Vibration analysis of an nth order shear deformation nanoplate using the modified couple stress theory | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 191، دوره 13، شماره 2، مهر 2022، صفحه 2373-2387 اصل مقاله (464.33 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.23793.2779 | ||
| نویسندگان | ||
| Majid Eskandari Shahraki1؛ Mahmoud Shariati1؛ Reza Azarafza2؛ Mohsen Heydari Beni2؛ Jafar Eskandari Jam* 2 | ||
| 1Department of Mechanical Engineering, Ferdowsi University of Mashhad, P.O.Box. 9177948974, Mashhad, Iran | ||
| 2Faculty of Materials and Manufacturing Technologies, Malek Ashtar University of Technology, Tehran, Iran | ||
| چکیده | ||
| This paper attempts to study the vibration characteristics of a simply supported nth order rectangular nanoplate using the modified couple stress theory. The modified couple stress theory, which has only one length scale parameter, has been used to consider the small-scale effects. The basic and auxiliary equations of the nanoplate are obtained after determining the strain energy, kinetic energy, and external work and substituting them into Hamilton’s equation. Then, the vibrations of the simply supported nth order rectangular nanoplate with a thickness of h are investigated by substituting the boundary and force conditions into the governing equations. Navier’s method is used for the solution. The results indicate that the frequencies of the different modes of the nth order nanoplate decrease with an increase in the length-to-thickness ratio of the nanoplate. Furthermore, the frequency is the smallest when the effect of the size parameter is not considered (classical theory), and it increases with an increase in the size effect. In addition, the frequency is smallest for the first mode and increases for the subsequent modes. Also, the vibrational frequency increases with an increase in the order of the nanoplate. | ||
| کلیدواژهها | ||
| modified couple stress theory؛ nth order nanoplate؛ vibrations؛ Navier solution method | ||
| مراجع | ||
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