区间模型下声子晶体的带隙优化研究

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振动与冲击 ›› 2018, Vol. 37 ›› Issue (17) : 115-121.

论文

区间模型下声子晶体的带隙优化研究

刘坚陈俊煌夏百战满先锋

作者信息 +

Bandgap optimization of photonic crystal based on interval model

LIU Jian CHEN Junhuang XIA Baizhan MAN Xianfeng

Author information +

文章历史 +

摘要

目前对于声子晶体的优化设计都是基于确定性的声学模型。然而不确定性广泛存在于声子晶体，并严重影响其声学性质。针对这一现状，将区间模型引入声子晶体，描述其系统参数的不确定性。接着，采用Chebyshev多项式构建声子晶体能带结构的代理模型，以分析不确定参数对声子晶体带隙的影响。最后，以声子晶体带隙最大化为目标函数，以带隙的变化范围为约束条件，构建基于Chebyshev代理模型的区间声子晶体的可靠性优化模型，并采用遗传算法求解。数值分析结果表明，Chebyshev代理模型能高效且较精确地预测区间模型下声子晶体的带隙变化范围。以Chebyshev代理模型为基础的声子晶体优化模型，在考虑区间不确定性的条件下，最大化带隙的变化范围，极大地改善了声子晶体的声音屏蔽性能。

Abstract

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.

导出引用

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[J]. Journal of Vibration and Shock, 2018, 37(17): 115-121

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