基于Chebyshev展开的区间穿孔板超材料分析

目前对于声学超材料的传输特性分析和优化大多是基于确定的数值和确定的模型,然而在实际工程和结构设计中存在大量材料自身特性和几何物理参数的不确定性.如果忽略这些不确定变量对声学超材料传输特性分析和优化过程的影响,得到的结果可能不正确.针对这一现状,拟将切比雪夫区间模型引入多层穿孔板超材料,提出多层穿孔板超材料声学透射率的区间切比雪夫展开-蒙特卡洛模拟法(interval Chebyshev expansionMonte Carlo simulation method,ICE-MCSM).该方法采用截断切比雪夫多项式近似拟合多层穿孔板超材料的声学透射率响应曲线,构造声学透射率响应曲线的切比雪夫代理模型;然后采用蒙特卡洛模拟法(Monte Carlo simulation method,MCSM)随机生成一定数量的不确定区间变量的样本数据点,并将生成的不确定区间变量样本数据点代入切比雪夫代理模型,预测单个不确定区间变量和多个不确定区间变量条件下的多层穿孔板超材料声学透射率区间的上界和下界.数值分析结果表明,ICE-MCSM预测的声学透射率变化区间的上界和下界与直接蒙特卡洛法(direct Monte Carlo simulation method,DMCSM)预测的声学透射率上界和下界的结果非常接近.与DMCSM相比,ICE-MCSM具有更高的计算效率.因此,ICE-MCSM可有效且高效地分析不确定区间变量条件下多层穿孔板超材料声学透射率传输特性,具有良好的工程应用前景.

THE INTERVAL ANALYSIS OF MULTILAYER-METAMATERIALS WITH PERFORATED APERTURES BASED ON CHEBYSHEV EXPANSION 1)

Up to now, the response analysis and optimization of acoustic metamaterials are mostly based on deterministic parameters and deterministic models.However, in the real engineering world and structure design fields where there are many uncertainties, such as the uncertain of material properties and geometric parameters.If the effects of uncertain variables on analysis and optimization of acoustic metamaterials are not taken into account, the analysis and optimization results may not true.Aiming at this problem and situation, in this paper where the interval model is introduced into multilayer-metamaterials with perforated apertures, and interval Chebyshev expansion-Monte Carlo simulation method (ICE-MCSM) of multilayer-metamaterials with perforated apertures for transmission characteristic is proposed.In ICE-MCSM, truncated Chebyshev polynomials is applied to surrogate the transmittance of multilayer-metamaterials with perforated apertures;therefore, the surrogate model of transmittance is constructed.The samples of interval variables are produced by Monte Carlo method, then the values of these samples are substituted into the surrogate model of transmittance to predict the interval bounds of multilayer-metamaterials with perforated apertures under single-interval variable and multi-interval variables.The results of numerical analysis show that the upper interval bounds and lower interval bounds calculated by ICE-MCSM match the response yields by direct Monte Carlo simulation method (DMCSM).Compared to DMCSM, ICE-MCSM achieves a higher accuracy in interval bound analysis, so ICE-MCSM can effectively and efficiently analyze the interval bounds of multilayer-metamaterials with perforated apertures under uncertain interval variables.Thus, this proposed method in this paper can have promising prospects in real world engineering applications.