Non-linear vibration and parametric optimization of sandwich composite curved shell panels with graphene reinforced skins and auxetic honeycomb core

This study aims to investigate the non-linear free vibration behavior of composite sandwich panels composed of Graphene-reinforced composite (GRC) skins and honeycomb auxetic core. Here, modified Halpin-Tsai micromechanics and bottom-up multi-scale-based schemes are employed to compute the spatial-dependent elastic properties of Graphene nanocomposite and auxetic honeycomb core, respectively. The non-linear kinematic field is based on Kant's higher-order shear-deformation theory and the Green strain. Using the Hamilton principle, the nonlinear governing equations are affirmed and solved further through Picard's iteration-based 2D-isoparametric finite element approximations via Lagrangian elements. The mesh convergence and validation tests are executed to confirm the consistency and correctness of the developed model. The established sandwich model is further employed for various parametric conditions by varying the core-to-face sheet thickness, auxetic honeycomb properties, graphene volume fraction, shell configurations, temperature, and support conditions. These numerous results exemplify the non-linear frequencies at small-to-large amplitudes for the sandwich shell structures and are discussed in detail. In addition, parametric optimization is conducted using the response surface method to investigate the optimal values of auxetic honeycomb parameters, resulting in maximum frequency response. Findings confirm that, within the selected ranges of the geometric parameters of auxetic honeycomb core, higher values of the thickness of the cell rib (similar to 1.9 cm) and the length of the vertical cell rib (similar to 0.15 cm) and lower value of the core thickness (similar to 5 cm) yield the maximum frequency.