TY - JOUR
ID - 6243
TI - Vibration analysis of an nth order shear deformation nanoplate using the modified couple stress theory
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN -
AU - Eskandari Shahraki, Majid
AU - Shariati, Mahmoud
AU - Azarafza, Reza
AU - Heydari Beni, Mohsen
AU - Eskandari Jam, Jafar
AD - Department of Mechanical Engineering, Ferdowsi University of Mashhad, P.O.Box. 9177948974, Mashhad, Iran
AD - Faculty of Materials and Manufacturing Technologies, Malek Ashtar University of Technology, Tehran, Iran
Y1 - 2022
PY - 2022
VL - 13
IS - 2
SP - 2373
EP - 2387
KW - modified couple stress theory
KW - nth order nanoplate
KW - vibrations
KW - Navier solution method
DO - 10.22075/ijnaa.2021.23793.2779
N2 - 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 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.
UR - https://ijnaa.semnan.ac.ir/article_6243.html
L1 - https://ijnaa.semnan.ac.ir/article_6243_3a0e963954a7230477b3bbf4cdc8f775.pdf
ER -