The optimization of full band-gaps in multilayer films


  • Vetunia Chiroiu
  • Ligia Munteanu
  • Cristian Rugina
  • Dan Dumitriu
  • Dan Dumitriu
  • Pier Paolo Delsanto


dynamic optimization, multilayer film, full band-gap


The multilayer films are consisted of alternating layers of material with different mechanical properties, following a triadic Cantor sequence. The extremely low thresholds for subharmonic generation of ultrasonic waves has a significant importance in the generation of the full band-gaps due to the nonlinear coupling between the extended-mode (phonon) and the localized-mode (fracton) vibration regimes. In this paper, the optimization is performed with respect to most important features of sonic composites, such as the localized modes around interfaces and the size of the full band-gaps. The case of a relevant uncertainty of the design parameters which may change over frequency is taken into consideration. Uncertain parameters are related to the local band-gaps and boundary conditions where the displacement and the traction vectors can be discontinuous. Maximizing the full band-gaps is taken as the objective function, while the constant volume of the structure is taken as the constraint. The results show an unexpected influence of discontinuities upon the generation of the full band-gaps.


MIETTINEN, J., Nonlinear Multiobjective Optimization, Springer-Verlag, 1999.

HWANG, C-L., MASUD, A.S.M., Multiple objective decision making, methods and applications: A state-of-the-art survey, Springer-Verlag, 1979.

TRAPANI, G., KIPOUROS, T., SAVILL, A.M., The design of multi-element airfoils through multi-objective optimization techniques, CMES: Computer Modeling in Engineering & Sciences, 88, 2, pp. 107–140, 2012.

KAFESAKI, M., ECONOMOU, E.N., Interpretation of the bandstructure results for elastic and acoustic waves by analogy with the LCAO approach, Phys. Rev. B, 52, 18, pp. 13317–13331, 1995.

PSAROBAS, I.E., STEFANOU, N., MODINOS, A., Scattering of elastic waves by periodic arrays of spherical bodies, Phys. Rev. B, 62, 1, pp. 278–291, 2000.

MARTÍNEZ-SALA, R., SANCHO, J., SÁNCHEZ, J.V., GÓMEZ, V., LLINARES, J., MESEGUER, F., Sound attenuation by sculpture, Nature, 378, p. 241, 1995.

HIRSEKORN, M., DELSANTO, P.P., BATRA, N.K., MATIC, P., Modelling and simulation of acoustic wave propagation in locally resonant sonic materials, Ultrasonics, 42, 1, pp. 231–235, 2004.

JOANNOPOULUS, J.D., JOHNSON, S.G., WINN, J.N., MEADE, R.D., Photonic Crystals. Molding the Flow of Light, Princeton University Press, 2008.

MIYASHITA, T., TANIGUCHI, R., SAKAMOTO, H., Experimental full band-gap of a soniccrystal slab structure of a 2D lattice of aluminum rods in air, Proc. 5th World Congress on Ultrasonics TO-PM04.02, 2003.

MIYASHITA, T., Full band gaps of sonic crystals made of acrylic cylinders in air-numerical and experimental investigations, Jpn. J. Appl. Phys. 41, 5S, p. 3170.

GOFFAUX, C., SANCHEZ-DEHESA, J., Two-dimensional phononic crystals studied using a variational method: application to lattices of locally resonant materials, Phys. Rev. B, 67, 14, p. 144301, 2003.

GOFFAUX, C., MASERI, F.,VASSEUR, J.O., DJAFARI-ROUHANI, B., LAMBIN, P., Measurements and calculations of the sound attenuation by a phononic band gap structure suitable for an insulating partition application, Appl. Phys. Lett., 83, 2, pp. 281–283, 2003.

GUPTA, B.C., YE, Z., Theoretical analysis of the focusing of acoustic waves by two-dimensional sonic crystals, Phys. Rev. E., 67, 3, p. 036603, 2003.

LIU, Z., ZHANG, X., MAO, Y., ZHU, Y.Y., YANG, Z., CHAN, C.T., SHENG, P., Locally resonant sonic materials, Science, 289, 5485, pp. 1734–1736, 2000.



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