A modified fractional-order generalized piezoelectric thermoelasticity model with variable thermal conductivity

Guo, Hongjian; Chenlin, Li; Tian, Xiaogeng

doi:10.1080/01495739.2018.1522987

Cited by 18 publications

(4 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The selection of an appropriate fractional derivative and fractional order is of utmost importance in the modeling process since it can significantly impact the outcomes. Furthermore, it is evident that the procedure for computing the differential equation using the AB derivative is very straightforward and advantageous, a characteristic that is absent in other forms of fractional derivatives 51 , 52 . The results of this study can be used to learn more about the physical properties of fractional viscoelastic thermoelastic models with fractional differential AB operator.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…In recent years, the number of studies focusing on developing the theory of thermoelasticity (MGT) has witnessed significant growth 46 – 50 . Later studies have changed the extended thermoelastic theory into fractional ones by adding different time-fractional derivatives to hyperbolic heat transfer and mass diffusion equations 51 , 52 . The growing number of fractional calculus applications in both science and engineering served as the impetus for this extension.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Coupled responses of thermomechanical waves in functionally graded viscoelastic nanobeams via thermoelastic heat conduction model including Atangana–Baleanu fractional derivative

Abouelregal,

Marin,

Foul

et al. 2024

Sci Rep

View full text Add to dashboard Cite

Accurately characterizing the thermomechanical parameters of nanoscale systems is essential for understanding their performance and building innovative nanoscale technologies due to their distinct behaviours. Fractional thermal transport models are commonly utilized to correctly depict the heat transfer that occurs in these nanoscale systems. The current study presents a novel mathematical thermoelastic model that incorporates a new fractional differential constitutive equation for heat conduction. This heat equation is useful for understanding the effects of thermal memory. An application of a fractional-time Atangana–Baleanu (AB) derivative with a local and non-singular kernel was utilized in the process of developing the mathematical model that was suggested. To deal with effects that depend on size, nonlocal constitutive relations are introduced. Furthermore, in order to take into consideration, the viscoelastic behaviour of the material at the nanoscale, the fractional Kelvin–Voigt model is utilized. The proposed model is highly effective in properly depicting the unusual thermal conductivity phenomena often found in nanoscale devices. The study also considered the mechanical deformation, temperature variations, and viscoelastic characteristics of the functionally graded (FG) nanostructured beams. The consideration was made that the material characteristics exhibit heterogeneity and continuous variation across the thickness of the beam as the nanobeam transitions from a ceramic composition in the lower region to a metallic composition in the upper region. The complicated thermomechanical features of simply supported viscoelastic nanobeams that were exposed to harmonic heat flow were determined by the application of the model that was constructed. Heterogeneity, nonlocality, and fractional operators are some of the important variables that contribute to its success, and this article provides a full study and illustration of the significance of these characteristics. The results that were obtained have the potential to play a significant role in pushing forward the design and development of tools, materials, and nanostructures that have viscoelastic mechanical characteristics and graded functions.

show abstract

Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Coupled responses of thermomechanical waves in functionally graded viscoelastic nanobeams via thermoelastic heat conduction model including Atangana–Baleanu fractional derivative

Abouelregal,

Marin,

Foul

et al. 2024

Sci Rep

View full text Add to dashboard Cite

show abstract

“…28 In particular, for microstructures suffering ultrafast heating, the applicability of integer-order heat conduction models is increasingly questionable. 29,30 To alter such situation, the fractional order calculus provides a feasible way. 31 In fractional-order heat transfer model, the fractional calculus plays the role in characterizing the history-dependent feature of heat transfer process, that is, the current state relies on its past states.…”

Section: Introductionmentioning

confidence: 99%

Fractional dual-phase-lag thermal-mechanical response of an functionally graded spherical microshell with size-dependent effect

Peng,

Pan

2024

The Journal of Strain Analysis for Engineering Design

View full text Add to dashboard Cite

Functionally graded materials (FGM) have attracted much attention due to their superior thermal shock resistance in extreme thermal environment. In addition, the memory-dependent feature of transient heat transfer progress can’t be reflected in the frame of integer-order heat conduction model due to the inability of depicting the effect of the past states on the current state. It is noticed that the size-dependent effect of elastic deformation has become significant due to the development of micro-devices. To describe the memory-dependent effect and the size-dependent effect in the functionally graded microstructures, the work aims a thermoelastic model by incorporating the fractional dual-phase-lag heat conduction model and the Eringen’s nonlocal model. To illustrate its application values, the modified model is used to investigate the dynamic performance of an functionally graded spherical microshell subjected to a thermal-mechanical loading. Governing equations including the modified parameters are derived and solved by Laplace transformation. The achieved results show that considering the influences of nonlocal effect and ceramic composition will reduce the thermal deformation under ultrafast heating condition.

show abstract

“…The TPL thermoelasticity has also been applied to studying structural dynamic behaviors of the spherical cavity heated by a thermal shock [32] and the porous half-space subjected to a ramp-type heating [33]. Especially, for microstructures working in ultrafast heating, the applicability of integer-order heat conduction models is increasingly questionable [34,35]. To amend such defect, the concept of fractional calculus provides a feasible mathematical tool for the theoretical analysis of heat transfer progress [36].…”

Section: Introductionmentioning

confidence: 99%

Transient thermo-mechanical analysis of a spherical microshell based on the three-phase-lag thermoelasticity incorporating small-scale and memory-dependent effects

Peng

2023

Mathematics and Mechanics of Solids

View full text Add to dashboard Cite

The applicability of the Green–Naghdi (GN-III) thermoelasticity is increasingly questionable because the theory predicts that heat transfers with an infinite speed. To address this deficiency, the three-phase-lag (TPL) thermoelasticity was developed by introducing the lagging times into the GN-III thermoelasticity. On another front, the small-scale effect on elastic deformation cannot be ignored with the miniaturization of structures or devices. Meanwhile, the memory-dependent feature of heat transfer process in the case of ultrafast heating cannot be described by the integer-order heat conduction models due to the inherent local limited definition. To capture the small-scale effect and the memory-dependent effect of the microstructures, as a first attempt, the present work focuses on developing a TPL thermoelastic model by considering the memory-dependent derivative (MDD) heat conduction model and Eringen’s nonlocal model. Then, the refined model is used to investigate the transient characteristics of a spherical microshell induced by thermal and mechanical loadings. The governing equations containing the modified parameters are derived and then solved by Laplace transform method. Some parametric results are demonstrated to display the effects of the time-delay factor, the kernel function, and the nonlocal parameter on the considered physical quantities.

show abstract

A modified fractional-order generalized piezoelectric thermoelasticity model with variable thermal conductivity

Cited by 18 publications

References 44 publications

Coupled responses of thermomechanical waves in functionally graded viscoelastic nanobeams via thermoelastic heat conduction model including Atangana–Baleanu fractional derivative

Coupled responses of thermomechanical waves in functionally graded viscoelastic nanobeams via thermoelastic heat conduction model including Atangana–Baleanu fractional derivative

Fractional dual-phase-lag thermal-mechanical response of an functionally graded spherical microshell with size-dependent effect

Transient thermo-mechanical analysis of a spherical microshell based on the three-phase-lag thermoelasticity incorporating small-scale and memory-dependent effects

Contact Info

Product

Resources

About