Phononic properties of hexagonal chiral lattices. (English) Zbl 1231.82083
Summary: We report the outcome of investigations on the phononic properties of a chiral cellular structure. The considered geometry features in-plane hexagonal symmetry, whereby circular nodes are connected through six ligaments tangent to the nodes themselves. In-plane wave propagation is analyzed through the application of Bloch theorem, which is employed to predict two-dimensional dispersion relations as well as illustrate dispersion properties unique to the considered chiral configuration. Attention is devoted to determining the influence of unit cell geometry on dispersion, band gap occurrence and wave directionality. Results suggest cellular lattices as potential building blocks for the design of meta-materials of interest for acoustic wave-guiding applications.
MSC:
| 82D25 | Statistical mechanics of crystals |
References:
| [1] | Evans, K. E., Design of doubly curved sandwich panels with honeycomb cores, Comp. Struct., 17, 2, 95-111 (1991) |
| [2] | Scarpa, F.; Tomlinson, G., Theoretical characteristics of the vibration of sandwich plates with in-plane negative poissons ratio values, J. Sound Vibrations, 230, 1, 45-67 (2000) · Zbl 1235.74117 |
| [3] | Ruzzene, M.; Scarpa, F.; Soranna, F., Wave beaming effects in two-dimensional cellular structures, Smart Mater. Struct., 12, 3, 363-372 (2003) |
| [4] | Phani, A. S.; Woodhouse, J.; Fleck, N. A., Wave propagation in two-dimensional periodic lattices, J. Acoust. Soc. Am., 119, 4, 1995-2005 (2006) |
| [5] | Psarobas, I. E., Phononic crystals, sonic band-gap materials, J. Struct., Phys., Chem. Aspects Cryst. Mater., 220, 9-10 (2003) |
| [6] | M.I. Hussein, G. Hulbert, R. Scott, Tailoring of wave propagation characteristics in periodic structures with multilayer unit cells, in: Proceedings of 17th American Society of Composites Technical Conference, 2002.; M.I. Hussein, G. Hulbert, R. Scott, Tailoring of wave propagation characteristics in periodic structures with multilayer unit cells, in: Proceedings of 17th American Society of Composites Technical Conference, 2002. |
| [7] | Hussein, M. I.; Hamza, K.; Hulbert, G.; Saitou, K., Optimal synthesis of 2d phononic crystals for broadband frequency isolation, Waves Random Complex Media, 17, 4, 491-510 (2007) · Zbl 1191.74043 |
| [8] | Sigmund, O.; Jensen, J., Systematic design of phononic band-gap materials and structures by topology optimization, Phylosophical Trans. Roy. Soc. London, Series A, Math. Phys. Eng. Sci., 361, 1806, 1001-1019 (2003) · Zbl 1067.74053 |
| [9] | Diaz, A.; Haddow, A.; Ma, L., Design of band-gap grid structures, Struct. Multidisciplinary Optimization, 29, 6, 418-431 (2005) |
| [10] | Prall, D.; Lakes, R. S., Properties of a chiral honeycomb with a poisson’s ratio −1, Int. J. Mech. Sci., 39, 305-314 (1996) · Zbl 0894.73018 |
| [11] | Wojciechowski, K., Two-dimensional isotropic system with a negative poisson ratio, Phys. Lett. A, 137, 60-64 (1989) |
| [12] | Spadoni, A.; Ruzzene, M.; Scarpa, F., Dynamic response of chiral truss-core assemblies, J. Intelligent Mater. Syst. Struct., 17, 11, 941-952 (2005) |
| [13] | Spadoni, A.; Ruzzene, M., Static aeroelastic response of chiral-core airfoils, J. Intelligent Mater. Syst. Struct., 18, 1067-1075 (2007) |
| [14] | Cook, R. D.; Malkus, D. S.; Plesha, M. E.; Witt, R. J., Concepts and Applications of Finite Element Analysis (2001), Wiley |
| [15] | Agarwal, B. D.; Broutman, L. J., Analysis and Performance of Fiber Composites (1980), John Wiley: John Wiley New York |
| [16] | Love, A. E.H., A Treatise on the Mathematical Theory of Elasticity (1927), Dover Publications, (Chapter VI, Section 110) · Zbl 0063.03651 |
| [17] | Brillouin, L., Wave Propagation in Periodic Structures (1953), Dover: Dover New York, NY · Zbl 0050.45002 |
| [18] | Auld, B. A., Acoustic Fields and Waves in Solids, Vol. 1 (1990), Krieger Publ. Co.: Krieger Publ. Co. Malabar, FL |
| [19] | Bathe, K.-J., Finite Element Procedures (1996), Prentice Hall: Prentice Hall Upper Saddle River, NJ |
| [20] | Wolfe, J. P., Imaging Phonons: Acoustic Wave Propagation in Solids (1998), Cambridge University Press |
| [21] | Gonella, S.; Ruzzene, M., Homogenization and equivalent in-plane properties of two-dimensional periodic lattices, Int. J. Solids Struct., 45, 10, 2897-2915 (2008) · Zbl 1169.74529 |
| [22] | Lakes, R. S., Elastic and viscoelastic behavior of chiral materials, Int. J. Mech. Sci., 43, 7, 1579-1589 (2001) · Zbl 1049.74012 |
| [23] | Grima, J. N.; Gatt, R.; Farrugia, P.-S., On the properties of auxetic meta-tetrachiral structures, Phys. Status Solidi B, 245, 511-520 (2008) |
| [24] | Masters, I. G.; Evans, K. E., Models for the elastic deformation of honeycombs, Compos. Struct., 35, 4, 403-422 (1996) |
| [25] | Bornengo, D.; Scarpa, F.; Remillant, C., Morphing airfoil concept with chiral core structure, I MECH E Part G, J. Aerospace Eng., G3, 8, 185-192 (2005) |
| [26] | Pierre, C., Mode localization and eigenvalue loci veering phenomena in disordered structures, Develop. Mech., 14, 165-170 (1987) |
| [27] | Chan, H.; Liu, J., Mode localization and frequency loci veering in disordered engineering structures, Chaos, Solitons Fractals, 11, 10, 1493-1504 (2000) · Zbl 0969.74028 |
| [28] | Perkins, N.; Mote, C., Comments on curve veering in eigenvalue problems, J. Sound Vibration, 106, 3, 451-463 (1986) |
| [29] | Taylor, B.; Maris, H. J.; Elbaum, C., Phonon focusing in solids, Phys. Rev. Lett., 23, 416 (1969) |
| [30] | Taylor, B.; Maris, H. J.; Elbaum, C., Focusing of phonons in crystalline solids due to elastic anisotropy, Phys. Rev. B, 3, 1462 (1971) |
| [31] | Maris, H. J., Enhancement of heat pulses in crystals due to elastic anisotropy, J. Acoustical Soc. Am., 50, 812 (1971) |
| [32] | Whitham, G. B., Linear and Nonlinear Waves (1999), Wiley Interscience: Wiley Interscience New York, NY · Zbl 0373.76001 |
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