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Background <p>The dynamic stability of rotating nanoplates subjected to time‑varying angular velocities is a critical but still unresolved issue for next‑generation micro‑ and nano‑electromechanical systems (MEMS/NEMS). In such systems, the interaction between nonlocal effects and parametric excitation directly affects operational reliability.</p> Methods <p>A comprehensive stability analysis framework is established by integrating Eringen’s nonlocal elasticity with Mindlin plate theory through the Hellinger–Reissner variational principle. This approach inherently avoids the boundary paradoxes that commonly arise in differential nonlocal models. An existing 8‑node hybrid plate element (MHAS‑24β) is employed to achieve consistent displacement–stress coupling, enabling accurate static, free vibration, and parametric stability analyses under both uniform and periodically varying rotation. Stability maps are constructed using the Floquet theory.</p> Results <p>The results show that nonlocal softening dominates over centrifugal stiffening, significantly reducing the effective structural stiffness and lowering the parametric resonance threshold. The stability maps further reveal that the mean angular velocity not only raises the instability threshold through centrifugal stiffening but also fundamentally reshapes the unstable frequency bands.</p> Conclusions <p>The quantitative stability boundaries obtained in this work provide direct design guidance for micro‑ and nanorotors. Elevated mean angular velocities can enhance stability, whereas pronounced nonlocal effects require stricter control of velocity fluctuations to avoid resonance‑induced failure.</p>

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Dynamic Response and Parametric Instability of Rotating Nanoplates Under Periodic Angular Velocity Fluctuation

  • 期刊论文

  • 发表日期：

    2026年5月14日

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  • X. Zhang,
  • H. N. Li,
  • C. Li,
  • G. W. Wang,
  • S. Q. Zhou

摘要

Background

The dynamic stability of rotating nanoplates subjected to time‑varying angular velocities is a critical but still unresolved issue for next‑generation micro‑ and nano‑electromechanical systems (MEMS/NEMS). In such systems, the interaction between nonlocal effects and parametric excitation directly affects operational reliability.

Methods

A comprehensive stability analysis framework is established by integrating Eringen’s nonlocal elasticity with Mindlin plate theory through the Hellinger–Reissner variational principle. This approach inherently avoids the boundary paradoxes that commonly arise in differential nonlocal models. An existing 8‑node hybrid plate element (MHAS‑24β) is employed to achieve consistent displacement–stress coupling, enabling accurate static, free vibration, and parametric stability analyses under both uniform and periodically varying rotation. Stability maps are constructed using the Floquet theory.

Results

The results show that nonlocal softening dominates over centrifugal stiffening, significantly reducing the effective structural stiffness and lowering the parametric resonance threshold. The stability maps further reveal that the mean angular velocity not only raises the instability threshold through centrifugal stiffening but also fundamentally reshapes the unstable frequency bands.

Conclusions

The quantitative stability boundaries obtained in this work provide direct design guidance for micro‑ and nanorotors. Elevated mean angular velocities can enhance stability, whereas pronounced nonlocal effects require stricter control of velocity fluctuations to avoid resonance‑induced failure.