Purpose <p>This paper aims to investigate how lever flexibility affects the isolation performance of lever-type dynamic anti-resonant vibration isolators with and without negative stiffness, and to assess the validity of the conventional rigid-lever model.</p> Method <p>The lever is modeled as a Timoshenko beam with its pivots represented by artificial springs, and discretized using the Rayleigh–Ritz method. The equations of motion, derived from Hamilton’s principle, are solved by the harmonic balance method with arc-length continuation. A prototype is fabricated and tested for validation.</p> Results <p>Negative stiffness lowers the first natural frequency and broadens the isolation bandwidth, but the attainable bandwidth is ultimately limited by the lever's bending resonance. Under the parameter settings considered in this study, with a Young's modulus of <i>E</i> = 2.1 × 10<sup>11</sup>&#xa0;Pa, the rigid-lever model can produce substantial errors (exceeding 10%) in the predicted anti-resonance characteristics, especially when either the lever ratio <i>α</i> or the main stiffness <i>k</i> is large (i.e., <i>α</i> &gt; 4 or <i>k</i> &gt; 6 × 10<sup>5</sup> N/m). These theoretical analyses are verified experimentally on a fabricated prototype.</p> Conclusion <p>Lever flexibility is a key factor governing the anti-resonance characteristics and effective isolation bandwidth of such isolators, and the proposed model provides a more accurate basis than the rigid-lever model for their analysis and design.</p>

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Effect of Lever Flexibility on Dynamic Anti-Resonant Vibration Isolators with and without Negative Stiffness

  • Niuniu Liu,
  • Fuming Lin,
  • Zhiyang Lei,
  • Jialiang Zhou

摘要

Purpose

This paper aims to investigate how lever flexibility affects the isolation performance of lever-type dynamic anti-resonant vibration isolators with and without negative stiffness, and to assess the validity of the conventional rigid-lever model.

Method

The lever is modeled as a Timoshenko beam with its pivots represented by artificial springs, and discretized using the Rayleigh–Ritz method. The equations of motion, derived from Hamilton’s principle, are solved by the harmonic balance method with arc-length continuation. A prototype is fabricated and tested for validation.

Results

Negative stiffness lowers the first natural frequency and broadens the isolation bandwidth, but the attainable bandwidth is ultimately limited by the lever's bending resonance. Under the parameter settings considered in this study, with a Young's modulus of E = 2.1 × 1011 Pa, the rigid-lever model can produce substantial errors (exceeding 10%) in the predicted anti-resonance characteristics, especially when either the lever ratio α or the main stiffness k is large (i.e., α > 4 or k > 6 × 105 N/m). These theoretical analyses are verified experimentally on a fabricated prototype.

Conclusion

Lever flexibility is a key factor governing the anti-resonance characteristics and effective isolation bandwidth of such isolators, and the proposed model provides a more accurate basis than the rigid-lever model for their analysis and design.