声学黑洞（Acoustic Black Hole ,简称 ABH）效应已被证明是一种潜在的振动控制和能量收集方法，但由于其局部厚度小，面临结构强度问题。本文针对ABH板结构，采用解析法建立了随机激励下ABH板振动疲劳寿命预测的解析模型。基于假设振型法，推导了ABH板的应力频响函数，在考虑随机激励的基础上，得到了结构的随机振动位移功率谱密度（Power Spectral Density,简称PSD）函数。同时基于遗传算法对材料AL6061进行了P-S-N曲线估计。另外，采用COMSOL与MATLAB软件对模型及其预测结果的正确性进行了验证，研究发现两者的固有频率偏差仅为0.11%,且位移PSD精度也十分吻合。疲劳寿命分析表明，截断厚度h_0越小和黑洞半径r_abh越大，ABH效应越好，但寿命也越小。
Abstract
The acoustic black hole (ABH) effect has been shown to be a potential method for vibration control and energy harvesting. However, it faces structural strength problems due to its small localized thickness. In this paper, for the acoustic black hole plate structure, an analytical model for vibration fatigue life prediction of acoustic black hole plate under random excitation is developed by using analytical method. Based on the assumed vibration mode method, the stress frequency response function of the acoustic black hole plate is derived, and the random vibration displacement power spectral density function of the structure is obtained based on the consideration of random excitation. The P-S-N curve of the material AL6061 was also estimated based on the genetic algorithm. In addition, the correctness of the model and its prediction results were verified by using COMSOL and MATLAB software, and it was found that the intrinsic frequency deviation of the two was only 0.11%, and the accuracy of the displacement PSD was in good agreement. The fatigue life analysis shows that the smaller the truncated thickness h_0 and the larger the black hole radius〖 r〗_abh, the better the ABH effect but also the smaller the life.
关键词
声学黑洞板 /
随机激励 /
P-S-N曲线 /
疲劳寿命预测
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Key words
Acoustic black hole plate /
random excitation /
P-S-N curve /
fatigue life prediction
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