Free vibration analysis of arbitrary-shaped FG microplates considering strain gradient effects

Abstract

In the present article, based on the first-order shear deformation theory (FSDT) and strain gradient theory (SGT), vibrational characteristics of plate-type microstructures made of functionally graded materials (FGMs) with arbitrary shape are numerically investigated. To this end, first, the governing equations are obtained within the frameworks of Mindlin’s SGT and FSDT. The relations are presented in a vector–matrix form so as to use in a numerical approach. Also, the developed SGT-based formulation can be reduced to various simplified theories including MCST and MSGT. Then, the variational differential quadrature (VDQ)-transformed method is applied to the variational statement of problem in the solution procedure. FG microplates under various edge conditions are considered whose free vibration response is analyzed. The developed approach can be used to address the problem for various geometries. Natural frequencies of FG skew, triangular and sector plates are computed, and the effects of thickness-to-length-scale parameter and vibration mode number on the results are studied. It is shown that natural frequencies are considerably decreased by increasing the thickness-to-length-scale parameter ratio. © The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature 2025.