Nonlocal elasticity and thermal dual‐phase‐lag effect on the vibration analysis of transversely isotropic electro‐magneto generalized thermoelastic sphere with voids

Sharma, Sita Ram; Mehalwal, Jai Chand; Sarkar, Nantu; Sharma, Dinesh Kumar

doi:10.1002/zamm.202100200

Cited by 11 publications

(7 citation statements)

References 55 publications

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“…So far, based on the DPL model considering thermal memory‐dependent effect and size‐dependent effect, the results show that there are few thermo‐elasto‐diffusive coupling models involving time‐fractional derivative in both elastic strain and heat/mass transport [43–51]. In the present work, a refined nonlocal thermoelastic diffusion model is developed by combining the fractional order and DPL heat conduction model.…”

Section: Introductionmentioning

confidence: 93%

Dual‐phase‐lag thermoelastic diffusion analysis of a size‐dependent microplate based on modified fractional‐order heat conduction model

Tian

Peng

2022

Z Angew Math Mech

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With the rapid evolution of small-scale devices, the effect of size dependence on elastic deformation becomes more and more obvious. Furthermore, the physical processes usually involve memory and inheritance for some anomalous diffusion that the constitutive relation does not obey the standard gradient rate. Owing to capturing the memory-dependent effect and the size-dependent effect, the existing thermoelastic diffusion theories cannot be applicable. To further refine the thermoelastic diffusion model for micro/nano structures, a refined nonlocal thermoelastic diffusion model is developed by combining the fractional-order dual-phase-lag (DPL) heat conduction model and fractional-order diffusion model in this paper. In addition, the Tempered-Caputo (TC) definition is an extension of the Caputo definition without the fractional derivative of the singular kernel, which is adopted for the first time to reflect the memory-dependent effects of heat conduction and stress-strain relationship. Then, this new model is applied to investigating the transient response of an elastic microplate subjected to a sinusoidal thermal loading. The corresponding governing equations are formulated and solved by the Laplace transform method and its numerical inversion. In calculation, the influences of the fractional-order parameter, the tempered parameter and the nonlocal parameter on the variations of the considered quantities are presented and discussed in detail. It is expected to provide new insights into thermoelastic diffusion behaviors of structures at the micro/nanoscale.

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Section: Introductionmentioning

confidence: 93%

Dual‐phase‐lag thermoelastic diffusion analysis of a size‐dependent microplate based on modified fractional‐order heat conduction model

Tian

Peng

2022

Z Angew Math Mech

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“…B B C j  vanishes if and only if the coupled system of eight algebraic linear equations has a non-trivial solution. This non-trivial solution leads to determinant equations for thermally insulated and isothermal spherical curved plate which gives 2 different classes of vibrations as discussed by Ding et al [17] as given below…”

Section: Frequency Equationsmentioning

confidence: 99%

“…Sharma et al [15] studied generalized thermoelastic hollow cylinder analytically with the effect of 3-phase-lag model and analyzed the results graphically. Sharma et al [16,17] explored the free vibration analysis of electro-magneto nonlocal elastic cylinder and sphere with voids in the context of generalized thermoelasticity.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Free Vibrations in Homogeneous Isotropic Rigidly Fixed Thermoelastic Circumferential Spherical Curved Plates

Sharma¹,

Sharma

2022

Trends Sci

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The 1st and 2nd class vibrations of rigidly fixed thermoelastic spherical curved plates have been presented in this article. After mathematical modeling, the obtained equations have been solved by applying normal mode analysis. The uncoupled equation has been considered as 1st class vibrations named toroidal vibrations, remains independent of temperature variations. The coupled system of equations which is considered as 2nd class vibrations named spheroidal vibrations. The series solution of matrix Fröbenius method has been applied to coupled system of ordinary differential equations to obtain potentials and temperature. Fixed point iteration numerical technique has been applied to analytical results with the assistance of MATLAB software tools. Computational techniques have been applied to analytical results and numerically generated data has been represented graphically for frequencies, dissipation factor, displacements and temperature. HIGHLIGHTS The 1st and 2nd class vibrations of rigidly fixed thermoelastic spherical curved plates have been presented in this article The uncoupled equation has been considered as 1st class vibrations named toroidal vibrations, remains independent of temperature variations The coupled system of equations which is considered as 2nd class vibrations named spheroidal vibrations The series solution of matrix Fröbenius method has been applied to couple system of ordinary differential equations to obtain potentials and temperature Computational techniques have been applied to analytical results and numerically generated data has been represented graphically for frequencies, dissipation factor, displacements and temperature GRAPHICAL ABSTRACT

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“…With the aid of Eringen's nonlocal elasticity theory, Gupta et al (2021b) determined the basic equations for a fractured porous solid and an anisotropic fiberreinforced material and exhibited the dynamic response of a layered model due to a moving load. Recently, many researchers (Kumar et al, 2021;Gupta et al, 2022cGupta et al, , 2022dHilal, 2022;Sharma et al, 2022;Sheoran et al, 2022aSheoran et al, , 2022b have used Eringen's nonlocal elasticity theory in their works. Abo-Dahab et al (2019) illustrated the impacts of gravity on a rotating thermo-diffusive medium with voids under magnetic field subjected to both LS and DPL models.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal fiber-reinforced double porous material structure under fractional-order heat and mass transfer

Dutta

Das

Gupta

et al. 2023

HFF

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Purpose The purpose of this study is to analyze the thermo-diffusion process in a semi-infinite nonlocal fiber-reinforced double porous thermoelastic diffusive material with voids (FRDPTDMWV) in light of the fractional-order Lord–Shulman thermo-elasto-diffusion (LSTED) model. By virtue of Eringen’s nonlocal elasticity theory, the governing equations for the considered material are developed. The free surface of the substrate is governed by the inclined mechanical load and thermal and chemical shocks. Design/methodology/approach With the aid of the normal mode technique, the solutions of the nondimensional coupled governing equations have been obtained. Findings The expressions of field variables are obtained analytically. By using MATHEMATICA software, various graphical implementations are presented to describe the impacts of angle of inclination, fractional-order and nonlocality parameters. The present model is also validated on the basis of some comparative studies with some preestablished cases. Originality/value As observed from the literature survey, many different studies have been carried out by taking into account the deformation analysis in nonlocal double porous thermoelastic material structures and thermo-mechanical interaction in fiber-reinforced medium under fractional-order thermoelasticity theories. However, to the best of the authors’ knowledge, no research emphasizing the thermo-elasto-diffusive interactions in a nonlocal FRDPTDMWV has been carried out. Moreover, the effect of fractional-order LSTED theory on fiber-reinforced thermoelastic diffusive half-space with double porosity has not been illuminated till now, which significantly defines the novelty of the conducted research.

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Nonlocal elasticity and thermal dual‐phase‐lag effect on the vibration analysis of transversely isotropic electro‐magneto generalized thermoelastic sphere with voids

Cited by 11 publications

References 55 publications

Dual‐phase‐lag thermoelastic diffusion analysis of a size‐dependent microplate based on modified fractional‐order heat conduction model

Dual‐phase‐lag thermoelastic diffusion analysis of a size‐dependent microplate based on modified fractional‐order heat conduction model

Analysis of Free Vibrations in Homogeneous Isotropic Rigidly Fixed Thermoelastic Circumferential Spherical Curved Plates

Nonlocal fiber-reinforced double porous material structure under fractional-order heat and mass transfer

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