An approach for obtaining approximate formulas for the Rayleigh wave velocity

The effect of auxeticity on the velocity of elastic wave propagation is investigated herein for isotropic solids. Three types of dimensionless wave velocities are proposed for investigating longitudinal waves in prismatic bars, plane waves of dilatation, plane waves of distortion, and surface waves. Results show that the velocity of surface waves is slightly less than that of plane waves of distortion for conventional solids, but the difference becomes large for auxetic solids. The velocity of longitudinal waves in prismatic bars is higher than that of plane waves of distortion for conventional solids but the gap narrows for solids of the low auxetic range of À0.5 < n < 0. The velocity of longitudinal waves in prismatic bars become lower than that of plane waves of distortion for intermediate auxetic range of À0.733 < n < À0.5, and lower than that of surface waves for high auxetic range of À1 < n < À0.733.

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“…To observe the variation of α for the whole range of the Poisson's ratio, values of α have been obtained for −1 ≤ ν ≤ 0.5, as shown in Fig. .…”

Section: Review Of Typical Elastic Wavesmentioning

confidence: 99%

Wave motion in auxetic solids

Lim

Cheang

Scarpa

2013

Phys. Status Solidi B

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“…Since these approximate formulas are simpler than the exact ones and have a very high accuracy, they are useful in applications. Following Vinh and Malischewsky [25], one can see that in the interval [x 0 , 1], the best approximate second-order polynomial of x 3 in the sense of least squares is…”

Section: Approximate Formulas For the Velocity Of Rayleigh Wavesmentioning

confidence: 99%

New results on Rayleigh waves in incompressible elastic media subjected to gravity

Vinh

Linh

2012

Acta Mech

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In this paper, the following new results related to Rayleigh waves in incompressible elastic media under the influence of gravity are presented: (i) the exact formulas for the velocity of Rayleigh waves propagating along the free-surface of an incompressible isotropic elastic half-space under the gravity are derived, and (ii) two approximate formulas for the velocity of the Rayleigh waves are established and it is shown that their accuracy is very high. To derive the exact formulas, we use the theory of cubic equation, and to establish the approximate formulas, we employ the best approximate second-order polynomials of the cubic power. The obtained formulas are powerful tools for analyzing the effect of gravity on the propagation of Rayleigh waves and for solving the inverse problem.

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“…While a large number of formulas for the Rayleigh wave velocity have been derived, see for examples, [6][7][8][9][10][11][12][13][14][15][16], only few formulas for the Rayleigh wave H/V ratio have been obtained. They are, for example, the exact Rayleigh wave H/V ratio formula for a compressible layered half-space with traction-free surface [2], the exact and an approximate formula for that model of incompressible media [17].…”

Section: Introductionmentioning

confidence: 99%

Approximate formula for the H/V ratio of Rayleigh waves in incompressible orthotropic half-spaces coated by a thin elastic layer

2017

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This paper is concerned with the propagation of Rayleigh waves in an incompressible orthotropic elastic half-space coated with a thin incompressible orthotropic elastic layer. The main purpose of the paper is to establish an approximate formula for the Rayleigh wave H/V ratio (the ratio between the amplitudes of the horizontal and vertical displacements of Rayleigh waves at the traction-free surface of the layer). First, the relations between the traction amplitude vector and the displacement amplitude vector of Rayleigh waves at two sides of the interface between the layer and the half-space are created using the Stroh formalism and the effective boundary condition method. Then, an approximate formula for the Rayleigh wave H/V ratio of third-order in terms of dimensionless thickness of the layer has been derived by using these relations along with the Taylor expansion of the displacement amplitude vector of the thin layer at its traction-free surface. It is shown numerically that the obtained formula is a good approximate one. It can be used for extracting mechanical properties of thin films from measured values of the Rayleigh wave H/V ratio.Keywords: Rayleigh waves, the Rayleigh wave H/V ratio, incompressible orthotropic elastic half-space, thin incompressible orthotropic elastic layer, approximate formula for the Rayleigh wave H/V ratio.

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An approach for obtaining approximate formulas for the Rayleigh wave velocity

Cited by 39 publications

References 14 publications

Wave motion in auxetic solids

Wave motion in auxetic solids

New results on Rayleigh waves in incompressible elastic media subjected to gravity

Approximate formula for the H/V ratio of Rayleigh waves in incompressible orthotropic half-spaces coated by a thin elastic layer

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