Free vibration and nonlinear transient analysis of functionally graded graphene origami-enabled auxetic metamaterial cylindrical shells: Analytical and artificial neural network approaches

This study examines the free vibration and nonlinear transient response of functionally graded graphene origami-enabled auxetic metamaterial (GOEAM) cylindrical shells under thermal conditions. The multilayered shells feature GOri distributions across their thickness, introducing distinct auxetic and thermal properties. Material properties are modeled using micromechanical models optimized via genetic programming. Employing Reddy's third-order shear deformation theory and von K & aacute;rm & aacute;n's nonlinear geometric assumptions, nonlinear kinematic relationships are formulated and solved using Galerkin method. A novel contribution is the analysis of Winkler-Pasternak elastic foundations in two configurations: centrally distributed along the shell length and concentrated at both ends. Foundation effects are quantified by integrating stiffness coefficients across contact areas, offering insights into foundation-shell interactions. Artificial Neural Networks (ANNs) are developed to predict natural frequencies with high accuracy. Trained using the Levenberg-Marquardt algorithm and tan-sigmoid transfer function, these models demonstrate robust performance through metrics like validation performance plots, regression analysis, and error histograms. Validation against literature confirms the reliability of both ANN and analytical approaches. Key findings reveal that increased GOri folding enhances the negative Poisson's ratio but reduces Young's modulus, decreasing shell stiffness, natural frequencies, and increasing vibration amplitudes. Additionally, centrally concentrated elastic foundations yield higher natural frequencies and smaller vibration amplitudes compared to foundations distributed at the shell ends. By integrating advanced analytical techniques with state-of-the-art ANN modeling, this study not only provides a comprehensive understanding of the dynamic behavior of FG-GOEAM cylindrical shells but also offers valuable insights for the design, optimization, and application of auxetic metamaterial structures in thermal environments.