Purpose <p>Vehicle transportation generates longitudinal ultra-low-frequency vibration that may cause severe damage to equipment. In this paper, a novel stacked metamaterial structure with localized resonators (NSMS-LR) is proposed to mitigate longitudinal vibration below 25&#xa0;Hz.</p> Methods <p>The dispersion relations are calculated using the finite element method (FEM). The generating mechanism of the band gap is investigated through modal analysis. The parameter analysis is conducted to reveal the variation pattern of the band gap. A stacked optimization method is proposed, realized by connecting units in parallel. Additionally, a multi-start adversarial perturbation long-short optimization method based on a surrogate model (APLSO-SM) is proposed. The metamaterial structure is optimized using the APLSO-SM in conjunction with the stacked optimization method. The 4 × 4 periodic metamaterial structures are fabricated via 3D printing to verify the band gap effect.</p> Results <p>The ultra-low-frequency band gap (10.16–25.01&#xa0;Hz) is obtained through structural parameter optimization. Furthermore, the band gap range is expanded (9.86–29.59&#xa0;Hz) utilizing the stacked optimization method. The proposed metamaterial is capable of effectively suppressing longitudinal vibrations across the targeted frequency range.</p> Conclusion <p>The novel stacked optimization enables an effective reduction in the lower limit of the band gap. The APLSO-SM enhances the efficiency and accuracy of metamaterial parameter optimization. The optimized metamaterial is shown to exhibit an increased band gap width (from 10.43 to 25.17&#xa0;Hz to 9.86–29.59&#xa0;Hz). The proposed optimization strategy provides a practical approach for designing ultra-low-frequency metamaterials. Furthermore, the study offers an effective approach for the isolation of longitudinal vibrations below 25&#xa0;Hz in vehicle transportation.</p>

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Optimal Design of a Novel Stacked Metamaterial for Ultra-Low-Frequency Vibration Isolation

  • Xingyu Huo,
  • Yutong Jin,
  • Shijie Dai

摘要

Purpose

Vehicle transportation generates longitudinal ultra-low-frequency vibration that may cause severe damage to equipment. In this paper, a novel stacked metamaterial structure with localized resonators (NSMS-LR) is proposed to mitigate longitudinal vibration below 25 Hz.

Methods

The dispersion relations are calculated using the finite element method (FEM). The generating mechanism of the band gap is investigated through modal analysis. The parameter analysis is conducted to reveal the variation pattern of the band gap. A stacked optimization method is proposed, realized by connecting units in parallel. Additionally, a multi-start adversarial perturbation long-short optimization method based on a surrogate model (APLSO-SM) is proposed. The metamaterial structure is optimized using the APLSO-SM in conjunction with the stacked optimization method. The 4 × 4 periodic metamaterial structures are fabricated via 3D printing to verify the band gap effect.

Results

The ultra-low-frequency band gap (10.16–25.01 Hz) is obtained through structural parameter optimization. Furthermore, the band gap range is expanded (9.86–29.59 Hz) utilizing the stacked optimization method. The proposed metamaterial is capable of effectively suppressing longitudinal vibrations across the targeted frequency range.

Conclusion

The novel stacked optimization enables an effective reduction in the lower limit of the band gap. The APLSO-SM enhances the efficiency and accuracy of metamaterial parameter optimization. The optimized metamaterial is shown to exhibit an increased band gap width (from 10.43 to 25.17 Hz to 9.86–29.59 Hz). The proposed optimization strategy provides a practical approach for designing ultra-low-frequency metamaterials. Furthermore, the study offers an effective approach for the isolation of longitudinal vibrations below 25 Hz in vehicle transportation.