Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682213220220701Vibration analysis of an nth order shear deformation nanoplate using the modified couple stress theory23732387624310.22075/ijnaa.2021.23793.2779ENMajid Eskandari ShahrakiDepartment of Mechanical Engineering, Ferdowsi University of Mashhad, P.O.Box. 9177948974, Mashhad, IranMahmoud ShariatiDepartment of Mechanical Engineering, Ferdowsi University of Mashhad, P.O.Box. 9177948974, Mashhad, IranReza AzarafzaFaculty of Materials and Manufacturing Technologies, Malek Ashtar University of Technology, Tehran, Iran0000-0002-7957-3295Mohsen Heydari BeniFaculty of Materials and Manufacturing Technologies, Malek Ashtar University of Technology, Tehran, IranJafar Eskandari JamFaculty of Materials and Manufacturing Technologies, Malek Ashtar University of Technology, Tehran, IranJournal Article20210820This 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 Hamiltonâ€™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. Navierâ€™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.https://ijnaa.semnan.ac.ir/article_6243_3a0e963954a7230477b3bbf4cdc8f775.pdf