Chun-Hui He, Mostafa Mohammadian
Understanding the behavior of nonlinear vibrations in stringer-stiffened shell structures is crucial for enhancing the stability and efficiency of advanced aerospace and marine systems. These systems often exhibit complex responses due to geometric and material intricacies, which require analytical methods capable of effectively capturing critical dynamics. This study presents three efficient analytical methods for deriving closed-form expressions for the nonlinear frequency of such systems: the adaptive location point-based He’s formulation (ALPF), the square error minimizing-based frequency formulation (SEMF), and the Hamiltonian-based frequency-amplitude formulation (HFAF). These methods offer efficient and straightforward solutions for analyzing nonlinear oscillators without requiring complex iterative procedures. The nonlinear frequency of the stringer-stiffened shell is determined using each method and validated against both exact analytical solutions and numerical results. The results show that the first two methods yield high accuracy for small amplitudes, while their accuracy decreases at higher amplitudes. In contrast, the Hamiltonian-based method maintains high accuracy over a wider range of amplitudes. The original He's formulation is recognized for its simplicity and computational efficiency, making it a practical tool for rapid frequency estimation in stringer-stiffened shell systems. This comparative study offers guidance for selecting appropriate analytical tools for nonlinear vibration analysis of complex mechanical and physical systems.