Machine learning-assisted vibration analysis of graphene-origami metamaterial beams immersed in viscous fluids

This paper investigates the free and forced vibration behaviours of functionally graded graphene origami-enabled auxetic metamaterial (FG-GOEAM) beams submerged in Newtonian fluids, with a particular focus on the understanding of the influence of negative Poisson's ratio (NPR) on the natural frequencies and dynamic responses of the beam. To this end, a novel accurate and efficient machine learning-assisted model based on the genetic programming (GP) algorithm and theoretical formulations is proposed. The deformation of the beam is governed by the first-order shear deformation theory, and numerical solutions are obtained using the differential quadrature method (DQM) together with Newmark-β method. The fluid-structure interaction (FSI) is described using a simplified model based on the Navier-Stokes equation for fluid momentum. The results obtained from the machine learning-assisted model showcase its high accuracy and efficiency in predicting the vibration behaviours of FG-GOEAM beams. Extensive parametric studies reveal that the incorporation of graphene origami (GOri) reinforcement results in FG-GOEAM beams with superior NPR characteristics compared to their metallic counterparts, leading to significantly increased fundamental frequencies and improved resistance to dynamic deflections. The study demonstrates the effectiveness of the machine learning model in analysing and optimising the vibration characteristics of metamaterial composite structures.