On the existence of surface waves in an elastic half-space with impedance boundary conditions

Godoy, E.; Durán, Mario; Nédélec, Jean-Claude

doi:10.1016/j.wavemoti.2012.03.005

Cited by 48 publications

(24 citation statements)

References 21 publications

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“…If we put = * 3 0 Z in equation (19), then the resulting secular equation fairly agrees with those obtained by Godoy et al [12] (iii). In absence of impedance parameters and microrotation, the frequency equation (17) reduces to…”

Section: Governing Equations and Solutionsupporting

confidence: 87%

“…For example, Malischewsky [11] studied the Rayleigh waves with Tiersten's impedance boundary conditions and obtained a secular equation. Godoy et al [12] studied the existence and uniqueness of Rayleigh waves with impedance boundary conditions. Vinh and Hue [13] investigated the propagation of Rayleigh waves in an orthotropic and monoclinic half-space with impedance boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

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Rayleigh Wave in a Micropolar Elastic Medium with Impedance Boundary Conditions

Singh¹

2017

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Abstract. In this paper, a problem on Rayleigh surface wave in an isotropic micropolar elastic solid half-space with impedance boundary conditions is investigated. It is assumed that the normal force traction, shear force traction and shear couple traction vary linearly with the normal displacement component, tangential displacement component and microrotation component multiplied by the frequency, where the impedance corresponds to the constants of proportionality. The linear governing equations of an isotropic micropolar elastic medium are solved for general surface wave solutions. The appropriate particular solutions satisfying the radiation conditions in a half-space of medium are applied at the free surface of the half-space with impedance boundary conditions. The secular equation for Rayleigh surface wave under impedance boundary conditions is derived in the explicit form. In the absence of impedance and microrotation, the secular equation reduces to classical secular equation for Rayleigh wave in an isotropic elastic half-space with traction free boundary conditions. The non-dimensional speed of propagation of Rayleigh wave is computed for an aluminium-epoxy composite as an example of a micropolar elastic solid and is shown graphically against nondimensional material constant, frequency and impedance parameters.

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Section: Governing Equations and Solutionsupporting

confidence: 87%

Section: Introductionmentioning

confidence: 99%

Rayleigh Wave in a Micropolar Elastic Medium with Impedance Boundary Conditions

Singh¹

2017

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“…We take the origin at plane surface and negative y− axis normally into the half-space which is thus represented by y < 0. Following Godoy [25] and Vinh and Hue [26], we assume that the surface y = 0 is subjected to impedance boundary conditions, where normal and tangential tractions depend linearly on normal and tangential displacements times frequency, respectively. We choose the x-axis in the direction of propagation of waves.…”

Section: Governing Equations Of Linear Elasticitymentioning

confidence: 99%

“…Malischewsky [24] investigated the Rayleigh waves with TierstenâĂŹs impedance boundary conditions and obtained a secular equation. Godoy et al [25] proved the existence and uniqueness of Rayleigh waves with impedance boundary conditions. Vinh and Hue [26] discussed the propagation of Rayleigh waves in an orthotropic and monoclinic half-space with impedance boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Reflection of Elastic Waves from Plane Surface of a Half-space with Impedance Boundary Conditions

Singh¹

2017

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In the present work, a problem on the reflection of elastic waves at a plane surface of an elastic half-space is considered. The elastic half-space is assumed homogeneous and isotropic. The plane surface of half-space is subjected to impedance boundary conditions, where normal and tangential tractions are proportional to normal and tangential displacement times frequency, respectively. The reflection coefficients of reflected P and SV are obtained in closed form for incidence of P or SV waves. These reflection coefficients depend on the angle of incidence, impedance parameters and other material parameters. The material parameters of Diabase (dark-colored igneous rock), Limestone (sedimentary rock) and Gneiss (high grade metamorphic rock) are chosen to compute the reflection coefficients for certain ranges of angle of incidence and impedance parameters. The effect of impedance boundary on the reflection phenomena is shown graphically for three different rock materials (Diabase, Limestone and Gneiss).

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“…The study of free waves in a half-space (waves propagating with amplitudes determined by accuracy of arbitrary amplitude factor) for classical-traditional and auxetic-non-traditional materials is carried out in [18][19][20][21][22][23][24][25]. The propagation of Rayleigh waves in isotropic elastic semi-space (plane deformation) with impedance boundary conditions (on the semi-space boundary normal and tangential stresses are linear in corresponding displacement component multiplied by the frequency) are studied in [28][29][30][31][32]. The existence and uniqueness of the wave is proved and an analytical formula for the Rayleigh wave speed is obtained using the method of complex functions.…”

Section: Introductionmentioning

confidence: 99%