动力实时子结构试验中心差分法的稳定性

Stability of central difference method for dynamic RST

在实时子结构试验中,如果试件的反力不仅与位移有关,还与速度和加速度有关,那么对拟动力试验而言为显式方法的标准中心差分法变为隐式方法。为了使算法成为显式方法,需要引入速度和加速度的附加假定,这将导致算法的数值性能发生变化。为研究新算法的数值稳定性,在前期工作的理论基础上,针对动力子结构试件进行了试验研究。研究表明:算法的稳定性受试验子结构与数值子结构质量比的影响,且当试验子结构为动力子结构时,只要数值子结构与试验子结构的阻尼均为零,算法就是无条件不稳定的。

In real-time substructure testing （RST）, if the reaction force from the specimen depended not only on the displacement but also on the velocity and acceleration, the central difference method （CDM） which is explicit for PDT turned to be an implicit algorithm. Some extra velocity and acceleration formulations have to be assumed to maintain the advantage over its implicit counterpart. This may change the numerical behavior of the algorithm. The numerical stability issues were investigated through a dynamic RST with a dynamic specimen. The study indicated that the stability of the CDM in RST is affected by the mass ratio of the specimen to the numerical substructure, and the algorithm is unstable when the damping of the whole structure is eoual to zero with the dynamic experimental substructure.