Nonlinear Flutter Characteristics of Gradient Porous Panels under Pre-stretching Displacement

Aiming at the problem of flutter and instability of supersonic panel. the nonlinear dynamic control equation of pre-stretched porous panel is established based on Von Kármán thin plate large deflection theory and first-order piston aerodynamic load model. The dynamic model incorporates pre-stretching effects in functionally graded porous panels. Considering three different pore distribution modes. The Galerkin method transforms the governing equations into nonlinear systems through chordwise integration. Stability criteria are derived via Routh-Hurwitz analysis and Hopf bifurcation theory. Closed-form solutions for critical frequency and flutter velocity are obtained. Numerical validation is performed using fourth-order Runge-Kutta integration. Results demonstrate superior performance in symmetric distribution cases: It demonstrates the best flutter resistance, followed by asymmetric and then uniform distributions. The application of merely $$0.02\% $$ pre-stretching strain results in significant improvements in both critical flutter velocity and flutter frequency; when compared to the non-pre-stretched condition, the pre-stretched configuration delays the system critical point occurrence, effectively reducing flutter incidence. The pre-stretching-porosity coupling control methodology proposed in this study, establishes a new theoretical paradigm for panel design: prioritizing symmetric porosity distribution with optimal pre-stretching strain, can effectively suppress flutter while enhancing stability performance.