Toward wind-resilient cable-supported photovoltaic system: nonlinear stiffness, dynamic identification, and parametric instability

Cable-supported flexible photovoltaic (FPV) system is emerging as lightweight low-carbon power-generation structures, but their large-span, low-stiffness configuration makes them susceptible to large-amplitude wind-induced oscillations, for which the conventional small-amplitude assumption no longer provides a valid basis for dynamic analysis. This study establishes a finite-amplitude nonlinear dynamic framework for two-cable FPV systems, in which vibration-induced cable-force evolution is explicitly incorporated into the governing equations as time-varying stiffness. Based on this framework, deviations in dynamic characteristic identification are investigated, and practical testing strategies are proposed and validated through scaled aeroelastic model tests. Undamped free-vibration analysis reveals that the nonlinear stiffness of FPV systems is governed by nonlinear Mathieu and asymmetric Duffing mechanisms. The single-degree-of-freedom (S-DOF) response follows a Duffing oscillator, where the initial equilibrium state induces restoring-force asymmetry, amplitude deviation, and spontaneous shift of the oscillation center. In multi-degree-of-freedom (M-DOF) vibration, parametric resonance (PR) with bifurcation occurs near a unit torsional-to-bending frequency ratio, with unidirectional energy pumping from the lower-order to the higher-order mode. Coupled and uncoupled equivalent linear stiffness formulations are presented for frequency-domain analysis of flutter. These findings have direct implications for the operational lifespan, maintenance costs, and levelized cost of energy (LCOE) of FPV systems, as the amplitude-dependent stiffness evolution and parametric resonance identified in this study govern the cyclic stress levels and deformation amplitudes that drive fatigue accumulation in cables and connectors, as well as micro-cracking in PV cells. By linking finite-amplitude stiffness evolution to measurable modal properties and flutter-relevant design variables, the framework offers a mechanics-based route to wind-resilient design and reliable long-term deployment of FPV energy infrastructure.