The nonlinear free vibration analysis-based an enhanced finite element procedure of tri-functionally graded sandwich plates with a square central cutout

The main goal of this article is to study the nonlinear free vibration of tri-functionally graded sandwich (Tr-FGSW) plates with a square central cutout using an enhanced FEM based on an improved FSDT (so-called i-FSDT). The Tr-FGSW plates include two 3D-FGM skin layers and a 2D-FGM core layer. The geometrical nonlinearity arising from mid-plane stretching is modeled using the von Kármán assumption. The governing equation is established by using Hamilton’s concept. The accuracy and efficiency of the proposed method are verified through comparative examples. Then, the effect of the geometrical dimensions, material properties, BCs, and central cutout size on the nonlinear free vibration of Tr-FGSW plates is investigated in detail. The obtained results show that increasing the volume ratio indices leads to a decrease in the frequency of Tr-FGSW plates while increasing the 2D-FGM core layer thickness as well as the central cutout size increases the frequency of Tr-FGSW plates. These results are expected to be useful for future design and manufacturing processes involving the nonlinear response of these structures. © 2024 Taylor & Francis Group, LLC.