Green’s function for SH-waves in inhomogeneous anisotropic elastic solid with power-function velocity variation

Daros, C.H.

doi:10.1016/j.wavemoti.2012.07.004

Cited by 29 publications

(7 citation statements)

References 12 publications

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“…Influences of different parameters, such as pore pressure, radial stress, hoop stress, and shear stress on dynamic stress at different points at the cylinder, were illustrated. Daros researched Green's function for SH waves in inhomogeneous anisotropic elastic solid. The wave velocity have a expression of power‐function, and Green's function was derived to model transient SH waves.…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of anisotropic half space containing an elliptical inclusion under SH waves

Jiang

Yang

Sun

et al. 2020

Math Methods in App Sciences

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Based on the methods of complex function, conformal mapping, and multipolar coordinate system, dynamic response of an elliptical inclusion embedded in an anisotropic half space is investigated. In order to find the solution of SH waves, the governing equation is transferred into its normalized form. Then, the scattering wave induced by the inclusion and the standing wave in the inclusion is deduced. Different incident wave angles and the corresponding anisotropy of the half space are considered to obtain the reflected waves. The elliptical inclusion is transferred into a unit circle by conformal mapping method, and then the undetermined coefficients in scattering wave and standing wave are solved by using the continuous condition at the boundary of the inclusion. Subsequently, the dynamic stress concentration factor (DSCF) around the inclusion is calculated and analyzed. Numerical results demonstrate that the distribution of the DSCF is mainly influenced by the incident wave angle and the incident wave number. It is affected by anisotropic parameters as well. KEYWORDSanisotropy, complex function method, dynamic stress concentration factor (DSCF), elliptical inclusion, wave scattering MSC CLASSIFICATION 74J20Math Meth Appl Sci. 2020;43:6888-6902. wileyonlinelibrary.com/journal/mma

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Section: Introductionmentioning

confidence: 99%

Dynamic analysis of anisotropic half space containing an elliptical inclusion under SH waves

Jiang

Yang

Sun

et al. 2020

Math Methods in App Sciences

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“…The inhomogeneous feature of elastic materials or solids makes a strong basis for the consideration in the study of geomechanical problems. Many researchers considered various kinds of inhomogeneous media in their studies (Daros, 2013; Vishwakarma and Xu, 2016; Zhou et al, 2014). Kumari et al (2016) presented a model for magneto-elastic shear wave propagation in an inhomogeneous viscoelastic material under the effect of point source.…”

Section: Introductionmentioning

confidence: 99%

Love-type wave propagation in a hydrostatic stressed magneto-elastic transversely isotropic strip over an inhomogeneous substrate caused by a disturbance point source

Alam

Kundu

Gupta

2018

Journal of Intelligent Material Systems and Structures

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Propagation of Love-type waves emanating due to a disturbance point source in a transversely isotropic layer of finite thickness laid over a semi-infinite half-space is investigated. The layer is assumed under the influence of magnetic field and hydrostatic state of stress, while the half-space is inhomogeneous. The source point is situated at the common interface of the layer and half-space. Maxwell’s equation and generalized Ohm’s law have been taken into account to calculate the Laurent force induced in the layer. Green’s function technique and Fourier transform are used as a powerful tool to calculate the interior deformations of the model; consequently, we obtain a closed-form dispersion relation for the wave. Six numerical examples for the transversely isotropic layer, namely, beryl, magnesium, cadmium, zinc, cobalt, and simply isotropic, have been considered. The role of magneto-elastic coupling parameter, hydrostatic stress, inhomogeneity, the order of the depth variation in inhomogeneity function, and different examples of the layer on the propagation of Love-type wave has been observed by numerical examples and graphical demonstrations.

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“…Several parameters were considered and DSCFs around the cavity were calculated. Moreover, wave phenomena in inhomogeneous, anisotropic media were studied by Daros [20]. A Green's function was derived to model transient SH waves in inhomogeneous and anisotropic media.…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of a cylindrical cavity in inhomogeneous elastic half-space subjected to SH waves

Yang

Jiang

Tang

et al. 2017

Mathematics and Mechanics of Solids

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Based on complex function methods and a multipolar coordinate system, the scattering induced by a cylindrical cavity in a radially inhomogeneous half-space is investigated. Mass density of the half-space varies depending on the distance from the centre of the cavity while the shear modulus is always constant. The wave velocity is expressed as a function of radius vector and the Helmholtz equation is a partial differential equation with a variable coefficient. By means of a conformal mapping technique, the Helmholtz equation with a variable coefficient is transferred into its normal form. Then, displacement fields and corresponding stress components are deduced. Applying the boundary conditions, dynamic stress concentration factors around the cavity are obtained and analyzed. Typical numerical results are presented to demonstrate the distribution of dynamic stress concentration factors when influencing parameters are assumed.

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Green’s function for SH-waves in inhomogeneous anisotropic elastic solid with power-function velocity variation

Cited by 29 publications

References 12 publications

Dynamic analysis of anisotropic half space containing an elliptical inclusion under SH waves

Dynamic analysis of anisotropic half space containing an elliptical inclusion under SH waves

Love-type wave propagation in a hydrostatic stressed magneto-elastic transversely isotropic strip over an inhomogeneous substrate caused by a disturbance point source

Dynamic analysis of a cylindrical cavity in inhomogeneous elastic half-space subjected to SH waves

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