The vibration of viscothermoelastic static pre-stress nanobeam based on two-temperature dual-phase-lag heat conduction and subjected to ramp-type heat

Youssef, Hamdy M.; Al-Lehaibi, Eman A. N.

doi:10.1177/03093247221119303

Cited by 3 publications

(2 citation statements)

References 43 publications

(52 reference statements)

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“…In the case of a semi-infinite conductor [50], the temperature peak diffuses with time progress, leaving the boundary surface. Here, in the finite domain setting, because of the presence of the reflecting boundary condition on the lower boundary (36) and the acute heat flux precedence, τ θ τ q , the heat flux vector reverses its direction between the dimensionless instants t = 0.08 and t = 0.09, so that the upper surface always has the highest temperature though the overall dissipation of heat (i.e., the decrease in temperature value with time). This behavior is also attributed to the immobilization characteristic of the Jeffreys "DPL" equation referred to in the literature; see [2,21,62].…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…When τ ε → 0 , the Hookean response is recovered, i.e., σ = Eε. The Kelvin-Voigt thermoelasticity has been considered in a variety of viscoelastic applications, e.g., unbounded thermoviscoelastic domain with spherical cavity [35], vibration of an Euler Bernoulli beam [36,37], and micropolar thermoelasticity [38], and has been extended to the second-gradient media [39].…”

Section: Introductionmentioning

confidence: 99%

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Anomalous Thermally Induced Deformation in Kelvin–Voigt Plate with Ultrafast Double-Strip Surface Heating

et al. 2023

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The Jeffreys-type heat conduction equation with flux precedence describes the temperature of diffusive hot electrons during the electron–phonon interaction process in metals. In this paper, the deformation resulting from ultrafast surface heating on a “nanoscale” plate is considered. The focus is on the anomalous heat transfer mechanisms that result from anomalous diffusion of hot electrons and are characterized by retarded thermal conduction, accelerated thermal conduction, or transition from super-thermal conductivity in the short-time response to sub-thermal conductivity in the long-time response and described by the fractional Jeffreys equation with three fractional parameters. The recent double-strip problem, Awad et al., Eur. Phy. J. Plus 2022, allowing the overlap between two propagating thermal waves, is generalized from the semi-infinite heat conductor case to thermoelastic case in the finite domain. The elastic response in the material is not simultaneous (i.e., not Hookean), rather it is assumed to be of the Kelvin–Voigt type, i.e., σ=Eε+τεε˙, where σ refers to the stress, ε is the strain, E is the Young modulus, and τε refers to the strain relaxation time. The delayed strain response of the Kelvin–Voigt model eliminates the discontinuity of stresses, a hallmark of the Hookean solid. The immobilization of thermal conduction described by the ordinary Jeffreys equation of heat conduction is salient in metals when the heat flux precedence is considered. The absence of the finite speed thermal waves in the Kelvin–Voigt model results in a smooth stress surface during the heating process. The temperature contours and the displacement vector chart show that the anomalous heat transfer characterized by retardation or crossover from super- to sub-thermal conduction may disrupt the ultrafast laser heating of metals.

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Section: Numerical Results and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Anomalous Thermally Induced Deformation in Kelvin–Voigt Plate with Ultrafast Double-Strip Surface Heating

et al. 2023

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Influence of the static pre-stress on the thermal quality factor of a micro-resonator under the dual-phase-lag heat conduction model

Al-Lehaibi

2023

Acta Mech

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Transient Finite-Speed Heat Transfer Influence on Deformation of a Nanoplate with Ultrafast Circular Ring Heating

et al. 2023

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The present study provides a theoretical estimate for the thermal stress distribution and the displacement vector inside a nano-thick infinite plate due to an exponentially temporal decaying boundary heating on the front surface of the elastic plate. The surface heating is in the form of a circular ring; therefore, the axisymmetric formulation is adopted. Three different hyperbolic models of thermal transport are considered: the Maxwell-Cattaneo-Vernotte (MCV), hyperbolic Dual-Phase-Lag (HDPL) and modified hyperbolic Dual-Phase-Lag (MHDPL), which coincides with the two-step model under certain constraints. A focus is directed to the main features of the corresponding hyperbolic thermoelastic models, e.g., finite-speed thermal waves, singular surfaces (wave fronts) and wave reflection on the rear surface of the plate. Explicit expressions for the thermal and mechanical wave speeds are derived and discussed. Exact solution for the temperature in the short-time domain is derived when the thermalization time on the front surface is very long. The temperature, hydrostatic stress and displacement vector are represented in the space-time domain, with concentrating attention on the thermal reflection phenomenon on the thermally insulated rear surface. We find that the mechanical wave speeds are approximately equal for the considered models, while the thermal wave speeds are entirely different such that the modified hyperbolic dual-phase-lag thermoelasticity has the faster thermal wave speed and the Lord-Shulman thermoelasticity has the slower thermal wave speed.

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The vibration of viscothermoelastic static pre-stress nanobeam based on two-temperature dual-phase-lag heat conduction and subjected to ramp-type heat

Cited by 3 publications

References 43 publications

Anomalous Thermally Induced Deformation in Kelvin–Voigt Plate with Ultrafast Double-Strip Surface Heating

Anomalous Thermally Induced Deformation in Kelvin–Voigt Plate with Ultrafast Double-Strip Surface Heating

Influence of the static pre-stress on the thermal quality factor of a micro-resonator under the dual-phase-lag heat conduction model

Transient Finite-Speed Heat Transfer Influence on Deformation of a Nanoplate with Ultrafast Circular Ring Heating

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