The traditional optimization design of photonic crystal is based on a deterministic acoustic model. However,uncertainties widely exist in photonic crystal and seriously affect its acoustic properties. Here,an interval model was introduced to describe uncertainties of its system parameters. Then,Chebyshev polynomial was employed to construct the surrogate model of energy band structure of photonic crystal to analyze influences of uncertain parameters on photonic crystal’s bandgap. Finally,taking photonic crystal bandgap’s maximization as the objective function,taking bandgap variation range as the constrained condition,the interval photonic crystal reliability optimization model based on Chebyshev surrogate model was constructed. The genetic algorithm was used to solve this optimization model. Numerical results showed that Chebyshev surrogate model can effectively and accurately predict the bandgap variation range of photonic crystal based on the interval model; when interval uncertainties are considered,the optimization model of photonic crystal based on Chebyshev surrogate model can maximize the bandgap variation range to significantly improve the sound shielding performance of photonic crystal.
刘坚 陈俊煌 夏百战 满先锋. 区间模型下声子晶体的带隙优化研究[J]. 振动与冲击, 2018, 37(17): 115-121.
LIU Jian CHEN Junhuang XIA Baizhan MAN Xianfeng. Bandgap optimization of photonic crystal based on interval model. JOURNAL OF VIBRATION AND SHOCK, 2018, 37(17): 115-121.
[1] KUSHWAHA M S, HALEVI P, DOBRZYNSKI L, et al. Acoustic band structure of periodic elastic composites[J]. Physical Review Letters, 1993, 71(13)：2022-2025.
[2] ACHENBACH J D, HERRMANN G. Dispersion of free harmonic waves in fiber-reinforced composites[J]. AIAA Journal, 1968, 6(10)：1832-1836.
[3] LIU Z, ZHANG X, MAO Y, et al. Locally resonant sonic materials[J]. Science, 2000, 289(5485)：1734-1736.
[4] GOFFAUX C, SÁNCHEZ-DEHESA J, YEYATI A L, et al. Evidence of fano-like interference phenomena in locally resonant materials[J]. Physical Review Letters, 2002, 88(22)：225502.
[5] HO K, CHENG C, YANG Z, et al. Broadband locally resonant sonic shields[J]. Applied Physics Letters, 2003, 83(26)：5566-5568.
[6] ZHANG S, HUA J, CHENG J. Experimental and theoretical evidence for the existence of broad forbidden gaps in the three-component composite[J]. Chinese Physics Letters, 2003, 20(8)：1303.
[7] ZHANG S, CHENG J. Existence of broad acoustic bandgaps in three-component composite[J]. Physical Review B, 2003, 68(24)：245101.
[8] HIRSEKORN M. Small-size sonic crystals with strong attenuation bands in the audible frequency range[J]. Applied Physics Letters, 2004, 84(17)：3364-3366.
[9] HIRSEKORN M, DELSANTO P P, BATRA N K, et al. Modelling and simulation of acoustic wave propagation in locally resonant sonic materials[J]. Ultrasonics, 2004, 42(1)：231-235.
[10] ROMERO-GARCÍA V, SÁNCHEZ-PÉREZ J V, GARCÍA-RAFFI L M, et al. Hole distribution in phononic crystals: Design and optimization[J]. The Journal of the Acoustical Society of America, 2009, 125(6)：3774-3783.
[11] WANG Y, WANG Y. Complete bandgap in three-dimensional holey phononic crystals with resonators[J]. Journal of Vibration and Acoustics, 2013, 135(4)：041009.
[12] XIA B, CHEN N, XIE L, et al. Temperature-controlled tunable acoustic metamaterial with active band gap and negative bulk modulus[J]. Applied Acoustics, 2016, 112: 1-9.
[13] MOORE R E. Interval analysis[M]. Englewood Cliffs: Prentice-Hall, 1966.
[14] Edgecombe S, Linse P. Monte Carlo simulation of two interpenetrating polymer networks: Structure, swelling, and mechanical properties[J]. Polymer, 2008, 49(7)：1981-1992.
[15] 夏百战, 覃缘, 于德介, 等. 区间模型下声学超材料的可靠性优化[J]. 机械工程学报, 2016, 52(13).
XIA Baizhan, QIN Yuan, YU Dejie, et al. Reliability-based optimization of the acoustic metamaterial under theinterval model[J]. Chinese Journal of Mechanical Engineering, 2016, 52(13).
[16] 夏百战. 不确定声固耦合系统的数值分析与优化方法研究[D]. 湖南大学, 2015.
XIA Baizhan. A research on the numerical analysis and optimization method for the nondeterministic acoustic-structural coupled system[D]. Hunan University, 2015.
[17] LIU Z, WANG T, LI J. A trigonometric interval method for dynamic response analysis of uncertain nonlinear systems[J]. Science China Physics, Mechanics & Astronomy, 2015, 58(4)：1-13.
[18] XIA B, QIN Y, YU D, et al. Dynamic response analysis of structure under time-variant interval process model[J]. Journal of Sound and Vibration, 2016, 381：121-138.
[19] WU J, LUO Z, ZHANG N, et al. A new uncertain analysis method and its application in vehicle dynamics[J]. Mechanical Systems and Signal Processing, 2015, 50：659-675.
[20] WU J, LUO Z, ZHANG Y, et al. Interval uncertain method for multibody mechanical systems using Chebyshev inclusion functions[J]. International Journal for Numerical Methods in Engineering, 2013, 95(7)：608-630.
[21] 顾秉林，王喜坤. 固体物理学[M]. 北京：清华大学出版社，1997.
[22] 冯端,金国钧著.凝聚态物理学(上)[M]. 北京：高等教育出版社, 2003.
[23] T.J. Rivlin, An Introduction to the Approximation of Functions, Dover, New York, 1981.
[24] WU J, LUO Z, ZHANG Y, et al. An interval uncertain optimization method for vehicle suspensions using Chebyshev metamodels[J]. Applied Mathematical Modelling, 2014, 38(15): 3706-3723.
[25] M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, New York, 1972.
[26] 王艳锋. 含共振单元声子晶体的带隙特性及设计[D]. 北京交通大学, 2015, 6.
WANG Yanfeng. Bandgap properties and design of phononic crystals with resonantunits[D]. Beijing Jiaotong University, 2015, 6.
