Memory-dependent derivative approach on magneto-thermoelastic transversely isotropic medium with two temperatures

Kaur, Iqbal; Lata, Parveen; Singh, Kulvinder

doi:10.1186/s40712-020-00122-2

Cited by 22 publications

(6 citation statements)

References 30 publications

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“…Following Roy Choudhuri (2007), Eringen and Edelen (1972), Gupta et al (2023) and Kaur et al (2020b), the governing field equations for a nonlocal anisotropic piezothermoelastic medium in a HTT, three-phase lag with MDD and without considering heat source and body forces are: …”

Section: Field Equationsmentioning

confidence: 99%

Energy analysis at the interface of piezo/thermoelastic half spaces

Gupta

Kumar²,

Kumar³

et al. 2023

HFF

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Purpose This paper aims to study the energy ratios of plane waves on an interface of nonlocal thermoelastic halfspace (NTS) and nonlocal orthotropic piezothermoelastic half-space (NOPS). Design/methodology/approach The memory-dependent derivatives (MDDs) approach with a hyperbolic two-temperature (HTT), three-phase lag theory is used here to study how the energy ratios change at the interface with the angle of incidence. Findings Plane waves that travel through NTS and hit the interface as a longitudinal wave, a thermal wave, or a transversal wave send four waves into the NOPS medium and three waves back into the NTS medium. The amplitude ratios of the different waves that are reflected and transmitted are used to calculate the energy ratios of the waves. It is observed that these ratios are affected by the HTT, nonlocal and MDD parameters. Research limitations/implications The energy ratios correspond to four distinct models; nonlocal HTT with memory, nonlocal HTT without memory, local HTT with memory and nonlocal classical-two-temperature with memory concerning the angle of incidence from 0 degree to 90 degree. Practical implications This model applies to several fields, including earthquake engineering, soil dynamics, high-energy particle physics, nuclear fusion, aeronautics and other fields where nonlocality, MDD and conductive temperature play an important role. Originality/value The authors produced the submitted document entirely on their initiative, with equal contributions from all of them.

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Section: Field Equationsmentioning

confidence: 99%

Energy analysis at the interface of piezo/thermoelastic half spaces

Gupta

Kumar²,

Kumar³

et al. 2023

HFF

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“…In the absence of heat sources, the equation of heat conduction with MDD following Kaur et al [33][34][35] is, Wang and Li [18] presented the first-order MDD with the differentiable function f(t) w. r.t. > 0 for time t as: Depending on the material properties, we choose K (t − ) and . Following Kaur et al [33][34][35], the K(t − ξ) is considered as where and are constants.…”

Section: Basic Equationsmentioning

confidence: 99%

“…(25) in Eqs. ( 33)- (35), we derive the value of B i using cramer,s rule for solving linear equations with i = 6 variables as and Δ i (i = 1, 2, 3, … , 6) are obtained by replacing the columns by 0, 0, 0, 0, H(s), 0 in Δ i . Substituting the…”

Section: Declarationsmentioning

confidence: 99%

Functionally graded nonlocal thermoelastic nanobeam with memory-dependent derivatives

Kaur

Singh

2022

SN Appl. Sci.

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The purpose of this study is to investigate vibrations in 2D functionally graded nanobeams (FGN) with memory-dependent derivatives. A sinusoidal variation of temperature is assumed. The dimensionless expressions for axial displacement, thermal moment, lateral deflection, strain and temperature distribution are found in the transformed domain using Laplace Transforms, and the expressions in the physical domain are derived by numerical inversion techniques. The nanobeam is simply supported at the both ends and have constant temperatures. The FGN is a non-homogenous composite structure with constant structural variations along with the layer thickness, changing from ceramic at the bottom to metal at the top. Adding non-local MDD to thermoelastic models opens up new possibilities for the study of thermal deformations in solid mechanics. The effect of different kernel functions and periodic frequency of thermal vibration is illustrated graphically for lateral deflection, axial displacement, strain, temperature, and thermal moment. Article highlights A novel model of vibrations in a functionally graded nanobeams is presented. The medium is subjected to sinusoidal variation of temperature. Dynamic response of memory dependent derivative theory of thermoelasticity and non-local parameter is investigated. The effects of kernel functions and periodic frequency of thermal vibration on all physical fields are investigated and shown graphically.

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“…To describe damping in many oscillatory systems of complicated dissipation appliances in which memory influences could not be ignored, Al-Jamel et al 25 developed a memory-dependent derivative with respect to displacement. Using a two-temperature thermoelastic model, Kaur et al 26 investigated the effect of memory-dependent derivatives (MDD) on a two-dimensional isotropic thermoelastic material in the existence of a magnetic field. Kaur and Singh 27 presented a modified couple stress theory for a fiber-reinforced magneto-thermoelastic material with ramp-type distributed heat, Hall current, and hyperbolic two-temperature.…”

Section: Introductionmentioning

confidence: 99%

The theory of thermoelasticity with a memory-dependent dynamic response for a thermo-piezoelectric functionally graded rotating rod

Abouelregal

Askar

Marín

et al. 2023

Sci Rep

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By laminating piezoelectric and flexible materials during the manufacturing process, we can improve the performance of electronic devices. In smart structure design, it is also important to understand how the functionally graded piezoelectric (FGP) structure changes over time when thermoelasticity is assumed. This is because these structures are often exposed to both moving and still heat sources during many manufacturing processes. Therefore, it is necessary to conduct theoretical and experimental studies of the electrical and mechanical characteristics of multilayer piezoelectric materials when they are subjected to electromechanical loads and heat sources. Since the infinite speed of heat wave propagation is a challenge that classical thermoelasticity cannot address, other models based on extended thermoelasticity have been introduced. For this reason, the effects of an axial heat supply on the thermomechanical behavior of an FGP rod using a modified Lord-Shulman model with the concept of a memory-dependent derivative (MDD) will be explored in this study. The exponential change of physical properties in the direction of the axis of the flexible rod will be taken into account. It was also assumed that there is no electric potential between the two ends of the rod while it is fixed at both ends and thermally isolated. Applying the Laplace transform method, the distributions of the physical fields under investigation were calculated. The obtained results were compared to those in the corresponding literature with varying heterogeneity values, kernel functions, delay times, and heat supply speeds. It was discovered that the studied physical fields and the dynamic behavior of the electric potential are weakened by increasing the inhomogeneity index.

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Memory-dependent derivative approach on magneto-thermoelastic transversely isotropic medium with two temperatures

Cited by 22 publications

References 30 publications

Energy analysis at the interface of piezo/thermoelastic half spaces

Energy analysis at the interface of piezo/thermoelastic half spaces

Functionally graded nonlocal thermoelastic nanobeam with memory-dependent derivatives

The theory of thermoelasticity with a memory-dependent dynamic response for a thermo-piezoelectric functionally graded rotating rod

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