Vibrational characteristics of functionally graded graphene origami- enabled auxetic metamaterial beams with variable thickness in fluid

•Genetic programming (GP)-assisted micromechanics models are used to predict the material properties.•Governing equations of the beam-fluid interaction system are discretised and solved by differential quadrature method.•The hydrodynamic effect of fluid on vibrational characteristics of novel FG-GOEAM beam is comprehensively investigated.•The FG-GOEAM beam outperforms its pristine metallic counterpart in terms of vibration performance. Within the framework of Timoshenko beam theory, this paper examines the effect of negative Poisson’s ratio (NPR) on the free vibration characteristics of functionally graded (FG) graphene origami (GOri)-enabled auxetic metamaterial (GOEAM) beams with variable thickness submerged in fluid. Poisson’s ratio and other elastic properties of the beam are graded in a layer-wise manner along the thickness direction and are predicted by genetic programming (GP)-assisted micromechanics models. With the hydrodynamic pressure effect on the beam being modelled as added mass, the equations of motion are derived from Hamilton’s principle then discretised and solved using the differential quadrature (DQ) method in conjunction with an iterative process to determine its natural frequencies and mode shapes. The effects of GOri folding degree, metamaterial distribution, graphene distribution pattern and content, fluid temperature and density on the free vibration behaviour of FG-GOEAM beams are discussed in detail. It is found that the FG-GOEAM beam outperforms its pristine metallic counterpart in terms of vibration performance.