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<p>Large-scale membrane-based aerospace structures inherently exhibit complex nonlinear dynamic behaviors, presenting significant challenges for accurate response prediction and effective vibration attenuation. This work proposes an analytical modeling approach for membrane systems with discontinuous boundary configurations, offering a unified framework for nonlinear dynamic analysis under arbitrary boundaries. Finite element simulations confirm the accuracy of the method in predicting natural characteristics. By incorporating a nonlinear positive position feedback (NPPF) control strategy, the governing equation of the closed-loop system under thermo-mechanical coupling is established. Using the incremental harmonic balance (IHB) method, the effects of controller parameters and external disturbances on the nonlinear primary resonance are systematically examined. Furthermore, bifurcation diagrams, phase portraits, and Poincaré maps are employed to reveal the transition mechanisms of the global dynamics and motion evolution, clarifying the regulatory role of key parameters in system stability. Numerical results demonstrate that the NPPF controller effectively suppresses nonlinear vibrations and enhances stability by introducing additional damping, though its performance strongly depends on appropriate parameter selection. Specifically, moderate increases in control gain can suppress resonance and broaden the effective attenuation bandwidth, whereas excessive gains amplify responses and may induce instability. Higher controller damping improves suppression levels across the entire frequency range but slightly reduces efficiency at resonance. The cubic nonlinear coefficient adjusts the hardening or softening behavior of the response. In addition, pretension and temperature rise exert opposite effects on the dynamic characteristics. Overall, this study provides a comprehensive analytical framework for nonlinear vibration analysis and active control of membrane-type aerospace structures with complex discontinuous boundaries.</p>

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Nonlinear primary resonance analysis and motion evolution of the membrane with discontinuous boundaries under NPPF control

  • 期刊论文

  • 发表日期：

    2026年3月16日

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  • Xuan Sun,
  • Zhitong Li,
  • Leizhi Wang,
  • Jiaxi Jin,
  • Zhaobo Chen

摘要

Large-scale membrane-based aerospace structures inherently exhibit complex nonlinear dynamic behaviors, presenting significant challenges for accurate response prediction and effective vibration attenuation. This work proposes an analytical modeling approach for membrane systems with discontinuous boundary configurations, offering a unified framework for nonlinear dynamic analysis under arbitrary boundaries. Finite element simulations confirm the accuracy of the method in predicting natural characteristics. By incorporating a nonlinear positive position feedback (NPPF) control strategy, the governing equation of the closed-loop system under thermo-mechanical coupling is established. Using the incremental harmonic balance (IHB) method, the effects of controller parameters and external disturbances on the nonlinear primary resonance are systematically examined. Furthermore, bifurcation diagrams, phase portraits, and Poincaré maps are employed to reveal the transition mechanisms of the global dynamics and motion evolution, clarifying the regulatory role of key parameters in system stability. Numerical results demonstrate that the NPPF controller effectively suppresses nonlinear vibrations and enhances stability by introducing additional damping, though its performance strongly depends on appropriate parameter selection. Specifically, moderate increases in control gain can suppress resonance and broaden the effective attenuation bandwidth, whereas excessive gains amplify responses and may induce instability. Higher controller damping improves suppression levels across the entire frequency range but slightly reduces efficiency at resonance. The cubic nonlinear coefficient adjusts the hardening or softening behavior of the response. In addition, pretension and temperature rise exert opposite effects on the dynamic characteristics. Overall, this study provides a comprehensive analytical framework for nonlinear vibration analysis and active control of membrane-type aerospace structures with complex discontinuous boundaries.