Free vibration of functionally graded graphene origami-enabled auxetic metamaterials plates with complex cutouts

This study investigates the free vibration of the functionally graded (FG) graphene origami (GOri)-enabled auxetic metamaterials (GOEAMs) plate with a free complex cutout and double cracks, as well as the FG-GOEAM plate with two free complex cutouts, under thermal environments. Hamilton's principle is used to derive the governing equations of the plate from first-order shear deformation theory (FSDT). The governing equations are discretized, and the natural frequencies are solved using the generalized differential quadrature finite element method (GDQFEM). The accuracy and validity of the proposed method are validated by numerical results. Through numerical analysis using the FG-GOEAM plate with a free complex cutout and double cracks as an example, the effects of plate layers, sizes of cutouts and cracks, elastic foundation, temperature, width-tothickness ratio, aspect ratio, boundary conditions, GOri weight fractions (WGr), and distribution patterns on free vibration are discussed. Additionally, the effects of cutout positions and sizes on the free vibration of the FGGOEAM plate with two free complex cutouts are examined.