Internal resonance and nonlinear dynamics of an axially moving FGM sandwich cylindrical shell

This paper provides an in-depth study of the resonant responses and nonlinear dynamics of a novel axially moving functionally graded material (FGM) sandwich cylindrical shell structure, specifically designed for supersonic aircraft operating under various complex environments. We present the derivation of the mechanical parameters and the nonlinear dynamic equations associated with this FGM sandwich cylindrical shell. By analyzing the natural frequencies of the structure, which is clamped at both ends, we identify the necessary parametric conditions for the nonlinear system to exhibit 1:2 internal resonance and 1:1 principal parameter resonance. To further investigate the resonant responses, we utilize the pseudo-arc length continuation method. In addition, the fourth-order Runge-Kutta algorithm is employed to examine the nonlinear dynamic behaviors of this system. This research explores the impacts of different external conditions, such as external excitation and aerodynamic force, on the resonant response and nonlinear dynamics of the axially moving FGM sandwich cylindrical shell. The results indicate that both external excitation and aerodynamic force have a significant influence on the nonlinear vibrations of this structure. Understanding these factors is important for optimizing the flight performance of supersonic vehicles in adverse environmental conditions.