Abstract Dynamic fatigue crack growth (FCG) under chaotic excitations has not yet received due attentions. The current paper presents an analytical model for predicting the FCG in a metallic notched beam subject to external chaotic excitations. The proposed stand-alone analytical model only requires the physical properties of the cracked beam; initial crack conditions; the material constants for the Paris power law; and the time series of the external chaotic excitation. The validity of the analytical model proposed is verified using relevant experimental results from other researchers. The validated model is employed to conduct parametric studies on the coupled field FCG in a notched metallic beam vibrating under external chaotic excitations. The fatigue lives obtained under a group of statistically similar chaotic excitations significantly disperse. The ratio between the maximum and minimum fatigue lives is around 5.2. The ratio remains as high as 2.4, even when only the initial conditions in the chaotic excitations vary. The common practice Palmgren-Miner rule is also used to estimate the fatigue life under chaotic excitations. These predictions differ, by several times, from those provided by the current validated analytical model. Similar shortcomings were noticed in a previous experimental study, where the Palmgren-Miner rule, reportedly, considerably overestimated the fatigue damage under chaotic excitations. In the current study, both under and over-predictions are noted.

中文翻译：

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混沌激励下金属梁耦合场动态疲劳裂纹扩展的分析模型

摘要 混沌激励下的动态疲劳裂纹扩展（FCG）尚未得到应有的重视。目前的论文提出了一种分析模型，用于预测受到外部混沌激励的金属缺口梁中的 FCG。提出的独立分析模型只需要裂纹梁的物理特性；初始裂纹条件；巴黎幂律的物质常数；和外部混沌激励的时间序列。使用其他研究人员的相关实验结果验证了所提出的分析模型的有效性。验证模型用于对在外部混沌激励下振动的带缺口金属梁中的耦合场 FCG 进行参数研究。在一组统计上相似的混沌激励下获得的疲劳寿命显着分散。最大疲劳寿命与最小疲劳寿命之比约为 5.2。即使只有混沌激发中的初始条件发生变化，该比率仍然高达 2.4。常用的 Palmgren-Miner 规则也用于估计混沌激励下的疲劳寿命。这些预测与当前经过验证的分析模型提供的预测存在数倍的差异。在之前的实验研究中也发现了类似的缺点，据报道，Palmgren-Miner 规则大大高估了混沌激励下的疲劳损伤。在当前的研究中，低预测和高预测都被注意到。即使只有混沌激发中的初始条件发生变化。常用的 Palmgren-Miner 规则也用于估计混沌激励下的疲劳寿命。这些预测与当前经过验证的分析模型提供的预测存在数倍的差异。在之前的实验研究中也发现了类似的缺点，据报道，Palmgren-Miner 规则大大高估了混沌激励下的疲劳损伤。在当前的研究中，低预测和高预测都被注意到。即使只有混沌激发中的初始条件发生变化。常用的 Palmgren-Miner 规则也用于估计混沌激励下的疲劳寿命。这些预测与当前经过验证的分析模型提供的预测存在数倍的差异。在之前的实验研究中也发现了类似的缺点，据报道，Palmgren-Miner 规则大大高估了混沌激励下的疲劳损伤。在当前的研究中，低预测和高预测都被注意到。在之前的实验研究中也发现了类似的缺点，据报道，Palmgren-Miner 规则大大高估了混沌激励下的疲劳损伤。在当前的研究中，低预测和高预测都被注意到。在之前的实验研究中也发现了类似的缺点，据报道，Palmgren-Miner 规则大大高估了混沌激励下的疲劳损伤。在当前的研究中，低预测和高预测都被注意到。