Graphene origami-enabled auxetic metamaterial tapered beams in fluid: Nonlinear vibration and postbuckling analyses via physics-embedded machine learning model

Abstract

This paper presents a numerical study on nonlinear free vibration and postbuckling behaviours of functionally graded (FG) graphene origami (GOri)-enabled auxetic metamaterial (GOEAM) tapered beams immersed in fluid, with a particular focus on the effect of negative Poisson's ratio (NPR) on the nonlinear frequencies and postbuckling equilibrium paths. The metamaterial properties of the novel GOEAM are determined by a physics-embedded machine learning based micromechanics model. The beam deformation is governed by Timoshenko beam theory and von Kármán nonlinearity, and the governing equations are solved using the differential quadrature method (DQM). The fluid pressure exerted on the surface of the beam is calculated using the velocity potential function and Bernoulli's equation. Comprehensive parametric studies demonstrate that due to the use of GOri reinforcement, an FG-GOEAM beam with NPR outperforms its metallic counterpart with considerably increased nonlinear fundamental frequency and enhanced postbuckling resistance. The nonlinear free vibration and postbuckling behaviours of the beams can be effectively tuned through GOri parameters.