Nonlocal scale effect on Rayleigh wave propagation in porous fluid-saturated materials

Tong, Lihong; Lai, Shih-Kung; Zeng, Luolan; Xu, Changjie; Yang, Jie

doi:10.1016/j.ijmecsci.2018.08.028

Cited by 18 publications

(6 citation statements)

References 48 publications

(80 reference statements)

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“…where = le 0 (e 0 is the material constant, l is the atomic spacing) and ∇ = [ ∂ ∂x 1 , ∂ ∂x 2 , ∂ ∂x 3 ] T is the gradient operator; the researchers have carried out a large number of investigations of harmonic plane waves propagating in various nonlocal elastic media, including nonlocal purely elastic media [2,3], nonlocal thermoelastic media [4][5][6], nonlocal piezoelastic media [7][8][9], nonlocal micropolar elastic media [10][11][12][13][14][15], nonlocal porous elastic media [16][17][18], and nonlocal elastic solids with voids [19][20][21][22][23]. These works investigated the propagation of harmonic plane waves in infinite nonlocal continuum solids [2,4,6,7,10,14,16,17,19,21], the reflection of harmonic plane waves from free boundaries of nonlocal elastic half-spaces [3,4,6,10,13,15,16,19], the reflection and transmission of harmonic plane waves through plane interfaces of two nonlocal elastic half-spaces [8,9,12], the propagation characteristics of Rayleigh waves…”

Section: Introductionmentioning

confidence: 99%

“…where ϵ = l e 0 ( e 0 is the material constant, l is the atomic spacing) and ∇ = [ ∂ ∂ x 1 , ∂ ∂ x 2 , ∂ ∂ x 3 ] T is the gradient operator; the researchers have carried out a large number of investigations of harmonic plane waves propagating in various nonlocal elastic media, including nonlocal purely elastic media [2, 3], nonlocal thermoelastic media [4–6], nonlocal piezoelastic media [7–9], nonlocal micropolar elastic media [10–15], nonlocal porous elastic media [16–18], and nonlocal elastic solids with voids [19–23]. These works investigated the propagation of harmonic plane waves in infinite nonlocal continuum solids [2, 4, 6, 7,…”

Section: Introductionmentioning

confidence: 99%

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Expressions of nonlocal quantities and application to Stoneley waves in weakly nonlocal orthotropic elastic half-spaces

Anh

Vinh

2023

Mathematics and Mechanics of Solids

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In this paper, we introduce a novel model of nonlocal elasticity, called the weakly nonlocal elasticity, and provide explicit expressions of nonlocal quantities for harmonic plane waves propagating in the weakly nonlocal elastic solids. Then, we apply these expressions to investigate the propagation of Stoneley waves along the interface between two weakly nonlocal orthotropic elastic half-spaces. The half-spaces may be compressible or incompressible, and they are in welded contact. Our main aim is to derive explicit dispersion equations of Stoneley waves. First, we derive the explicit dispersion equation for the compressible case (when two half-spaces are compressible) using the surface impedance matrices of half-spaces. Then, the explicit dispersion equations for the incompressible cases (at least one half-space is incompressible) are obtained using the incompressible limit method. The simple and immediate derivation of these equations proves the convenience of the incompressible limit method. Some numerical examples are carried out to examine the effect of nonlocality and incompressibility on the Stoneley wave velocity.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Expressions of nonlocal quantities and application to Stoneley waves in weakly nonlocal orthotropic elastic half-spaces

Anh

Vinh

2023

Mathematics and Mechanics of Solids

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“…Two different methods, namely separation of variables and multiple scales analysis, are applied to the governing equation. Of course, many other numerical methods [16][17][18][19][20][21][22][23] can deal with nonlinear partial differential equations and other more complex models. For the linear vibration model of micro-rods in this study, the above two methods are enough to solve and the results with sufficient accuracy can be obtained.…”

Section: Introductionmentioning

confidence: 99%

Lateral Free Vibration of Micro-Rods Using a Nonlocal Continuum Approach

Xie

Zhang²,

Chen

et al. 2022

J. Adv. App. Comput. Math.

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The lateral free vibration of micro-rods initially subjected to axial loads based on a nonlocal continuum theory is considered. The effects of nonlocal long-range interaction fields on the natural frequencies and vibration modes are examined. A simply supported micro-rod is taken as an example; the linear vibration responses are observed by two different methods, including the separation of variables and multiple scales analysis. The relations between the vibration mode and dimensionless coordinate and the relations between natural frequencies and nonlocal parameters are analyzed and discussed in detail. The numerical comparison shows that the theoretical results by two different approaches have a good agreement, which validates the present micro-rod model that can be used as a component of the micro-electromechanical system.

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“…In Balu et al (2017), wave characteristics are computed at the fixed heterogeneous and magnetic poroelastic coupling factor. Tong et al (2018) studied the Rayleigh wave propagation in porous fluid saturated materials and concluded that the nonlocal parameter does not have significant influence on the characteristics of Rayleigh waves within a low frequency range when compared to that of classical Biot theory. Effect of several parameters of reinforced sandwich porous plates such as aspect ratios, volume fraction, types of reinforcement and thickness of plate on bending is investigated by Medani et al (2019).…”

Section: Introductionmentioning

confidence: 99%

Shear wave propagation in magneto poroelastic medium sandwiched between self-reinforced poroelastic medium and poroelastic half space

Ala

Gurijala

Perati

2020

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Purpose The purpose of this paper is to investigate the effect of reinforcement, inhomogeneity and initial stress on the propagation of shear waves. The problem consists of magneto poroelastic medium sandwiched between self-reinforced medium and poroelastic half space. Using Biot’s theory of wave propagation, the frequency equation is obtained. Design/methodology/approach Shear wave propagation in magneto poroelastic medium embedded between a self-reinforced medium and poroelastic half space is investigated. This particular setup is quite possible in the Earth crust. All the three media are assumed to be inhomogeneous under initial stress. The significant effects of initial stress and inhomogeneity parameters of individual media have been studied. Findings Phase velocity is computed against wavenumber for various values of self-reinforcement, heterogeneity parameter and initial stress. Classical elasticity results are deduced as a particular case of the present study. Also in the absence of inhomogeneity and initial stress, frequency equation is discussed. Graphical representation is made to exhibit the results. Originality/value Shear wave propagation in magneto poroelastic medium embedded between a self-reinforced medium, and poroelastic half space are investigated in presence of initial stress, and inhomogeneity parameter. For heterogeneous poroelastic half space, the Whittaker’s solution is obtained. From the numerical results, it is observed that heterogeneity parameter, inhomogeneity parameter and reinforcement parameter have significant influences on the wave characteristics. In addition, frequency equation is discussed in absence of inhomogeneity and initial stress. For the validation purpose, numerical results are also computed for a particular case.

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Nonlocal scale effect on Rayleigh wave propagation in porous fluid-saturated materials

Cited by 18 publications

References 48 publications

Expressions of nonlocal quantities and application to Stoneley waves in weakly nonlocal orthotropic elastic half-spaces

Expressions of nonlocal quantities and application to Stoneley waves in weakly nonlocal orthotropic elastic half-spaces

Lateral Free Vibration of Micro-Rods Using a Nonlocal Continuum Approach

Shear wave propagation in magneto poroelastic medium sandwiched between self-reinforced poroelastic medium and poroelastic half space

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