一种新的高斯双模态随机疲劳损伤分析方法

Development of a new frequency-domain method for fatigue damage assessment in bimodal Gaussian random processes

摘要:

为能够准确地对高斯双模态随机过程的疲劳损伤进行评估,提出了一种名为改进频带法的疲劳损伤频域计算方法。该方法从功率谱分割的角度出发,首先分别将低频模态和高频模态的功率谱密度函数分割成很多份极窄的频带,利用损伤等效原则进行等效转换,得到相应的等效窄带过程。然后,将高频等效窄带过程向低频等效窄带过程再次进行等效转换。在此过程中,为考虑低频模态与高频模态之间的相互作用,引入与一个高、低频模态频率比、能量比以及S-N曲线材料参数m有关的修正因子对总零阶谱矩进行修正。最后,利用窄带过程疲劳损伤解析解即可计算高斯双模态过程的总疲劳损伤。以时域雨流计数法计算的疲劳损伤结果作为基准,分别采用理想矩形双模态谱和真实双模态谱进行数值试验,将该方法与多种现有频域疲劳损伤分析方法进行了对比。研究结果表明,提出的改进频带法与传统频域方法相比,具有计算精度更高并且易于编程的优点,该方法在实际工程应用中将具有很大的潜力。

Abstract:

To accurately evaluate the fatigue damage of bimodal Gaussian random process, a new frequency-domain analysis method called as the improved bands method was proposed. The basic idea of the proposed method was developed from the spectral decomposition approach. Firstly, the power spectrum density functions of low-frequency and high-frequency modes were split into a large number of infinitesimal frequency bands. According to the damage equivalence principle, the equivalent conversions were separately performed for the low-frequency and high-frequency components to obtain the corresponding equivalent narrow-band processes. Subsequently, another equivalent conversion from high-frequency equivalent narrow-band process to low-frequency mode was conducted. In order to account for the interaction between the low-frequency and high-frequency modes, a correction factor, which depends on characteristic frequency ratio, energy ratio and material parameter m of the S-N curves, was introduced to modify the summed zero-order spectral moment. When the final equivalent narrow-band process was obtained, the total damage of bimodal Gaussian process could be calculated by the analytical solution of narrow-band fatigue damage. Through numerical tests of ideal rectangular bimodal spectrum and real bimodal spectrum, by taking the fatigue damage estimated by time-domain rain-flow counting method as reference, the accuracy and robustness of the present method was validated against several popular frequency-domain methods. Results showed that the improved bands method is not only more accurate than other traditional frequency-domain methods but also easier to be implemented in computer programming, which also indicates its great potential in actual engineering practice.