Phononic Band Gaps in Periodic Cellular Materials

The dynamic mechanical properties of finite two-dimensional periodic cellular materials are investigated by finite element eigenmode analysis for different architectures of the unit cell. Frequency band gaps are examined in quadratic and hexagonal lattice topologies with regular, inverted, and chiral architecture. Pronounced band gaps develop for chiral lattices. The formation of band gaps can be traced back to the resonance behavior of the elementary building blocks of the cellular structure for different boundary conditions (mode transition). Based on the findings of this work periodic lattice materials with specific band gaps can be designed.

[1]  A. Krishnan,et al.  A SIMPLE CUBIC LINEAR ELEMENT FOR STATIC AND FREE VIBRATION ANALYSES OF CURVED BEAMS , 1998 .

[2]  T. Weller,et al.  On the feasibility of introducing auxetic behavior into thin-walled structures , 2009 .

[3]  R. Singer,et al.  Design of Auxetic Structures via Mathematical Optimization , 2011, Advanced materials.

[4]  R. Singer,et al.  Cellular Ti-6Al-4V structures with interconnected macro porosity for bone implants fabricated by selective electron beam melting. , 2008, Acta biomaterialia.

[5]  Robert F. Singer,et al.  Cellular Titanium by Selective Electron Beam Melting , 2007 .

[6]  Daniela Addessi,et al.  On the linear normal modes of planar pre-stressed curved beams , 2005 .

[7]  Massimo Ruzzene,et al.  Phononic properties of hexagonal chiral lattices , 2009 .

[8]  Roderic S. Lakes,et al.  Analytical parametric analysis of the contact problem of human buttocks and negative Poisson's ratio foam cushions , 2002 .

[9]  Maurice Petyt,et al.  Free vibration of a curved beam , 1971 .

[10]  Massimo Ruzzene,et al.  Analysis of in-plane wave propagation in hexagonal and re-entrant lattices , 2008 .

[11]  Steve Haake,et al.  Strain rate dependence of stiffness and Poisson's ratio of auxetic open cell PU foams , 2007 .

[12]  D. Swanson,et al.  Higher-frequency wavenumber shift and frequency shift in a cracked, vibrating beam , 2008 .

[13]  Per-Gunnar Martinsson,et al.  VIBRATIONS OF LATTICE STRUCTURES AND PHONONIC BAND GAPS , 2003 .

[14]  Noel C. Perkins,et al.  Planar vibration of an elastica arch : theory and experiment , 1990 .

[15]  Massimo Ruzzene,et al.  Directional and band‐gap behavior of periodic auxetic lattices , 2005 .

[16]  R. Lakes.  Foam Structures with a Negative Poisson's Ratio , 1987, Science.

[17]  A. Haddow,et al.  Design of band-gap grid structures , 2005 .

[18]  Constantinos Soutis,et al.  Delamination detection in composite laminates from variations of their modal characteristics , 1999 .

[19]  M. V. de Hoop,et al.  Generalized‐Screen Approximation and Algorithm for the Scattering of Elastic Waves , 2003 .

[20]  Tanya Tarnopolskaya,et al.  Asymptotic Analysis of The Free In-Plane Vibrations of Beams With Arbitrarily Varying Curvature And Cross-Section , 1996 .