The transient response of a functionally graded piezoelectric rod subjected to a moving heat source under fractional order theory of thermoelasticity

Ma, Yongbin; He, Tianhu

doi:10.1080/15376494.2016.1196783

Cited by 25 publications

(8 citation statements)

References 38 publications

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“…When the body is examined for the phenomenon of heat transfer, moving heat sources are those physical situations in which thermal excitation regularly changes its location and intensity. Assume we have a stationary heat source with an intensity that is turned on at time and moves continuously along the -axis with a constant velocity 36 : where the function denotes the Dirac delta.…”

Section: Problem Formulationmentioning

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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Section: Problem Formulationmentioning

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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“…Ma et al. [20, 21] investigated two‐dimensional coupling problem under fractional order theory of thermoelasticity, dynamic response of an infinite medium with a spherical cavity on temperature‐dependent properties subjected to a thermal shock [22, 23] and the dynamic response of a generalized piezoelectric‐ thermoelastic problem [24–26].…”

Section: Introductionmentioning

confidence: 99%

Nonlocal response of multi‐field coupling elastic medium based on fractional order strain

Wang

Huang

2021

Z Angew Math Mech

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In this work, a three‐dimensional model of the generalized thermoelasticity with fractional order stain and nonlocal effect is established. Nonlocal effect is used to depict size‐dependence feature and fractional order strain is considered to describe memory‐dependence properties. The Laplace and double Fourier transform techniques are applied to the three‐dimensional half‐space model subjected to thermal shock and traction free surface. A complex inversion formula of the transform with the techniques of the Fourier expansion been applied to obtain the inverses of double Fourier transforms, and Laplace transforms. Numerical results for the temperature, stress, strain and displacement are represented graphically based on various values of the fractional order strain parameter and elastic nonlocal parameter. The fractional order strain and nonlocal parameter has a limited effect on the thermal waves while it has significant effects on the mechanical waves.

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“…Ma and He [27] discussed the dynamic response of a generalized piezoelectric‐thermoelastic problem under fractional order theory of thermoelasticity. Ma and He [28] also discussed the transient response of a functionally graded piezoelectric rod subjected to a moving heat source under fractional order theory of thermoelasticity. Ma et al.…”

Section: Introductionmentioning

confidence: 99%

Thermoelastic responses of a nonlocal elastic rod due to nonlocal heat conduction

Sarkar

2020

Z Angew Math Mech

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This is an attempt to design a dynamic model of nonlocal heat conduction in a nonlocal elastic bounded rod. This model is drafted using the Lord-Shulman theory of generalized thermoelasticity due to the involvement of one relaxation time to the heat conduction equation and the equation of motion. This model is then employed to discuss the thermal behavior of the rod when subjected to a moving heat source. Both ends of the rod are assumed to be rigidly fixed and thermally insulated. Analytical solutions for the distribution of temperature, displacement and thermal stresses are obtained using integral transform in the Laplace transform technique is used to obtain the analytical solutions for the field variables such as temperature, displacement and stress. The inverse Laplace transform based on the Zakian method is used to invert the results in the space-time domain. Specific attention is paid to study the effect of thermal nonlocal parameter and the velocity of the moving heat source on the distribution of the field variables. K E Y W O R D SLaplace transform, LS model, nonlocal heat conduction, thermal nonlocal parameter, Zakian algorithm

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The transient response of a functionally graded piezoelectric rod subjected to a moving heat source under fractional order theory of thermoelasticity

Cited by 25 publications

References 38 publications

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

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

Nonlocal response of multi‐field coupling elastic medium based on fractional order strain

Thermoelastic responses of a nonlocal elastic rod due to nonlocal heat conduction

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