基于Chebyshev展开的区间穿孔板超材料分析

发布时间：2018-07-09 10:34

本文选题：超材料 + 声学透射率　；参考：《力学学报》2017年01期

【摘要】：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.
[Abstract]:At present, the analysis and optimization of the transmission characteristics of acoustic supermaterials are mostly based on the determined values and the determined models. However, there are many uncertainties in the properties of the materials and the geometric physical parameters in the actual engineering and structural design. If these uncertain variables are ignored, the analysis and optimization of the transmission characteristics of the acoustic supermaterials are ignored. The results may not be correct. Aiming at this situation, the Chebyshev interval model is introduced into the multilayer perforated plate supermaterial, and the interval Chebyshev expansion Monte Carlo simulation method (interval Chebyshev expansionMonte Carlo simulation method, ICE-MCSM) is proposed for the acoustic transmittance of the multilayer perforated plate supermaterial. The schebyshev polynomial approximated the acoustic transmittance response curve of the multi-layer perforated plate supermaterial and constructed the Chebyshev proxy model of the acoustic transmittance response curve. Then the Monte Carlo simulation (Monte Carlo simulation method, MCSM) was used to generate the sample data points of a certain number of uncertain interval variables. An uncertain interval variable sample data point is replaced by the Chebyshev proxy model to predict the upper and lower boundary of the acoustic transmittance interval of a multi-layer perforated plate supermaterial under the condition of a single uncertain interval variable and multiple uncertain interval variables. The numerical analysis shows that the upper and lower bounds of the range of the acoustic transmittance variation predicted by ICE-MCSM are in the upper and lower bounds. The results are very close to the results of the upper and lower bounds of the acoustic transmittance predicted by the direct Monte C Lofa (direct Monte Carlo simulation method, DMCSM). Compared with the DMCSM, ICE-MCSM has a higher computational efficiency. Therefore, ICE-MCSM can effectively and efficiently analyze the acoustic transmittance transmission of the multi-layer perforated plate supermaterial under the condition of uncertain interval variables. Characteristics and good prospects for engineering applications.
【作者单位】：湖南大学汽车车身先进设计制造国家重点实验室;
【基金】：国家自然科学基金(11402083) 中央高校基本科研业务费资助项目
【分类号】：TB34

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