# An Investigation into Thermal Vibrations Caused by a Moving Heat Supply on a Spinning Functionally Graded Isotropic Piezoelectric Bounded Rod

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## Abstract

**:**

## 1. Introduction

#### List of Symbols

## 2. Governing System of Equations

## 3. Problem Formulation

## 4. Solution Technique

## 5. Computational Inversion of the Transformed Functions

## 6. Numerical Example and Results

**Figure 4.**Variation of electric potential $\phi $ for various values of the gradient coefficient $N$.

**Figure 5.**Variation of thermal stress ${\sigma}_{zz}$ for various values of the gradient coefficient $N$.

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**MDPI and ACS Style**

Abouelregal, A.E.; Marin, M.; Abusalim, S.M.
An Investigation into Thermal Vibrations Caused by a Moving Heat Supply on a Spinning Functionally Graded Isotropic Piezoelectric Bounded Rod. *Mathematics* **2023**, *11*, 1739.
https://doi.org/10.3390/math11071739

**AMA Style**

Abouelregal AE, Marin M, Abusalim SM.
An Investigation into Thermal Vibrations Caused by a Moving Heat Supply on a Spinning Functionally Graded Isotropic Piezoelectric Bounded Rod. *Mathematics*. 2023; 11(7):1739.
https://doi.org/10.3390/math11071739

**Chicago/Turabian Style**

Abouelregal, Ahmed E., Marin Marin, and Sahar M. Abusalim.
2023. "An Investigation into Thermal Vibrations Caused by a Moving Heat Supply on a Spinning Functionally Graded Isotropic Piezoelectric Bounded Rod" *Mathematics* 11, no. 7: 1739.
https://doi.org/10.3390/math11071739