Effect of dual-phase-lag model on free vibrations of isotropic homogenous nonlocal thermoelastic hollow sphere with voids

Sharma, Dinesh Kumar; Thakur, Prakash Chand; Sarkar, Nantu

doi:10.1080/15397734.2020.1824792

Cited by 14 publications

(6 citation statements)

References 44 publications

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“…, then the governing equations and the free vibration analysis have been reduced to transversely isotropic elastic cylinder which agree with Kele and Tutuncu [45] in the absence of functionally graded materials.…”

Section: Elastic Cylindermentioning

confidence: 73%

“…Sharma et al [43,44] explored free vibrations of thermoelastic cylinder and sphere with voids material in the reference of generalized thermoelasticity. Keles and Tutuncu [45] used Laplace transformation to examine the vibration analysis of inhomogeneous elastic cylinder/sphere and presented the analysis for free and forced vibrations. Lots of research work based on vibrations of wave propagation in the reference of homogeneous/non-homogeneous materials was done by many authors and researchers such as Sharma et al [46], Youssef [47], Sharma et al [48,49], etc.…”

Section: Introductionmentioning

confidence: 99%

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Vibrations of Phase-Lags on Electro-Magneto Nonlocal Elastic Solid with Voids in Generalized Thermoelastic Cylinder/Disk

Mehalwal

Sharma²,

Sharma³

2022

Trends Sci

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The stress-strain-temperature relations, strain-displacement relations and governing equations have been addressed for electro-magneto transversely isotropic nonlocal elastic hollow cylinder with voids in the reference of 3-phase-lag effect of heat conduction. The strength of the magnetic field proceeds in the direction of the z-axis of the hollow cylinder/disk. The simultaneous differential equations have been eliminated by applying elimination technique to obtain unknown field functions such as dilatation, equilibrated voids volume fraction, temperature, displacement and stresses. Free vibration analysis has been explored by applying stress free and thermally insulated/isothermal boundaries. Analytical results are verified by employing numerically analyzed results for unknown field functions and presented graphically for the vibrations of stress free field functions such as thermoelastric damping, frequencies and frequency-shift. The results have been authenticated by analyzing analytical and numerical results with existing literature with earlier published work. The study of present paper based on 3-phase-lag model of generalized thermoelasticity may receive better approach to allow voids and relaxation time parameters, which have many applications in the field of science, technology and engineering. The study may also be useful in the area of seismology for mining and drilling in the earth’s crust. HIGHLIGHTS The analysis for electro-magneto transversely isotropic nonlocal thermoelastic hollow cylinder with voids in the reference of 3-phase-lag effect of heat conduction The strength of the magnetic field proceeds in the direction of the z-axis of the nonlocal thermoelastic hollow cylinder/disk Free vibration analysis has been explored by applying stress free and thermally insulated/isothermal boundaries Analytical results are verified by employing numerically analyzed results for unknown field functions and presented graphically for the vibrations of stress free field functions such as damping, frequencies and frequency-shift GRAPHICAL ABSTRACT

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Section: Elastic Cylindermentioning

confidence: 73%

Section: Introductionmentioning

confidence: 99%

Vibrations of Phase-Lags on Electro-Magneto Nonlocal Elastic Solid with Voids in Generalized Thermoelastic Cylinder/Disk

Mehalwal

Sharma²,

Sharma³

2022

Trends Sci

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“…Zenkour [47] explored the problem in which a rigid core has been developed for the analysis of functionally graded infinite cylinder in respect of dynamical bending. Sharma et al [48,49] studied vibration analysis of nonlocal elastic sphere/cylinder with voids material under the effects of generalized thermoelasticity. Keles and Tutuncu [50] investigated the vibration analysis of the elastic cylinder/sphere using Laplace transform technique.…”

Section: Introductionmentioning

confidence: 99%

“…Sharma et al. [48, 49] studied vibration analysis of nonlocal elastic sphere/cylinder with voids material under the effects of generalized thermoelasticity. Keles and Tutuncu [50] investigated the vibration analysis of the elastic cylinder/sphere using Laplace transform technique.…”

Section: Introductionmentioning

confidence: 99%

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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“…To eliminate such paradox, the non-Fourier heat conduction models, for example, thermal wave model [25] and the generalized thermoelastic theories have been subsequently developed by Lord and Shulman, [26] Green and Lindsay [27] and Green and Naghdi [28,29]. Based on these theories and their further generalizations, a number of works on thermoelastic dynamic responses [30][31][32], mass diffusion [33][34][35], wave propagation [36][37][38], magnetic field effect [39][40][41], nonlocal effect [42][43][44][45][46][47][48][49] and so on have been contributed. Along with the development of the generalized thermoelasticity with integer order derivative, due to the successful applications of fractional order derivative in characterizing the anomalous heat conduction [50][51][52] and in modifying many existing models in viscoelasticity, bioengineering and heat conduction etc.…”

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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Effect of dual-phase-lag model on free vibrations of isotropic homogenous nonlocal thermoelastic hollow sphere with voids

Cited by 14 publications

References 44 publications

Vibrations of Phase-Lags on Electro-Magneto Nonlocal Elastic Solid with Voids in Generalized Thermoelastic Cylinder/Disk

Vibrations of Phase-Lags on Electro-Magneto Nonlocal Elastic Solid with Voids in Generalized Thermoelastic Cylinder/Disk

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

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

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