The kurtoses of stress responses have significant influences on the fatigue life of in-service structures. To estimate the potential fatigue damage based on excitation information, the kurtoses transmission through linear structures have been studied. However, much of the research up to now has been restricted on the single-input dynamic models. The transmission of kurtosis from multiple input forces to stress responses is rarely examined, particularly the role of input correlation in this process. To address this gap, the paper proposes a mathematical model of response kurtoses of a dynamic system under multiple stationary non-Gaussian excitations. High-order spectrum theory is employed and extended to estimate both the raw and the mixed moments of response components. Based on the moment estimation method, the response kurtosis is formulated with inputs and system parameters. To verify the model, several numerical examples are provided. The kurtoses transmission evolution brought by the input correlation situations is investigated with the examples. The study finds that setting the phase of the cross-power spectral density of multi-excitation forces to zero can slightly increase the kurtosis of the response, while adjusting the coherence coefficient of the cross-power spectral density of the excitation forces can significantly alter the kurtosis of the response. As the structural damping decreases, the adjustment effect of phase and coherence coefficient on the kurtosis of structural response will weaken. Finally, an experiment is carried out for a further verification on a cantilever beam. Both the numerical and the experimental examples show that the proposed mathematical model is feasible and of high accuracy.

中文翻译：

---

使用高阶谱方法研究线性结构在多重相关平稳非高斯随机载荷下的峰度传递


应力响应的峰度对在用结构的疲劳寿命有显着影响。为了根据激励信息估计潜在的疲劳损伤，研究了通过线性结构的峰度传输。然而，迄今为止的大部分研究都仅限于单输入动态模型。很少研究峰度从多个输入力到应力响应的传递，特别是输入相关性在此过程中的作用。为了解决这一差距，本文提出了多个稳态非高斯激励下动态系统响应峰度的数学模型。采用并扩展高阶谱理论来估计响应分量的原始矩和混合矩。基于矩估计方法，响应峰度由输入和系统参数制定。为了验证该模型，提供了几个数值示例。并结合算例研究了输入相关情况所带来的峰度传输演化。研究发现，将多激振力互功率谱密度的相位设置为零可以略微增加响应的峰度，而调整激振力互功率谱密度的相干系数可以显着改变响应的峰度。响应的峰度。随着结构阻尼的减小，相位和相干系数对结构响应峰度的调节作用会减弱。最后通过悬臂梁实验进行进一步验证。数值算例和实验算例均表明所提出的数学模型是可行的且具有较高的精度。