Vibration analysis of an nth order shear deformation nanoplate using the modified couple stress theory

Eskandari Shahraki, Majid; Shariati, Mahmoud; Azarafza, Reza; Heydari Beni, Mohsen; Eskandari Jam, Jafar

doi:10.22075/ijnaa.2021.23793.2779

Vibration analysis of an nth order shear deformation nanoplate using the modified couple stress theory

Document Type : Research Paper

Authors

Majid Eskandari Shahraki ¹

Mahmoud Shariati ¹

Reza Azarafza ²

Mohsen Heydari Beni ²

Jafar Eskandari Jam ²

¹ Department of Mechanical Engineering, Ferdowsi University of Mashhad, P.O.Box. 9177948974, Mashhad, Iran

² Faculty of Materials and Manufacturing Technologies, Malek Ashtar University of Technology, Tehran, Iran

10.22075/ijnaa.2021.23793.2779

Abstract

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.

Keywords

modified couple stress theory

nth order nanoplate

vibrations

Navier solution method

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