机械结构在随机振动载荷的持续作用下易激起自身部分阶模态，从而引发共振导致疲劳破坏，而对其进行寿命估算分析可有效预防结构疲劳失效，具有重要的工程意义。本文区别于传统从概率密度函数出发建立经验模型的振动疲劳寿命估算方法，从功率谱密度分割角度着手，运用理论推导和数值仿真相结合的方法，探讨了功率谱密度共振与非共振区的划分依据，分割形式对损伤估算的影响，并研究了多模态响应之间的耦合效应。结果表明，仅考虑功率谱密度共振区能提高损伤的估算精度，其分割形式对损伤估算并无影响，相较于常用Dirlik法和T-B法，本文多模态耦合损伤估算表达式对随机振动疲劳的损伤估算具有更强的适用性。

In the presence of sustained random vibration loads， mechanical structures easily induce their own partial-order modes， leading to resonance and fatigue failure. Life expectancy analysis effectively prevents structural fatigue failure， exhibiting important engineering significance. Diverging from traditional approaches that establish empirical models based on probability density functions， this study focuses on the power spectral density segmentation. Combining theoretical derivation and numerical simulation， the research explores the dividing criteria for power spectral density resonance and non-resonance regions， investigates the impact of segmentation forms on damage estimation， and explores the coupling effects among multi-modal responses. The results indicate that considering only the power spectral density resonance region enhances damage estimation accuracy. The segmentation form has no effect on damage estimation. The proposed expression for multi-modal coupled damage estimation demonstrates superior applicability to random vibration fatigue compared to commonly used Dirlik and T-B methods.