Three-dimensional vibration analysis of functionally graded graphene origami-enabled auxetic metamaterial circular plates

This research explores the free vibration characteristics, both in-plane and transverse, of a circular plate made from functionally graded graphene origami-enabled auxetic metamaterial (GOEAM). An AI-assisted model is utilized to calculate the micromechanical properties of the metamaterial. Three-dimensional linear elasticity theory is utilized to formulate constitutive relations and equations of motion of the plate. By using two pairs of transformation functions, these equations are transformed into a couple of independent state-space equations corresponding to three-dimensional vibration of the plate. Graphene origami (GOri) platelets are distributed with four different dispersion patterns along the thickness. Also, the folding degree of the GOri can vary. Two boundary condition types are considered: elastic simple and rigidly slipping. State-space relations are solved through the transfer matrix approach, and frequency equations are obtained for both in-plane and out-of-plane vibrations. The effects of various parameters on the vibration frequencies of the GOEAM plate are explored. The findings indicate that incorporating highly folded graphene origami enhances stiffness, with a more noticeable impact on in-plane vibrations. Distinct dispersion patterns demonstrate peak natural frequencies for both in-plane and transverse vibrations. Although transverse vibrations show a declining trend, the degree of folding initially strengthens the structure, resulting in higher natural frequencies before reaching a maximum.