Abstract
The current work deals with the study of a thermo-piezoelectric modified model in the context of generalized heat conduction with a memory-dependent derivative. The investigations of the limited-length piezoelectric functionally graded (FGPM) rod have been considered based on the presented model. It is assumed that the specific heat and density are constant for simplicity while the other physical properties of the FGPM rod are assumed to vary exponentially through the length. The FGPM rod is subject to a moving heat source along the axial direction and is fixed to zero voltage at both ends. Using the Laplace transform, the governing partial differential equations have been converted to the space-domain, and then solved analytically to obtain the distributions of the field quantities. Numerical computations are shown graphically to verify the effect of memory presence, graded material properties, time-delay, Kernel function, and the thermo-piezoelectric response on the physical fields.
Highlights
The classical coupled Fourier heat conduction model is no longer valid and can only predict the unlimited speed of heat propagation
One of the most important physical properties of functionally graded material (FGM) is that they work under very high thermal conditions, which in turn may lead to vibratory motion, when exposed to an unexpected change in thermal conditions [2]
A better definition than a fractional to reverse the effect of memory, a memory-dependent derivative is defined in an integral form of a common derivative with a kernel function over a sliding interval, which is more intuitive to comprehend the physical meanings
Summary
The classical coupled Fourier heat conduction model is no longer valid and can only predict the unlimited speed of heat propagation. Since piezoelectric materials can be used in many applications, especially where the environment is thermogenic where temperature variation is often one of the most significant criteria in analyzing their behavior, many investigators have attempted to take in this in governing equations for the study of thermopiezoelectricity [14,15,16,17,18] In this regard, Abouelregal [19] applied the fractional-order thermoelasticity model for a thermo-piezoelectric semi-infinite medium concerned to a ramp-type heating and temperature-dependent properties. Some thought-provoking thermoelastic investigations based on the memory-dependent differential equation can be found in [36,37,38,39,40,41,42] Taking benefit of these advantages of the coupling between the mechanical and electric fields in piezoelectric materials, piezoelectric is wide as smart structures like power transformers, actuators and sensors. Some comparisons in order to assess the results are offered graphically, which revealed the effects of the memory dependent, nonhomogeneity index and piezoelectric on all studied fields
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