Research on combined resonance response and chaotic bifurcation characteristics of flexible photovoltaic rectangular plates

Flexible photovoltaic (PV) structures have broad new energy prospects for their light weight and terrain adaptability, but their high flexibility makes them prone to nonlinear vibration, bifurcation, chaos and other complex dynamic behaviors under wind loads, severely impairing service reliability. This paper models PV arrays as a continuous, homogeneous, isotropic flexible thin plate with fixed short edges. Nonlinear dynamic governing equations are derived from classical laminated plate theory, von Karman large deformation theory and Hamilton's principle. Multi-software cross-verification shows the maximum relative error of the first three natural frequencies between the equivalent model and the original discrete PV array is 5.82%. After Galerkin order reduction, the Runge-Kutta method investigates how external excitation, parametric excitation and damping affect system chaotic bifurcation. For the 1:3 internal resonance between the first two modes, the multiple-scale method and numerical continuation reveal amplitude-frequency and force-amplitude responses under combined resonance. Results show parameter adjustment effectively alters structural motion states, and primary resonant modes exhibit distinct hardening spring characteristics under coupled resonance. Notably, strong parametric excitation forms a complex five-solution bifurcation structure; low damping in second-order primary resonance re-excites the first mode, causing unconventional double-peak resonance and multi-modal coordinated motion. These instabilities are effectively suppressed by reducing frequency detuning, parametric excitation amplitude, or increasing damping. These findings provide a solid theoretical basis for structural optimization and robust anti-vibration design of flexible PV rectangular plates.