周期性高斯结构薄板的隔声降噪研究

发布时间：2018-06-04 23:32

本文选题：周期性复合结构 + 禁带　；参考：《湖南大学》2014年硕士论文

【摘要】：本文在讨论了周期性复合材料现有基本理论和研究方法的基础上，提出了一种新的周期性材料，并研究了这种周期性高斯结构薄板的禁带特性和隔声降噪性能，对其禁带进行了优化，寻求最低频带隙最宽时薄板的结构参数，，探究其用于工程结构中振动噪声控制的可行性。主要研究内容包括：利用本征模式匹配法计算了周期性高斯结构薄板的能带结构，并且采用有限元法对能带结构进行了验证，发现两种不同方法计算得出的结果吻合得较好，而用有限元法计算的传输谱进一步验证了本征模式匹配法的合理性与准确性。当把薄板中的高斯结构替换成同面积同高度的长方形时，本文提出的结构能产生更宽的低频带隙。从另一种理论的角度，采用“弹簧—质量”方法估算了两种结构的低频带隙，比较得出，周期性高斯机构薄板产生的低频带隙更宽，从而验证了以上发现。此外，本文发现当结构中高斯区域的高度、薄板厚度以及填充率三个几何参数变化时，能带结构将会发生显著的变化。由此，探究了当三个参数在一定范围内渐变时，能带结构中最低的三条带隙的变化情况，旨在寻找能够发挥更好的隔声降噪功能的结构，它应当具有较宽的低频带隙并且该低频带隙有恰当的起始频率与截止频率。此外，优化了周期性高斯结构薄板的最低频带隙，以及周期性长方结构薄板的最低频带隙，目标为带隙最宽。采用的方法为RBF径向基函数、拉丁超立方采样和遗传算法。最终，本文提出结构的最宽低频带隙优化值为0.1523MHz，真实值为0.1501MHz，而周期性长方结构薄板的最宽低频带隙优化值为0.1604MHz，真实值为0.1553MHz。两种结构的优化值与真实值之间的误差均不大于5%，这证明优化结果是正确可靠的，并且，利用RBF径向基函数及遗传算法对低频带隙进行优化也是比较准确的。
[Abstract]:On the basis of discussing the basic theories and research methods of periodic composite materials, this paper presents a new periodic material, and studies the forbidden band characteristics and noise reduction and noise reduction performance of this periodic Gauss structure sheet, optimizes the band gap and seeks the structural parameters of the thin plate with the widest band gap, and explores its application. The feasibility of vibration and noise control in engineering structures is discussed.
The energy band structure of the periodic Gauss structural plate is calculated by the eigenmode matching method, and the finite element method is used to verify the energy band structure. It is found that the results calculated by the two different methods are in good agreement, and the transmission spectra calculated by the finite element method further verify the rationality and accuracy of the eigenmode matching method. When the Gauss structure in a thin plate is replaced with a same area of same height, the structure proposed in this paper can produce a wider low frequency band gap. From the point of view of another theory, the "spring mass" method is used to estimate the low frequency band gap of the two structures. It is found that the low frequency band gap produced by the periodic Gauss mechanism thin plate is more wide, thus the testing of the low frequency band gap is obtained. In addition, it is found that when the height of the Gauss region, the thickness of the plate and the three geometric parameters of the filling rate are changed in the structure, the band structure will be changed significantly. Thus, the change of the lowest three band gaps in the energy band structure when the three parameters are gradually changed in a certain range is explored in order to find the possible hair. The structure of better sound insulation and noise reduction function should have a wider low frequency band gap and the low frequency band gap has the appropriate starting frequency and cut-off frequency.
In addition, the most low frequency band gap of periodic Gauss structure plate and the lowest band gap of periodic rectangular thin plate are optimized. The aim is the band gap is the most wide. The method is RBF radial basis function, Latin hypercube sampling and genetic algorithm. Finally, the optimum value of low frequency band gap is 0.1523MHz, and the true value is 0.1501MHz The optimum value of the maximum low frequency band gap of the periodic rectangular plate is 0.1604MHz, and the error between the real value and the real value of the two structures of 0.1553MHz. is not more than 5%, which proves that the optimization results are correct and reliable, and it is also more accurate to optimize the low frequency band gap by using the RBF radial basis function and genetic algorithm.
【学位授予单位】：湖南大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TB535

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