| 李骜,陈国海,杨迪雄.随机声子晶体不确定性分析的直接概率积分法[J].计算力学学报,2023,40(5):701~709 |
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| 随机声子晶体不确定性分析的直接概率积分法 |
| Direct probability integral method for uncertainty analysis of stochastic phonon crystals |
| 投稿时间：2023-05-25 修订日期：2023-07-20 |
| DOI：10.7511/jslx20230525006 |
| 中文关键词: 声子晶体 直接概率积分法 可靠度 概率密度函数 带隙特性 |
| 英文关键词:phonon crystals direct probability integral method reliability probability density integral equation bandgap characteristic |
| 基金项目:国家自然科学基金(12032008;12102080)资助项目. |
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| 中文摘要: |
| 由于制造工艺存在大量不确定因素,声子晶体材料属性不可避免地具有随机不确定性,使得声子晶体的物理响应呈现随机性,进而对声子晶体的减振降噪性能造成不利影响。如果采用传统的蒙特卡洛方法对随机声子晶体的物理响应进行不确定性量化,则计算代价昂贵。为此,本文基于高效的直接概率积分法对含随机材料参数的声子晶体开展不确定性量化研究。首先,在直接概率积分法框架下,对随机声子晶体能带结构的上下边界频率、带隙宽度和频率响应函数进行了不确定性量化,考察了随机参数大变异性对声子晶体带隙宽度的影响。然后,建立了声子晶体减振降噪可靠度计算公式,对考虑随机不确定性影响下的声子晶体减振降噪性能进行了定量评估。通过与蒙特卡洛方法比较,两个算例验证了直接概率积分法在随机声子晶体不确定性传播和减振降噪可靠性评估中的准确性和高效性。最后,基于直接概率积分法对局域共振型随机声子晶体进行了可靠度分析。结果表明,橡胶材料的随机性对局域共振型声子晶体减振降噪性能有较大影响。 |
| 英文摘要: |
| Since there exist uncertainty factors in the manufacturing process,the material properties of phononic crystals possess randomness,resulting in the random physical response and affecting the vibration and noise reduction performance of phononic crystals.It is computationally expensive to quantify the uncertainty of the physical responses of phononic crystals by using Monte Carlo simulation (MCS).To this end,based on the efficient direct probability integral method (DPIM),this study examines the uncertainty propagation of phononic crystals with random material parameters.In the context of DPIM,firstly,the uncertainties of the upper and lower edge frequencies,bandgap width of the energy band structure and frequency response function of the random phononic crystals are quantified,and the influences of large variability of random parameters on the band gap width of the phononic crystals are investigated.Then,the computational formula of vibration and noise reduction reliability of the phononic crystal is established,and its performance of vibration and noise reduction considering the random uncertainty is evaluated quantitatively.By comparing the results with those of MCS,two numerical examples demonstrate the accuracy and high efficiency of DPIM for uncertainty quantification and vibration and noise reduction reliability evaluation of the random phononic crystals.Finally,the reliability of locally resonant random phononic crystals is assessed based on DPIM.It is shown that the randomness of rubber material imposes a larger influence on the vibration and noise reduction performance of the locally resonant phononic crystals than others. |
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