation for our discussion of the third topic, but the problem is of much interest in its own right. We show how the dispersion relation can be expressed elegantly in terms of the surface-impedance matrices associated with the layer and the half-space. We derive a two-term expression for the wave speed in the long-wavelength limit.(iii) Periodic and solitary waves in a coated elastic half-space. An uncoated elastic half-space cannot in general support solitary waves due to lack of dispersion although it has been argued previously that the nonlocal character of nonlinearity may give rise to the existence of steady travelling waves. We derive the nonlinear evolution equation for small-amplitude long-wavelength travellingThe original publication is available at www.springerlink.com http://www.springerlink.com/content/978-3-211-73571-8/#section=264495&page=2&locus=50 2 waves propagating in a coated elastic half-space where the thin coating induces weak dispersion. When this evolution equation is linearized, we recover the two-term dispersion relation obtained in (ii). We explain a simple method that can be used to compute periodic or solitary travelling-wave solutions.

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Nonlinear surface acoustic waves on an elastic solid of general anisotropy

Cited by 39 publications

References 7 publications

The spreading of nonlinear elastic surface waves

The spreading of nonlinear elastic surface waves

Antisymmetric Waves in a Thin Plate with Geometric and Material Nonlinearities According to a Higher Order Theory

Linear and Nonlinear Wave Propagation in Coated or Uncoated Elastic Half-spaces

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