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24-26 September 2008, Rome, Italy2.5(a)2.5(b) a=1.4µm2.02.0frequency (GHz)1.51.0frequency (GHz)1.51.00.50.50.00.0 0.2 0.4 0.6 0.8 1.0e (µm)0.0MΓreduced wavevectorXFig.6. (a) Evolution of the gaps of Fig. 5c as a function of the thickness of the plate, keeping constant the other geometrical parameters (h=2.7µm and β=56.4%).(b) Dispersion curves for a low filling fraction β=38% (lattice parameter a=1.4µm) and the geometrical parameters h=2.7µm and e=0.2µmIII. CONCLUSIONIn conclusion, we have investigated the phononic bandstructure of a periodic array of dots deposited on a plate. Weput emphasis on the possibility of a low frequency gap andits existence conditions against various geometrical andphysical parameters. We also showed the existence of highergaps, especially by increasing the height of the cylinders.Similar studies should be performed for different shapes ofthe dots, hollow or coated cylinders, etc… The calculationshould also be extended to higher frequencies. This is a firststep towards the study of the effect of phonon dispersion onthermal transport in such nanostructured materialsREFERENCES[1] M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani,“Acoustic band structure of periodic elastic composites,” Phys. Rev.Lett. 71, 2022, 1993.[2] Y. Pennec, B. Djafari-Rouhani, J.O. Vasseur, A. Khelif, and P.A.Deymier, “Tunable filtering and demultiplexing in phononiccrystals with hollow cylinders,” Phys. Rev. E 69, 046608, 2004.[3] A. Khelif, B. Djafari-Rouhani, J.O. Vasseur, P.A. Deymier, Phys.Rev. B 68, 024302 (2003)[4] Z. Liu, X. Zhang, Y. Mao, Y.Y. Zhu, Z. Yang, C.T. Chan, P. Sheng,Science 289, 1734 (2000)[5] H. Larabi, Y. Pennec, B. Djafari-Rouhani, and J. O. Vasseur,“Multicoaxial cylindrical inclusions in locally resonant phononiccrystals,” Phys. Rev. E 75, 066601, 2007.[6] Y. Tanaka and S. Tamura, Phys. Rev. B 60, 13294 (1999)[7] V. Laude, M. Wilm, S. Benchabane, and A. Khelif, Phys. Rev. E71, 036607 (2005)[8] T. Wu, L. C. Wu, and Z. G. Huang, J. Appl. Phys. 97, 094916(2005)[9] J. O. Vasseur, P. A. Deymier, B. Djafari-Rouhani, and Y. Pennec,Proceedings of IMECE 2006, ASME International MechanicalEngineering Congress and Exposition, Chicago, Illinois, 5–10,November 2006.[10] J. C. Hsu and T. T. Wu, Phys. Rev. B 74, 144303 (2006)[11] A. Khelif, B. Aoubiza, S. Mohammadi, A. Adibi, and V. Laude,Phys. Rev. E 74, 046610 (2006)[12] J.O. Vasseur, A.-C. Hladky-Hennion, B. Djafari-Rouhani, F. Duval,B. Dubus, and Y. Pennec, “Waveguiding in two-dimensionalpiezoelectric phononic crystal plates,” J. Appl. Phys. 101, 114904,2007.©EDA Publishing/THERMINIC 2008 167ISBN: 978-2-35500-008-9