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<p>In practical engineering, deviation from the design load inevitably leads to a drift in the equilibrium position, causing the quasi-zero stiffness system to deviate from its optimal operating point. To accurately capture such load-mismatch-induced dynamics, a single-degree-of-freedom model with fifth-order restoring-force characteristics is established, in which higher-order stiffness effects beyond the conventional cubic approximation are retained. A unified dynamic formulation is further developed for both base excitation and force excitation, allowing the two practical excitation cases to be analyzed within the same theoretical framework. The incremental harmonic balance method is employed to solve for higher-order periodic responses and track unstable branches, while Floquet theory is utilized to assess system stability. Numerical integration validates the analytical results. The study reveals that the interaction between the static bias induced by non-ideal load conditions and the inherent fifth-order nonlinearity renders the system highly susceptible to 1/3 subharmonic resonance. Consequently, the response manifests as a period-3 motion characteristic of 1/3 subharmonic resonance, characterized by a distinct constant term and dominant subharmonic components. Furthermore, multi-stability and jump phenomena are observed in the low-frequency region. Parametric analysis shows that load mismatch, stiffness ratio, damping ratio, and excitation amplitude significantly affect the bias response, resonance bandwidth, multi-solution characteristics, and stability boundary. These findings provide theoretical guidance for parameter matching, subharmonic-response suppression, and robust design of QZS-VI under load uncertainty.</p>

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Subharmonic Response of a Quasi-Zero Stiffness Vibration Isolator Under Non-Ideal Load: Higher-Order Analysis for Base or Force Excitations Conditions

  • 期刊论文

  • 发表日期：

    2026年6月1日

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  • Qingbo Zhu,
  • Kai Chai,
  • Jingjun Lou

摘要

In practical engineering, deviation from the design load inevitably leads to a drift in the equilibrium position, causing the quasi-zero stiffness system to deviate from its optimal operating point. To accurately capture such load-mismatch-induced dynamics, a single-degree-of-freedom model with fifth-order restoring-force characteristics is established, in which higher-order stiffness effects beyond the conventional cubic approximation are retained. A unified dynamic formulation is further developed for both base excitation and force excitation, allowing the two practical excitation cases to be analyzed within the same theoretical framework. The incremental harmonic balance method is employed to solve for higher-order periodic responses and track unstable branches, while Floquet theory is utilized to assess system stability. Numerical integration validates the analytical results. The study reveals that the interaction between the static bias induced by non-ideal load conditions and the inherent fifth-order nonlinearity renders the system highly susceptible to 1/3 subharmonic resonance. Consequently, the response manifests as a period-3 motion characteristic of 1/3 subharmonic resonance, characterized by a distinct constant term and dominant subharmonic components. Furthermore, multi-stability and jump phenomena are observed in the low-frequency region. Parametric analysis shows that load mismatch, stiffness ratio, damping ratio, and excitation amplitude significantly affect the bias response, resonance bandwidth, multi-solution characteristics, and stability boundary. These findings provide theoretical guidance for parameter matching, subharmonic-response suppression, and robust design of QZS-VI under load uncertainty.