Multi-objective optimization for vibration suppression and weight reduction in composite sandwich shallow-spherical shells with functionally graded coating

This study is the first to integrate the composite sandwich shallow spherical shell (CSSS) with functionally graded coating (FGC) and an improved meta-heuristic algorithm, and optimize the vibration suppression and lightweight performance. Initially, using the mixing principle, high-order displacement field theory, complex modulus method, Lagrange equation and Newmark-β method, a theoretical model of the FGC-CSSS subjected to base excitation is established to analyze the free and forced vibrations of the structure. Then, the vibration suppression, stiffness and lightweight performance of the FGC-CSSS are optimized by a multi-objective approach utilizing the improved walrus optimization algorithm (IWOA). The minimum of the first resonant response amplitude, the minimum of the equivalent overall mass of the FGC-CSSS and the minimum of the reciprocal of the sum of natural frequencies are taken as objective functions, respectively. Also, the core thickness ratio, the coating thickness ratio, and the honeycomb cell thickness are selected as design variables. The effectiveness of the IWOA is validated through an example of engineering, and the data obtained from the theoretical model are compared with the literature and experimental results to ensure robust validation. Finally, an optimization method of the FGC-CSSS is conducted, and the landmark optimization results and corresponding variations on pareto front are displayed. These results demonstrate that the IWOA has better multi-objective optimization capability than NSGA-Ⅱ, and design variables C₁ and C₂ can improve vibration suppression, lightness, and structural stiffness performance by 85.5%, 43.5%, and 8.7%, respectively.