Reflection and refraction of plane wave in piezo-thermoelastic diffusive half spaces with three phase lag memory dependent derivative and two-temperature

Kaur, Iqbal; Lata, Parveen; Singh, Kulvinder

doi:10.1080/17455030.2020.1856451

Cited by 26 publications

(9 citation statements)

References 38 publications

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“…In the absence of heat sources, the equation of heat conduction with MDD following Kaur et al [33][34][35] is, Wang and Li [18] presented the first-order MDD with the differentiable function f(t) w. r.t. > 0 for time t as: Depending on the material properties, we choose K (t − ) and . Following Kaur et al [33][34][35], the K(t − ξ) is considered as where and are constants.…”

Section: Basic Equationsmentioning

confidence: 99%

Functionally graded nonlocal thermoelastic nanobeam with memory-dependent derivatives

Kaur

Singh

2022

SN Appl. Sci.

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The purpose of this study is to investigate vibrations in 2D functionally graded nanobeams (FGN) with memory-dependent derivatives. A sinusoidal variation of temperature is assumed. The dimensionless expressions for axial displacement, thermal moment, lateral deflection, strain and temperature distribution are found in the transformed domain using Laplace Transforms, and the expressions in the physical domain are derived by numerical inversion techniques. The nanobeam is simply supported at the both ends and have constant temperatures. The FGN is a non-homogenous composite structure with constant structural variations along with the layer thickness, changing from ceramic at the bottom to metal at the top. Adding non-local MDD to thermoelastic models opens up new possibilities for the study of thermal deformations in solid mechanics. The effect of different kernel functions and periodic frequency of thermal vibration is illustrated graphically for lateral deflection, axial displacement, strain, temperature, and thermal moment. Article highlights A novel model of vibrations in a functionally graded nanobeams is presented. The medium is subjected to sinusoidal variation of temperature. Dynamic response of memory dependent derivative theory of thermoelasticity and non-local parameter is investigated. The effects of kernel functions and periodic frequency of thermal vibration on all physical fields are investigated and shown graphically.

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Section: Basic Equationsmentioning

confidence: 99%

Functionally graded nonlocal thermoelastic nanobeam with memory-dependent derivatives

Kaur

Singh

2022

SN Appl. Sci.

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“…The coefficients and +3 , = 1, 2, 3 can be obtained through solving Equation (59). So far, the expressions of the undetermined parameters are obtained and the solutions of the considered physical quantities in Laplacian domain can thus be given.…”

Section: Solutions In Laplacian Domainmentioning

confidence: 99%

“…Subsequently, Ezzat [58] established another theory of fractional order generalized thermoelasticity by introducing new Taylor series expansion of fractional order derivative into the heat conduction equation. By applying the above mentioned theories, a large number of researches have been reported on the dynamic response problems [59][60][61][62].…”

Section: Introductionmentioning

confidence: 99%

Transient thermoelastic response of a size‐dependent nanobeam under the fractional order thermoelasticity

Peng

2021

Z Angew Math Mech

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With the miniaturization of structures, such as MEMS/NEMS, the sizedependent effect has become an issue and attracted much attention. The wellknown theories describing the size-dependent effect mainly include the nonlocal elasticity theory, the strain gradient theory and the modified coupled stress theory. Based on these theories, a number of works have been conducted to explore the size-dependent behaviors of structures or devices in micro/nanoscale, among them, majorities are on elastic performances, while, minorities are on thermoelastic performances. It is inevitable for structures suffering changeable temperature, as a consequence, thermal-induced stress and deformation occur in structures and they are worth being fully concerned. For thermoelastic behaviors limited to small scale problems, the classical Fourier's heat conduction law may fail, meanwhile, new models, for example, fractional order heat conduction model, have been developed to modify Fourier's law. In present paper, the transient thermoelastic response of a nanobeam subjected to a ramp heating is investigated by combining the nonlocal elasticity theory and the fractional order heat conduction model. The governing equations are formulated and then solved by Laplace transform and its numerical inversion. The non-dimensional temperature, displacement, stress, and deflection in the nanobeam are obtained and illustrated graphically. In calculation, the effects of the ramp-heating time parameter, the nonlocal parameter and the fractional order parameter on the considered physical quantities are examined and discussed in detail.

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“…The wave propagation in the thermoelastic anisotropic medium have been investigated by using a matricant method, for instance wave propagation waves in liquid crystals and in thermoelastic medium [11][12][13][14][15][16][17]. In the paper [18], authors consider the propagation of Rayleigh surface waves in a functionally graded isotropic thermoelastic half-space.…”

Section: Introductionmentioning

confidence: 99%

The Propagation of Thermoelastic Waves in Different Anisotropic Media Using Matricant Method

Ispulov

Zhumabekov

Qadir

et al. 2022

Advances in Mathematical Physics

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Thermoelasticity is a generalization of classical theories of elasticity and thermal conductivity and describes a wide range of phenomenon. The theory can precisely predict the propagation of thermoelastics waves in case of an isotropic medium. However, the propagation of thermoelastic waves in the anisotropic medium is not fully understood. In this case, the theory of elasticity employs an approximate theory of temperature stress which does not take into consideration the interactions of temperature and deformations. In this paper, an analytical study has been carried out by using method of matricant to investigate the propagation of longitudinal elastic and heat waves in the anisotropic medium of a monoclinic, trigonal, hexagonal, and cubical crystal systems. In this article, a solution to the problem of the propagation of thermal waves and the propagation of a thermal wave along z -axis has been obtained. The attenuation coefficient and phase velocity of thermal waves for various materials are determined. Specifically, the problem of propagation of heat waves in one dimension has been solved.

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Reflection and refraction of plane wave in piezo-thermoelastic diffusive half spaces with three phase lag memory dependent derivative and two-temperature

Cited by 26 publications

References 38 publications

Functionally graded nonlocal thermoelastic nanobeam with memory-dependent derivatives

Functionally graded nonlocal thermoelastic nanobeam with memory-dependent derivatives

Transient thermoelastic response of a size‐dependent nanobeam under the fractional order thermoelasticity

The Propagation of Thermoelastic Waves in Different Anisotropic Media Using Matricant Method

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