0
Research Papers

Wave Propagation in Auxetic Tetrachiral Honeycombs

[+] Author and Article Information
K. F. Tee

Department of Aerospace Engineering, University of Bristol, Bristol BS8 1TR, UK

A. Spadoni

Aerospace, California Institute of Technology, MC 105–50, Pasadena, CA 91125

F. Scarpa1

Department of Aerospace Engineering, University of Bristol, Bristol BS8 1TR, UKf.scarpa@bristol.ac.uk

M. Ruzzene

School of Aerospace Engineering, Georgia Institute of Technology, Ferst Drive, Atlanta, GA

1

Corresponding author.

J. Vib. Acoust 132(3), 031007 (Apr 22, 2010) (8 pages) doi:10.1115/1.4000785 History: Received March 11, 2009; Revised November 10, 2009; Published April 22, 2010; Online April 22, 2010

This paper describes a numerical and experimental investigation on the flexural wave propagation properties of a novel class of negative Poisson’s ratio honeycombs with tetrachiral topology. Tetrachiral honeycombs are structures defined by cylinders connected by four tangent ligaments, leading to a negative Poisson’s ratio (auxetic) behavior in the plane due to combined cylinder rotation and bending of the ribs. A Bloch wave approach is applied to the representative unit cell of the honeycomb to calculate the dispersion characteristics and phase constant surfaces varying the geometric parameters of the unit cell. The modal density of the tetrachiral lattice and of a sandwich panel having the tetrachiral as core is extracted from the integration of the phase constant surfaces, and compared with the experimental ones obtained from measurements using scanning laser vibrometers.

FIGURES IN THIS ARTICLE
<>
Copyright © 2010 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 2

Representative finite element unit cell for Bloch wave conditions

Grahic Jump Location
Figure 3

(a) RP tetrachiral lattice panel mounted on electrodynamic shaker and (b) flat sandwich tetrachiral lattice mounted on the same rig

Grahic Jump Location
Figure 4

First constant phase surface for tetrachiral lattice (α=6, β=0.4, γ=1)

Grahic Jump Location
Figure 5

Phase constant surfaces cascade for (a) tetrachiral lattice and (b) sandwich unit cells (α=6, β=0.4, γ=1)

Grahic Jump Location
Figure 1

Tetrachiral unit cell with representative geometric parameters

Grahic Jump Location
Figure 8

Dispersion curves in the wave number vector space for (a) tetrachiral lattice and (b) sandwich unit cell. Only the displacement along the z-direction is allowed.

Grahic Jump Location
Figure 9

Dispersion curves in the wave number vector space for the tetrachiral lattice unit cell. All degrees of freedom unconstrained.

Grahic Jump Location
Figure 10

Experimental spectrum of the average mobility for (a) tetrachiral lattice and (b) sandwich panel

Grahic Jump Location
Figure 11

Comparison between analytical, numerical, and experimental modal densities. (a) tetrachiral lattice and (b) sandwich panel.

Grahic Jump Location
Figure 6

First four eigenmodes of (6) for the tetrachiral lattice for different wave vector combinations

Grahic Jump Location
Figure 7

First four eigenmodes of (6) for the tetrachiral sandwich for different wave vector combinations

Grahic Jump Location
Figure 12

Sensitivity of eigensolutions versus the cell wall aspect ratio L/R for the tetrachiral core (a) kx=0, ky=0; (b) kx=π, ky=0; and (c) kx=π/4, ky=π/4. Only the z-displacement is allowed.

Grahic Jump Location
Figure 13

Sensitivity of eigensolutions versus the cell wall aspect ratio L/R for the sandwich panel: (a) kx=0, ky=0; (b) kx=π, ky=0; and (c) kx=π/4, ky=π/4. Only the z-displacement is allowed.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In