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<p>To achieve ultra-low-frequency broadband vibration isolation in space-constrained systems, this study proposes a sandwich shell metastructure (SSM) tuned via prescribed pre-displacement. A stability-aware framework is developed to determine band gaps under geometric nonlinearity, eliminating ambiguities introduced by unstable eigenbranches. The pre-displaced equilibrium configuration is used as the reference state, and dispersion relations are obtained via small-on-large linearization. Band gaps are extracted exclusively from stable branches to avoid spurious predictions. Increasing pre-displacement shifts the stable band gaps toward lower frequencies and broadens the effective isolation bandwidth to 7.6–395.7&#xa0;Hz. In the QZS regime, the first stable band gap reaches a maximum relative width of 64.7%. When pre-displacement exceeds 3.2&#xa0;mm, the first three eigenbranches become unstable, defining a critical design boundary. The widening of the first band gap is attributed to a transition from global bending to shell-dominated local resonance, accompanied by increased frequency separation between adjacent stable modes. Parametric analysis of the SSM shows that orifice diameter, neck length, and cavity diameter govern local stiffness and effective inertia. Approaching critical geometric limits degrades low-order band gaps. A practical guideline is to reduce the orifice diameter while maintaining sufficient neck length and cavity size, thereby preserving stable band gaps and broadening the isolation bandwidth. Finite-structure simulations confirm that transmissibility attenuation coincides with predicted stable band gaps, with localized vibration occurring within these ranges. Experiments on additively manufactured thermoplastic polyurethane samples demonstrate a 76% increase in effective isolation bandwidth (from 158.3 to 279.3&#xa0;Hz). This study provides a mechanics-based framework for tunable metastructures, offering explicit design guidelines and stability-informed operating boundaries.</p>

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Pre-displacement tuned sandwich shell metastructure for ultra-low-frequency broadband vibration isolation

  • 期刊论文

  • 发表日期：

    2026年6月15日

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  • Haoqiang Gao,
  • Wenxuan Jiao,
  • Jingxu Liu,
  • Yongtao Sun,
  • Liang Wang,
  • Hongge Han,
  • Qian Ding,
  • Zhixia Wang,
  • Anshuai Wang

摘要

To achieve ultra-low-frequency broadband vibration isolation in space-constrained systems, this study proposes a sandwich shell metastructure (SSM) tuned via prescribed pre-displacement. A stability-aware framework is developed to determine band gaps under geometric nonlinearity, eliminating ambiguities introduced by unstable eigenbranches. The pre-displaced equilibrium configuration is used as the reference state, and dispersion relations are obtained via small-on-large linearization. Band gaps are extracted exclusively from stable branches to avoid spurious predictions. Increasing pre-displacement shifts the stable band gaps toward lower frequencies and broadens the effective isolation bandwidth to 7.6–395.7 Hz. In the QZS regime, the first stable band gap reaches a maximum relative width of 64.7%. When pre-displacement exceeds 3.2 mm, the first three eigenbranches become unstable, defining a critical design boundary. The widening of the first band gap is attributed to a transition from global bending to shell-dominated local resonance, accompanied by increased frequency separation between adjacent stable modes. Parametric analysis of the SSM shows that orifice diameter, neck length, and cavity diameter govern local stiffness and effective inertia. Approaching critical geometric limits degrades low-order band gaps. A practical guideline is to reduce the orifice diameter while maintaining sufficient neck length and cavity size, thereby preserving stable band gaps and broadening the isolation bandwidth. Finite-structure simulations confirm that transmissibility attenuation coincides with predicted stable band gaps, with localized vibration occurring within these ranges. Experiments on additively manufactured thermoplastic polyurethane samples demonstrate a 76% increase in effective isolation bandwidth (from 158.3 to 279.3 Hz). This study provides a mechanics-based framework for tunable metastructures, offering explicit design guidelines and stability-informed operating boundaries.