Energy localization and spatiotemporal pattern evolution mechanism of spatial thin-film structures under parametric excitation

This paper investigates energy localization and spatiotemporal pattern evolution in spatial thin-film structures subjected to parametric excitation. A nonlinear thin-shell model is established by combining geometric nonlinearity, time-varying in-plane tension, damping, and multimodal coupling. A second-order multiple-scales perturbation procedure is then used to derive slow-flow modulation equations, and a high-fidelity finite element platform verifies the resulting localization and pattern-selection predictions. The analysis shows that pronounced localization occurs near the combined-resonance condition ω1 + ω2)/2, when the normalized tension fluctuation exceeds approximately γ > 0.20. The nonlinear modal coupling strength κ controls topology selection: stationary breathers dominate for κ < 0.35, whereas traveling patterns emerge for κ > 0.40, with a transition centered near κc ≈ 0.375. The pattern wavelength follows λ/L ≈ 0.28 for square and near-square membranes, while highly anisotropic geometries require direction-dependent correction. Long-term simulations over 2000 excitation cycles show decay rates below 3%, indicating attractor-like persistence within the verified numerical horizon. Frequency-wavenumber spectra further confirm selective modal amplification at resonance. The results provide quantitative criteria for pretension management, hot-spot prediction, and placement of stiffeners, dampers, or active actuators in deployable aerospace membrane structures.