Rayleigh-type wave in a nonlocal elastic solid with voids

This work is concerned with the propagation of surface waves is considered in an isotropic elastic homogeneous nonlocal generalized thermoelastic solid medium in the presence of a magnetic field and voids. The normal mode analysis and Lame’s potential theory are used to solve the resulting non-dimensional coupled equations. Dispersion relation for Rayleigh surface wave are derived for both thermally insulated and isothermal surfaces. The non-dimensional wave speed of Rayleigh surface wave is computed for a specific material. The non-dimensional wave speed of Rayleigh surface waves are found to be influenced by the presence of voids, magnetic field, thermal field, and elastic nonlocal parameter. For a particular model, the effect of magnetic field, void parameters, thermal parameter, and nonlocality has been studied numerically on the Rayleigh surface waves. All the computed results obtained have been depicted graphically and explained.

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“…In the absence of thermal parameter and magnetic field, the present analytical and numerical results agree with those shown by Karur et al 39…”

Section: Discussionsupporting

confidence: 90%

Effect of magnetic field and voids on Rayleigh waves in a nonlocal thermoelastic half-space

Abd-Alla

Abo‐Dahab

Ahmed

et al. 2021

The Journal of Strain Analysis for Engineering Design

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“…4(i), the non-dimensional speed V of plane wave is also plotted against the rotation parameter Ω 0 when θ = 45 • , δ = 6 and e = 0, 0.05 and 0.1. The feasible ranges of rotation parameter Ω 0 for existence of plane wave are determined by using inequality (31). For e = 0, 0.05 and 0.1, the feasible ranges of Ω 0 are determined as (−∞, ∞), (…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…Based on the nonlocal elasticity, Eringen [3,4] analyzed the bulk and surface waves and found that the elastic waves are dispersive in a nonlocal linearly elastic medium. The nonlocal elasticity was also employed in some other wave propagation problems by various researchers including Narasimhan and McCay [24], Inan and Eringen [25], Ke et al [26], Sapora et al [27], Roy et al [28], Tong et al [29], Singh et al [30], Kaur et al [31], Ma et al [32], Yan et al [33], Tung [34], Singh [35] 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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“…Some problems pertaining to wave propagation within the context of the nonlocal theory of elasticity have been attempted by Eringen (1983), Nowinski (1984), Rymarz (1988), Kaliski et al. (1992), Nowinski (1993), Chakraborty (2007), Reddy and Ramabrahmam (2010), Khurana and Tomar (2017) and Kaur et al. (2018).…”

Section: Introductionmentioning

confidence: 99%

“…Using the theory of nonlocality, several problems of waves and vibrations have been attempted in the past and gained momentum recently due to enormous applications in nano-materials/nano-porous material, in particular. Some problems pertaining to wave propagation within the context of the nonlocal theory of elasticity have been attempted by Eringen (1983), Nowinski (1984), Rymarz (1988), Kaliski et al (1992), Nowinski (1993), Chakraborty (2007), Reddy and Ramabrahmam (2010), Khurana and Tomar (2017) and Kaur et al (2018). Yang et al (2017aYang et al ( , 2017b proposed the local fractional Riccati differential equation method for an exact traveling wave solution for the local fractional twodimensional (2D) Burgers-type equations.…”

Section: Introductionmentioning

confidence: 99%

Love waves in a nonlocal elastic media with voids

Kaur

Singh

Tomar

2019

Journal of Vibration and Control

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The propagation of Love-type waves in a nonlocal elastic layer with voids resting over a nonlocal elastic solid half-space with voids has been studied. Dispersion relations are derived using appropriate boundary conditions of the model. It is found that there exist two fronts of Love-type surface waves that may travel with distinct speeds. The appearance of the second front is purely due to the presence of voids in layered media. Both fronts are found to be dispersive in nature and affected by the presence of the nonlocality parameter. The first front is found to be nonattenuating, independent of void parameters and analogous to the Love wave of classical elasticity, while the second front is attenuating and depends on the presence of void parameters. Each of the fronts is found to face a critical frequency above which it ceases to propagate. For a specific model, the variation of the phase speeds of both the fronts with frequency, nonlocality, voids and thickness parameters is shown graphically. Attenuation coefficient versus frequency for the second front has also been depicted separately. Some particular cases are deduced from the present formulation.

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Rayleigh-type wave in a nonlocal elastic solid with voids

Cited by 47 publications

References 28 publications

Effect of magnetic field and voids on Rayleigh waves in a nonlocal thermoelastic half-space

Effect of magnetic field and voids on Rayleigh waves in a nonlocal thermoelastic half-space

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

Love waves in a nonlocal elastic media with voids

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