基于Rosenbrock的耦合积分方法及其在实时子结构试验中的应用

Rosenbrock-based coupled time integration method and its application to real-time substructure testing

作为一种集计算机模拟和物理试验于一体的新型混合试验方法,实时子结构试验在过去20年得到迅速发展。该试验方法的关键在于如何保证数值子结构和试验子结构的实时耦联。对于复杂结构来说,更需要高效的数值积分方法以确保每步计算在一个采样步长内完成。鉴于此,本文在Rosenbrock实时积分方法的基础上,提出了一种具有完全并行计算格式的耦合积分方法,并基于单自由度分离质量模型分析了该方法的收敛性;再通过对三自由度分离质量模型的数值模拟,验证了该方法的收敛性;最后,在多自由度试验平台上完成了两自由度结构的实时子结构试验。理论分析、数值模拟及实时子结构试验表明,该方法具有良好的稳定性和2阶精度,与直接积分方法相比更适用于复杂结构的实时子结构试验。

As a hybrid computational-experimental technique,real-time substructure testing（RTST） was under rapid development in the last two decades.The challenge of RTST is to ensure that the numerical substructure and the experimental substructure interact in real time.For complex structures,this requires efficient numerical integration methods in order that the computation of each step completes during a sampling time step.With this in mind,based on the Rosenbrock real-time integrator,a coupled time integration method is proposed,which renders completely parallel computation.By virtue of a Single-DoF split-mass test problem,convergence analysis is performed theoretically for the coupled method.Moreover,numerical simulations of a Three-DoF split-mass system are conducted to validate the convergence of the coupled method.Last but not least,experimental validation of a Two-DoF system is conducted within a framework of Multi-DoF test-rig.The theoretical analyses,the numerical simulations and the experimental results reveal that the method exhibits favourable stability and second order accuracy.With respect to direct time integration methods,the proposed method is more desirable for RTST tests of complicated structures.