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Elastic wave control in reticulated plates using Schwarz primitive cells.

Aida Hejazi Nooghabi1, Henrik R Thomsen2, Bao Zhao1

  • 1Department of Civil Environmental and Geomatic Engineering, ETH Zurich, Zurich, Switzerland.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|July 29, 2024
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Summary

Researchers used Schwarz primitive unit cells to create elastic metamaterials. They demonstrated a bandgap and designed a metabarrier and metalens, achieving practical validation of wave focusing in a 3D printed plate.

Keywords:
Luneburg lensSchwarz primitive cellbandgapelastic wave propagationmetabarrier

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Area of Science:

  • Solid Mechanics
  • Materials Science
  • Acoustics

Background:

  • Metamaterials offer unique ways to control wave propagation.
  • The Schwarz primitive unit cell is a versatile building block for designing complex structures.

Purpose of the Study:

  • To utilize the Schwarz primitive unit cell for steering and focusing elastic vibrations.
  • To design and validate elastic metamaterial structures like metabarriers and metalenses.

Main Methods:

  • Experimental validation of Bragg-type bandgaps in 2D plates.
  • Numerical design of metabarriers and metalenses using modified Schwarz unit cells.
  • Mesoscale experimental validation of wave focusing in 3D printed structures.

Main Results:

  • Increasing mass and porosity of unit cells lowers the frequency of out-of-plane waves.
  • A metabarrier effectively shields an area from 1.4-3.4 kHz waves.
  • A metalens was designed by grading unit cell properties, achieving practical wave bending.

Conclusions:

  • Schwarz primitive unit cells are effective for elastic vibration control.
  • Metamaterial designs enable wave focusing and shielding with potential for lightweight and additive manufacturing benefits.