Inverse problem solution and optimization in the vibration analysis of nanocomposite cylindrical shell using L-BFGS-B algorithm

Functionally graded carbon nanotube-reinforced composite (FG-CNTRC) cylindrical shells are crucial in aerospace, marine, and energy industries, where lightweight structures with superior mechanical and thermal properties are essential. This study investigates both the forward and inverse problems of FG-CNTRC cylindrical shells subjected to lateral loading, providing a systematic approach to analyze vibrational responses and optimize design. In the forward problem, the fundamental frequencies and nonlinear displacement–time characteristics are analyzed using the theory of elasticity and von Kármán nonlinearity. The effects of shell thickness, CNT distribution patterns, CNT volume fraction, and applied forces on displacement are explored to enhance structural performance. The inverse problem focuses on identifying external forces responsible for specific vibrational responses and optimizing shell thickness to achieve target displacement performance. The optimization employs the Limited-memory Broyden–Fletcher–Goldfarb–Shanno with Box constraints (L-BFGS-B) algorithm, integrating noise handling and regularization techniques to ensure robustness. Model validation is conducted by comparing computed frequencies with existing studies, demonstrating accuracy and practical relevance. The proposed approach provides valuable insights and reliable design tools for FG-CNTRC shells, contributing to improved efficiency and performance in advanced engineering applications.