Bending and Vibration Analysis of a Mindlin Rectangular Nanoplate using Modified Couple Stress Theory and Navier's Solution

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Eskandari Shahraki Majid; SHARIATI MAHMOUD; Asiaban Naser

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Journal Paper

Paper Information

Journal: INTERNATIONAL JOURNAL OF ADVANCED DESIGN AND MANUFACTURING TECHNOLOGY Year:2022 | Volume:15 | Issue:1 Page(s): 21-28

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Information Journal Paper

Title

Bending and Vibration Analysis of a Mindlin Rectangular Nanoplate using Modified Couple Stress Theory and Navier's Solution

Author(s)

Eskandari Shahraki Majid | SHARIATI MAHMOUD | Asiaban Naser | Issue Writer Certificate

Keywords

Bending

Modified Couple Stress Theory

Mindlin Nanoplate

Navier's Solution

Vibration

Abstract

In this paper, a Mindlin rectangular nanoplate model is developed for the Bending and Vibration analysis of a graphene nanoplate based on a Modified Couple Stress Theory. In order to consider the small scale effects, the Modified Couple Stress Theory, with one length scale parameter, is used. In Modified Couple Stress Theory, strain energy density is a function of strain tensor, curvature tensor, stress tensor and symmetric part of couple stress tensor. After obtaining the strain and kinetic energy, external work and substituting them in the Hamilton’ s principle, the main and auxiliary equations of the nanoplate are obtained. Then, by manipulating the boundary conditions the governing equations are solved using Navier approach for Bending and Vibration of the nanoplate. The Bending rates and dimensionless Bending values under uniform surface traction and sinusoidal load and different mode frequencies are all obtained for various plate's dimensional ratios and material length scale to thickness ratios. The effect of material length scale, length, width and thickness of the nanoplate on the Bending and Vibration ratios are investigated and the results are presented and discussed in details.

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APA: Copy

Eskandari Shahraki, Majid, SHARIATI, MAHMOUD, & Asiaban, Naser. (2022). Bending and Vibration Analysis of a Mindlin Rectangular Nanoplate using Modified Couple Stress Theory and Navier's Solution. INTERNATIONAL JOURNAL OF ADVANCED DESIGN AND MANUFACTURING TECHNOLOGY, 15(1), 21-28. SID. https://sid.ir/paper/975219/en

Vancouver: Copy

Eskandari Shahraki Majid, SHARIATI MAHMOUD, Asiaban Naser. Bending and Vibration Analysis of a Mindlin Rectangular Nanoplate using Modified Couple Stress Theory and Navier's Solution. INTERNATIONAL JOURNAL OF ADVANCED DESIGN AND MANUFACTURING TECHNOLOGY[Internet]. 2022;15(1):21-28. Available from: https://sid.ir/paper/975219/en

IEEE: Copy

Majid Eskandari Shahraki, MAHMOUD SHARIATI, and Naser Asiaban, “Bending and Vibration Analysis of a Mindlin Rectangular Nanoplate using Modified Couple Stress Theory and Navier's Solution,” INTERNATIONAL JOURNAL OF ADVANCED DESIGN AND MANUFACTURING TECHNOLOGY, vol. 15, no. 1, pp. 21–28, 2022, [Online]. Available: https://sid.ir/paper/975219/en

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