Surface waves in nonlocal thermoelastic medium with state space approach

Pramanik, Abdush Salam; Biswas, Siddhartha

doi:10.1080/01495739.2020.1734129

Cited by 27 publications

(9 citation statements)

References 37 publications

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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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“…Analytical expressions for the reflection coefficients and their respective energy ratios for reflected thermoelastic waves were determined. Pramanik and Biswas [27] developed a new model of non-local thermoelasticity with energy dissipation and presented graphically the phase velocity, attenuation coefficients, specific loss with respect to frequency.…”

Section: Introductionmentioning

confidence: 99%

Reflection and Transmission in Non-Local Couple Stress Micropolar Thermoelastic Media

Gupta

Malik

Kumar

et al. 2022

International Journal of Applied Mechanics and Engineering

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We have studied the problem of homogenous, isotropic non-local couple stress micropolar thermoelastic solid in the absence of body forces, couple density and heat resources. The reflection and transmission of waves at the interface of two distinct media have been investigated. It is observed that amplitude ratios of various reflected and transmitted waves are functions of wave number of incident waves and are affected by the non-local parameter of thermoelastic solid.

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“…Moreover, Yu et al [12] studied the size-dependent damping of a nanobeam using nonlocal thermoelasticity. Pramanik and Biswas [13] employed state space approach to study surface waves in nonlocal thermoelastic medium. Biswas [14] solved thermoelastic boundary value problem of three-dimensional (3D) orthotropic medium on the basis of Eringen’s nonlocal elasticity.…”

Section: Introductionmentioning

confidence: 99%

The analysis and computation on nonlocal thermoelastic problems of blend composites via enriched second-order multi-scale computational method

Dong

Nie

et al. 2022

Mathematics and Mechanics of Solids

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This paper proposes an innovative enriched second-order multi-scale (SOMS) computational method to simulate and analyze the nonlocal thermoelastic problems of blend composites with stress and heat flux gradient behaviors. The multiple periodical heterogeneities and periodic configurations of investigated blend composites in different substructures result in a huge computational cost for direct numerical simulations. The significant characteristics of this study are as follows. (1) The nonlocal properties of blend composites in constitutive equations are converted into the source terms of thermoelastic balance equations. The novel macro-micro coupled SOMS computational model for these transformed nonlocal multi-scale problems is derived on the basis of multi-scale asymptotic analysis. The nonlocal thermoelastic behaviors of blend composites can be merely uncovered in the enriched SOMS solutions. (2) The error analysis in the pointwise sense is presented to elucidate the importance and necessity of establishing the enriched SOMS solutions. Furthermore, an explicit error estimate for the SOMS approximate solutions is obtained in the integral sense for these nonlocal multi-scale problems. (3) A multi-scale numerical algorithm is presented to effectively simulate nonlocal thermoelastic problems of blend composites based on finite element method (FEM). Finally, the capability of the proposed enriched SOMS computational method is demonstrated by typical two-dimensional (2D) and three-dimensional (3D) blend composites, presenting not only the excellent numerical accuracy but also the less computational cost. This work proposes a unified multi-scale computational framework for enabling nonlocal thermoelastic behavior analysis of blend composites.

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Surface waves in nonlocal thermoelastic medium with state space approach

Cited by 27 publications

References 37 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

Reflection and Transmission in Non-Local Couple Stress Micropolar Thermoelastic Media

The analysis and computation on nonlocal thermoelastic problems of blend composites via enriched second-order multi-scale computational method

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