Analytical determination of size-dependent natural frequencies of fully clamped rectangular microplates based on the modified couple stress theory

Amir R. Askari, Masoud Tahani

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


This paper presents an analytical and size-dependent model for vibrational analysis of fully clamped rectangular microplates. Modified couple stress theory (MCST) and the Kirchhoff plate model are considered, and Hamilton’s principle is employed to derive the sizedependent equation of motion that accounts for the effect of residual stresses. The natural frequencies of the microplate are extracted analytically by extended Kantorovich method. The present findings are validated with the available results in the literature, and an excellent agreement is observed between them. In addition, a parametric study is conducted to demonstrate the significant effects of couple stress components on the natural frequencies of fully clamped microplates. The ratio of MCST natural frequencies to those obtained with classical theory depends only on the Poisson’s ratio of the plate and is independent of the aspect ratio of the plate for cases with no residual stresses.

Original languageEnglish
Pages (from-to)2135-2145
Number of pages11
JournalJournal of Mechanical Science and Technology
Issue number5
Publication statusPublished - 16 May 2015
Externally publishedYes

Cite this