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Structural Engineering and Mechanics Volume 82, Number 6, June25 2022 , pages 701-711 DOI: https://doi.org/10.12989/sem.2022.82.6.701 |
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Nonlocal thermal vibrations of embedded nanoplates in a viscoelastic medium |
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Ashraf M. Zenkour
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| Abstract | ||
| The nonlocal elasticity as well as Mindlin's first-order shear deformation plate theory are proposed to investigate thermal vibrational of a nanoplate placing on a three-factor foundation. The Winkler-Pasternak elastic foundation is connected with the viscous damping to obtain the present three-parameter viscoelastic model. Differential equations of motion are derived and resolved for simply-supported nanoplates to get their natural frequencies. The influences of the nonlocal index, viscous damping index, and temperature changes are investigated. A comparison example is dictated to validate the precision of present results. Effects of other factors such as aspect ratio, mode numbers, and foundation parameters are discussed carefully for the vibration problem. Additional thermal vibration results of nanoplates resting on the viscoelastic foundation are presented for comparisons with future investigations. | ||
| Key Words | ||
| nanoplate; natural frequencies; nonlocal; thermal vibration; visco-Pasternak | ||
| Address | ||
| Ashraf M. Zenkour: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia; Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt | ||