基于首次穿越破坏的TMD体系频域可靠性分析

为了研究可靠度的频域特性及TMD(tuned mass damper)体系减震特性,基于首次穿越破坏准则,推导了结构在随机激励下关于谱矩截止频率的概率分布计算公式,采用向前差分方法求解关于频域的概率密度,利用概率分布计算公式分析了TMD结构体系可靠度的频域概率信息.结果表明:可靠度的频域概率密度为负值,且随着频带变宽频域可靠度趋近于直接按照首次穿越破坏准则的计算值;结构无控时前两阶频率处的可靠度下降比例为59.23%和35.45%, TMD结构体系的相应比例为34.54%和55.92%,从频域可靠度的角度表明了TMD结构体系主要控制一阶振型,并体现了减震的可靠性. 

Frequency-Domain Reliability Analysis of Tuned Mass Damper System by First-Passage Theory

In order to investigate the frequency-domain characteristic of reliability and the damping performance of a tuned mass damper (TMD) system, the probability distribution formula about the spectral moment of cut-off frequency of a structure under random excitations is derived based on the first-passage failure criterion, and the frequency-domain probability density is solved using the forward difference scheme. Then, the frequency-domain probability information of the TMD system is also analyzed by the above method. The results show that the frequency-domain probability density is negative, and the frequency-domain probability tends to the value calculated by the first-passage failure criterion as the frequency band increases. For a structure without control, the percentage of the reliability reduction at the first two mode frequencies are 59.23% and 35.45%, respectively, while counterparts of the TMD system are 34.54% and 55.92%. The frequency-domain reliability analysis reveals that the TMD system has a reliable damping effect, mainly by controlling the first mode vibration of the structure.