Numerical Analysis of Dynamic Stability of Flutter Panels in Supersonic Flow

This paper introduces a novel numerical method for investigating the dynamic stability of a flutter panel exposed to a supersonic gas flow and a fluctuating axial excitation force. Initially, the system equation of motion was derived using Lagrange’s equation, where the first two modes are coupled Mathieu–Hill equations with damping, constituting a system of linear second-order differential equations with periodically variable coefficients. Subsequently, a new numerical method was proposed to analyze the dynamic stability of coupled Mathieu–Hill equations with damping. This method involves breaking down an arbitrary parametric load into discrete segments to approximate the variable excitation function using a step function. The system responses of each segment are then accumulated in matrix form. The proposed numerical method proves particularly effective for dynamic systems whose parameters cannot be treated as small. In practical application, the method allows the construction of instability regions corresponding to natural frequencies, subharmonics, and combination frequencies. Dynamic stability diagrams were generated based on dynamic pressure ratio, air/panel density ratio, Mach number, panel thickness—length ratio, and excitation frequency. The results demonstrated general agreement with those obtained through Hsu’s perturbation method, however, our numerical results have proven more accurate. The paper concludes by offering suggestions for suppressing panel flutter through appropriate parameter combinations.