考虑模态质量耦合的随机振动准静态载荷计算

针对目前模态质量参与法没有考虑模态质量耦合影响而导致模态密集时随机振动准静态载荷计算出现较大误差，从多自由度振动方程出发，利用模态理论和随机谱理论，分析推导出包含模态质量耦合作用的完全模态质量参与法，分析了耦合项的影响规律。此改进的模态质量参与法可用于计算包括密集模态在内的随机振动准静态载荷，并针对模态频率比大于0.95的密集模态给出简化计算公式。以一个算例验证了密集模态的准静态加速度载荷计算。

Quasi Static Load Computation under Random Vibration Excitation with Consideration of Modal Mass Coupling

The modal mass coupling has not been taken into consideration in the current modal mass participation approach, and it could generate large errors in computation of the quasi-static acceleration for structures with dense modes. To solve this problem, the study is carried out to investigate the affect of modal mass coupling with modal analysis theory and random spectrum analysis theory. Based on the multi-degree vibration equations, the general modal mass participation approach taking the modal mass coupling into account is proposed to calculate the quasi-static acceleration for all structures including the structure with dense modes. The simplified form of the general modal mass participation approach is also given for the dense modes with frequency ratio larger than 0.95. Finally an example is presented to verify the computation of the quasi-static acceleration for the dense modes.