随机激励下声学黑洞梁裂纹疲劳扩展分析  

Crack Fatigue propagation analysis of acoustic black hole beam under random excitation

作　　者：项子建 杜伟奇 邱小彪 戴启雷 XIANG Zijian;DU Weiqi;QIU Xiaobiao;DAI Qilei(School of Mechanical and Electrical Engineering,China University of Mining and Technology,Xuzhou 221000,China;School of Mechanical Engineering and Mechanics,Ningbo University,Ningbo 315211,China;Great Group Company,Ningbo 315211,China;Hwaway Technology Corporation Limited,Zhuji,311800,China)

机构地区：[1]中国矿业大学机电工程学院,江苏徐州221116 [2]宁波大学机械工程与力学学院,宁波315211 [3]宁波更大集团有限公司,浙江宁波315211 [4]华纬科技股份有限公司,浙江诸暨311800

出　　处：《厦门大学学报(自然科学版)》2025年第2期346-352,共7页Journal of Xiamen University:Natural Science

基　　金：浙江省自然科学基金(LQ22A020002);宁波市重点研发项目(2023T013);浙江省省属高校基本科研业务费项目(SJLY2023001)。

摘　　要：[目的]声学黑洞(acoustics black hole,ABH)很薄的局部位置存在结构强度问题,并可能产生裂纹.本文对ABH梁随机振动的裂纹疲劳扩展分析理论进行研究,并对其疲劳寿命进行预测.[方法]采用Paris公式模拟裂纹疲劳的扩展速率,构建裂纹扩展速率与应力范围均方根的关系式;再基于假设振型法建立振动方程,通过应力频响函数推导出应力功率谱密度(power spectral density,PSD),进而计算随机激励下的应力范围均方根.最后将裂纹情况下等效弯曲刚度修正模型带入应力范围均方根,并提出了一种针对ABH梁的随机振动疲劳寿命预测流程.[结果]ABH梁中裂纹相对深度与疲劳寿命基本呈负相关.裂纹位置和ABH结构参数(包括黑洞半径、黑洞阶次和截断厚度)对裂纹疲劳寿命的影响具有明显的非线性特性;此外,增加阻尼能够有效延长裂纹疲劳寿命.[结论]当监测到ABH梁的裂纹时,需根据裂纹的位置和相对深度、黑洞半径、截断厚度等参数预测ABH梁的裂纹疲劳寿命.[Objective]In the thin local area of the acoustic black hole(ABH),structural strength issues exist,and cracks may develop.Herein,we attempt to theoretically analyze the random vibration crack fatigue growth of ABH beams and predicts their fatigue life.[Methods]The Paris formula is used to simulate the crack fatigue growth rate and to establish the relationship between the crack growth rate and the root mean square(RMS)of stress range.Then,the vibration equation is also established based on the assumed mode method,and the stress power spectral density is derived through the stress frequency response function.All these results lead to the computation of the RMS of stress range.Finally,the equivalent bending stiffness correction model under crack conditions is substituted into the RMS of stress range,and a random vibration fatigue life prediction process for ABH beams is proposed.[Results]The correctness of the method is validated by comparing the natural frequencies.The RMS of stress range values of ABH beams and uniform beams are compared,and it is found that the RMS of stress range values of ABH beams significantly exceeds than that of uniform beams,indicating a more obvious local stress concentration effect.Meanwhile,the relative depth of the crack in ABH beams is basically negatively correlated with the fatigue life.Furthermore,the influence of crack location and ABH structural parameters(including black hole radius,black hole order,and truncation thickness)on the crack fatigue life shows obvious nonlinear characteristics.In addition,increasing damping can effectively extend the crack fatigue life.[Conclusion]When cracks are detected in the ABH beam,the fatigue life of the ABH beam needs to be predicted based on parameters such as the location and the relative depth of cracks,the radius of the black hole,as well as the cutoff thickness.

关 键 词：声学黑洞梁 随机振动 裂纹扩展 应力功率谱 寿命预测 

分 类 号：TH113.1[机械工程—机械设计及理论]