Free vibration analysis of a nonlocal thermoelastic hollow cylinder with diffusion

Sharma, Dinesh Kumar; Thakur, Dinesh S.; Walia, Vishal; Sarkar, Nantu

doi:10.1080/01495739.2020.1764425

Cited by 45 publications

(8 citation statements)

References 40 publications

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“…In 3-D, Figs. [8][9][10][11][12][13] show the distributions of the temperature increment, volumetric strain, concentration, displacement, average stress, and chemical potential distributions, respectively, when = 0.2. All the studied functions have been figured in a dimensionless wide range of the radial distance 0 ≤ ≤ 4.0 and a dimensionless wide range of the time 0 ≤ ≤ 3.0 .…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…Hussein solved the problem of the spherical region in the context of the theory of generalized thermoelastic diffusion in a two-dimensions [12]. Sharma et al studied the free vibration analysis of a nonlocal thermoelastic hollow cylinder with diffusion [13]. El-Karamany and Ezzat solved a problem of thermoelastic diffusion with memory-dependent derivatives [14].…”

Section: Introductionmentioning

confidence: 99%

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Thermal shock problem of a generalized thermoelastic solid sphere affected by mechanical damage and thermal diffusion

Youssef¹

2021

J., eng., them. sci.

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A mathematical model was created in this article, which consists of a thermoelastic, unified, and isotropic rigid sphere subjected to thermal diffusion. Thermal and chemical potential shocks of a diffusive substance have loaded the sphere's bounding structure. The governing equations were established in the form of a theory of generalized thermoelastic diffusion with mechanical damage taken into account. The temperature increment, concentration, pressure, displacement, stress, and chemical potential numerical effects have been expressed in figures with different values of the mechanical damage parameter, thermal relaxation time, and diffusional relaxation time. All the studied functions are significantly affected by the mechanical damage parameter, radial distance, time, thermal, and diffusional relaxation times. In the Lord-Shulman model, heat, diffusion, and mechanical waves spread at finite speeds on the thermoelastic solid sphere.

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Section: Numerical Results and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Thermal shock problem of a generalized thermoelastic solid sphere affected by mechanical damage and thermal diffusion

Youssef¹

2021

J., eng., them. sci.

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“…Here 𝑃 𝑖 , 𝑄 𝑖 ; 𝑖 = 1, 2, 3 are constants that depend on Ω. 𝐽 1∕2 𝑎𝑛𝑑 𝑌 1∕2 are modified Bessel functions of order (1/2) with first and second kinds, respectively. Resolving cubical dilation ( ē) from Equation (27) for displacement Ū, we obtain…”

Section: Solution Of Mathematical Modelmentioning

confidence: 99%

“…Mondal et al [23] investigated plane wave propagation of time harmonics in an infinite nonlocal DPL model of generalized thermoelastic solid with voids. The nonlocal elasticity theory has been established thoroughly in detail in the context of continuum mechanics, by some authors and research groups such as Biswas and Sarkar [24], Bachher and Sarkar [25], Mondal [26], Sharma et al [27][28][29], Sur et al [30], etc.…”

Section: Introductionmentioning

confidence: 99%

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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

Sharma

Mehalwal²,

Sarkar

et al. 2022

Z Angew Math Mech

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The nonlocal elasticity together with electro‐magneto thermal dual‐phase‐lag (DPL) model to a transversely isotropic generalized thermoelastic hollow sphere with voids is addressed in radial direction. The governing equations and stress–strain‐displacement relations have been resolved by applying time harmonics technique. The elimination technique is employed to resolve the homogeneous equations to find the unknowns. The unknowns such as dilatation, displacement, voids volume fraction, temperature change, and radial/de‐hoop stresses have been calculated analytically. In order to discover the vibration analysis, the numerical Iteration method has been applied to thermally insulated/isothermal boundary conditions. For computation purpose the software like MATLAB tool has been used. The real parts of generated data obtained from the frequency equations have also been shown graphically to frequency shift and natural frequencies. The effects of DPL model of the theory of generalized transversely isotropic thermoelasticity with voids have been represented with and without the effects of magnetic field for nonlocal/local elastic materials and validated with existing literature.

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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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Free vibration analysis of a nonlocal thermoelastic hollow cylinder with diffusion

Cited by 45 publications

References 40 publications

Thermal shock problem of a generalized thermoelastic solid sphere affected by mechanical damage and thermal diffusion

Thermal shock problem of a generalized thermoelastic solid sphere affected by mechanical damage and thermal diffusion

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

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

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