Abstract The sectional geometry of sealing strips in an automotive door is generally in shape with a round bulb. It can be simplified to an idealized dual-membrane model to study the vibro-acoustic coupling characteristics. In the present study, a simple sealing model is adopted to investigate the sound insulation of the door seal. Among that, two flexible rectangular thin structures represent rubber layers and one cube represents the air cavity. The cavity mode with two coupling interfaces in the same direction is expressed as a Fourier cosine series with added simple sine-auxiliary function. The coupling frequencies obtained by the method of this paper are verified by literature results. This approach can enrich the vibro-acoustic coupling analysis of combined dual-membrane models. Then, two optimization setups using a modified simulated annealing algorithm are presented. Rubber layer height, layer thickness, the distance between layers are defined as design variables for optimal study on the radiated sound power of the two vibro-acoustic coupling models, in which the radiated sound power is numerically evaluated based on wavelet method. Optimized parameters of the sectional geometry make a corresponding annulus-shape model with significantly improved sound transmission loss. The effects study of sectional geometric parameters on radiated sound power exhibits that combined values of the height and thickness change coupling frequencies while increasing the distance between layers can lower the radiated power. The coupling characteristics explain the enhanced energy transmission in a particular frequency neighborhood. This work will open new avenues for the design of the cross-section shape of automotive bulb seals regarding sound insulation.

中文翻译：

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基于正弦辅助函数的振动声耦合模型的橡胶层和型腔截面几何优化研究

摘要 汽车门密封条的截面几何形状一般为球形。可以简化为理想化的双膜模型来研究振动声耦合特性。在本研究中，采用简单的密封模型来研究门密封件的隔音效果。其中，两个柔性矩形薄结构代表橡胶层，一个立方体代表气腔。具有两个同向耦合界面的腔模表示为傅里叶余弦级数，并添加了简单的正弦辅助函数。本文方法得到的耦合频率经文献结果验证。这种方法可以丰富组合双膜模型的振动声耦合分析。然后，介绍了使用修改的模拟退火算法的两种优化设置。橡胶层高度、层厚、层间距离被定义为优化研究两种振动声耦合模型辐射声功率的设计变量，其中辐射声功率基于小波方法进行数值评估。优化的截面几何参数使相应的环形模型具有显着改善的声音传输损失。截面几何参数对辐射声功率的影响研究表明，高度和厚度的组合值改变耦合频率，同时增加层间距离可以降低辐射功率。耦合特性解释了特定频率邻域中增强的能量传输。