Rayleigh waves with impedance boundary conditions in incompressible anisotropic half-spaces

Vinh, Pham Chi; Hue, Trinh Thi Thanh

doi:10.1016/j.ijengsci.2014.08.002

Cited by 16 publications

(4 citation statements)

References 40 publications

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“…Clarke and Burdess [43,44] recognized a device for possible use in rotation sensing and analysed the Rayleigh waves over a rotating isotropic half-plane. Some other linear rotating anisotropic model were investigated for wave features by various researchers including Fang et al [45], Destrade [46,47], Ting [48], Ogden and Singh [49], Vinh and Hue [50], Singh and Kaur [51,52] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Propagation of waves in an incompressible rotating transversely isotropic nonlocal elastic solid

Singh¹

2021

Vietnam J. Mech.

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In this paper, the nonlocal elasticity theory is applied to study the propagation of plane wave and Rayleigh-type surface wave in an incompressible, rotating and transversely isotropic material. The governing equations of motion for an incompressible, rotating, transversely isotropic and nonlocal elastic medium are specialized for a plane. The medium is assumed rotating about an axis perpendicular to the plane. The transverse isotropy axis is taken perpendicular to the surface. The specialized governing equations are first applied to derive a velocity equation for homogeneous plane wave. The specialized governing equations along with traction free boundary conditions are also applied to derive the secular equation governing the wave speed of Rayleigh wave. The speeds of plane wave and Rayleigh wave are computed and illustrated graphically to observe the effects of nonlocality, rotation, anisotropy, frequency and propagation direction. It is noticed from the theory and numerical results that the speeds of both plane wave and Rayleigh wave decrease sharply with an increase in nonlocal parameter or rotation parameter. The speeds of plane wave and Rayleigh wave increase logarithmically with anisotropy material parameter. The feasible ranges of nonlocality, rotation or anisotropy parameters for the existence of plane wave or Rayleigh surface wave are determined for a given wave speed when the values of other parameters are fixed.

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Section: Introductionmentioning

confidence: 99%

Propagation of waves in an incompressible rotating transversely isotropic nonlocal elastic solid

Singh¹

2021

Vietnam J. Mech.

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“…In addition, the propagation of such surface states has been investigated for different types of media, for instance, see the work of Chiri & Ghiba (2012) for Cosserat materials, Akbarov & Ozisik (2003) for pre-stressed and Vinh & Giang (2010) for pre-strained materials. In addition, surfaces waves in anisotropic media and thermo-elastic have been studied by Vinh & Anh (2014), Vinh & Hue (2014) and Tomita & Shindo (1979), Abouelregal (2011), respectively. Rayleigh-type waves in materials with micro-structure and couple-stress effects were investigated by Georgiadis & Velgaki (2003).…”

Section: Introductionmentioning

confidence: 99%

Rayleigh waves in micro-structured elastic systems: Non-reciprocity and energy symmetry breaking

Movchan

Carta

Pagneux

et al. 2020

International Journal of Engineering Science

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Rayleigh waves are analysed in gyroscopic elastic systems. The in-plane vector problems of elasticity for a triangular lattice and its long-wavelength/ low-frequency continuum approximation are considered. The analytical procedure for the derivation of the Rayleigh dispersion relation is fully detailed and, remarkably, explicit solutions for the Rayleigh waves for both the discrete and continuous systems are found. The dispersion at low wavenumbers and the softening induced by the gyricity are shown. Despite of the symmetry of the dispersion curves with respect to the wavenumber, the presence of the gyroscopic effect breaks the symmetry of the eigenmodes and makes the system non-reciprocal. Such an uncommon effect is demonstrated in a set of numerical computations, where a point force applied on the boundary generates surface and bulk waves that do not propagate symmetrically from the source.

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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%

“…From mathematical viewpoint, the derivation of the characteristic equation for the Rayleigh wave speed is a eigenvalue problem. In the case of impedance boundary conditions, [28][29][30][31][32] the eigenvalue also enters into the boundary conditions. Such eigenvalue problems are thoroughly studied in [33].…”

Section: Introductionmentioning

confidence: 99%

Three‐dimensional problem of Rayleigh waves propagating in a half‐space with restrained boundary

Belubekyan¹,

Sarkisyan²

2018

Z Angew Math Mech

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Rayleigh waves with impedance boundary conditions in incompressible anisotropic half-spaces

Cited by 16 publications

References 40 publications

Propagation of waves in an incompressible rotating transversely isotropic nonlocal elastic solid

Propagation of waves in an incompressible rotating transversely isotropic nonlocal elastic solid

Rayleigh waves in micro-structured elastic systems: Non-reciprocity and energy symmetry breaking

Three‐dimensional problem of Rayleigh waves propagating in a half‐space with restrained boundary

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