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On the low frequency flexural band gaps of a metamaterial plate with low porosity

Chaitanya Morey, Sundararajan Natarajan, Chandramouli Padmanabhan

TL;DR

The study addresses the challenge of achieving low-frequency flexural band gaps in plates with low porosity without relying on resonators. It develops a RMPT-based unit-cell model with Bloch periodic boundaries to compute dispersion and validates it against literature and experiments on 3×3 plates; a parametric survey shows that center-passing, high‑aspect‑ratio cross-shaped cutouts generate multiple low-frequency gaps in the first few modes at porosities around 11%. The main contributions are the design rule that center-cross shapes enable low-frequency gaps in low-porosity metamaterial plates and the accompanying experimental verification, demonstrating significant attenuation within predicted stop bands. This work offers a practical, lightweight approach to vibration isolation with potential for scalable manufacturing and design optimization.

Abstract

This paper demonstrates numerically and experimentally that it is possible to tailor flexural band gaps in the low-frequency regime by appropriate choice of cutout characteristics. The finite element method is used to obtain the numerical dispersion relation and band gaps. The influence of the cutout's shape, size, and location on the band gap is systematically studied. The study demonstrates that the cutout should pass through the center of the unit cell, and a large aspect ratio is required to introduce flexural band gaps in the low-frequency regime. This is validated by experiments on a finite plate with 3 $\times$ 3 unit cells.

On the low frequency flexural band gaps of a metamaterial plate with low porosity

TL;DR

The study addresses the challenge of achieving low-frequency flexural band gaps in plates with low porosity without relying on resonators. It develops a RMPT-based unit-cell model with Bloch periodic boundaries to compute dispersion and validates it against literature and experiments on 3×3 plates; a parametric survey shows that center-passing, high‑aspect‑ratio cross-shaped cutouts generate multiple low-frequency gaps in the first few modes at porosities around 11%. The main contributions are the design rule that center-cross shapes enable low-frequency gaps in low-porosity metamaterial plates and the accompanying experimental verification, demonstrating significant attenuation within predicted stop bands. This work offers a practical, lightweight approach to vibration isolation with potential for scalable manufacturing and design optimization.

Abstract

This paper demonstrates numerically and experimentally that it is possible to tailor flexural band gaps in the low-frequency regime by appropriate choice of cutout characteristics. The finite element method is used to obtain the numerical dispersion relation and band gaps. The influence of the cutout's shape, size, and location on the band gap is systematically studied. The study demonstrates that the cutout should pass through the center of the unit cell, and a large aspect ratio is required to introduce flexural band gaps in the low-frequency regime. This is validated by experiments on a finite plate with 3 3 unit cells.

Paper Structure

This paper contains 11 sections, 12 equations, 11 figures, 1 table.

Table of Contents

  1. Introduction
  2. Theoretical formulation
  3. Basics of Reissner-Mindlin plate theory
  4. Bloch Periodic boundary condition
  5. Numerical Results and Discussion
  6. Validation
  7. Effect of shape, size and location of cutouts
  8. Experimental Verification
  9. Experimental setup
  10. Results
  11. Conclusion

Figures (11)

  • Figure 1: Schematic of a periodic plate with uniform thickness, $h$ with its unit cell with an arbitrary cutout and the first irreducible Brillouin zone
  • Figure 2: Schematic representation of unit periodic cell and the notation for boundary nodes
  • Figure 3: Comparison of band gaps obtained from the present work with that of Huang et al. huang2018multiple.
  • Figure 4: Schematic representation of a unit cell with different cutout shapes: (a) ellipse, (b) intersecting ellipses, (c) intersecting rectangular slots, (d) cross, (e) unequal intersecting slots with centre offset and (f) Intersecting slots with centre offset.
  • Figure 5: Dispersion curves for the unit cell for a plate with various cutouts: (a) ellipse, (b) intersecting ellipses, (c) intersecting rectangular slots, (d) cross, (e) unequal intersecting slots with centre offset and (f) Intersecting slots with centre offset.
  • ...and 6 more figures