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首页> 外文期刊>Earthquake Engineering & Structural Dynamics >Discussion of paper 'Real-time hybrid testing using the unconditionally stable explicit CR integration algorithm' by Cheng Chen, James M. Ricles, Thomas M. Marullo and Oya Mercan,Earthquake Engineering and Structural Dynamics 2009; 38:23-44
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Discussion of paper 'Real-time hybrid testing using the unconditionally stable explicit CR integration algorithm' by Cheng Chen, James M. Ricles, Thomas M. Marullo and Oya Mercan,Earthquake Engineering and Structural Dynamics 2009; 38:23-44

机译：Cheng Chen，James M.Ricles，Thomas M.Marullo和Oya Mercan对论文“使用无条件稳定的显式CR集成算法进行实时混合测试”的讨论，地震工程与结构动力学2009； 38：23-44

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The paper by Chen et al. applies Chen and Ricles integration algorithm (CRM) for real-time hybrid testing, also known as real-time substructure testing. However, an unusual property was found for this algorithm and may limit its application to a system with high frequency modes. In fact, an overshooting effect for a high frequency mode was found and it becomes more significant as the natural frequency increases. To illustrate that the response obtained from CRM algorithm might overshoot the exact solution for a high frequency mode, the free vibration response of a linear elastic SDOF system is computed by using the time steps corresponding to Ω=ω(△t)=l, 10 and 100, where ω is the natural frequency of the system and At is a step size. An initial displacement of d_0= 1 with zero initial velocity is assumed. For comparison, Chang explicit method (CEM) [1,2] and the constant average acceleration method [3] (AAM) are also used to compute the responses and the results are shown in Figure 1. Because the numerical solutions obtained from AAM are exactly the same as those obtained from CEM, only the data points for CEM are plotted in this figure for brevity. It is clear that there is no overshoot in displacement in the complete response for both CEM and AAM while an overshooting effect is generally found for the displacement response obtained from CRM and it becomes significant as the value of Ω increases. This indicates that in a general structural dynamic problem, where the total response is dominated by low frequency modes, the total response might be contaminated or even destroyed by the high frequency responses because of a significant overshooting effect for CRM.
机译：Chen等人的论文。将Chen和Ricles集成算法（CRM）应用于实时混合测试，也称为实时子结构测试。但是，此算法发现了一个不寻常的属性，可能会将其限制在具有高频模式的系统中。实际上，发现了高频模式的过冲效应，并且随着固有频率的增加，过冲效应变得更加明显。为了说明从CRM算法获得的响应可能会超出针对高频模式的精确解，通过使用对应于Ω=ω（△t）= l，10的时间步长来计算线性弹性SDOF系统的自由振动响应和100，其中ω是系统的固有频率，而At是步长。假设初始位移为d_0 = 1，初始速度为零。为了进行比较，还使用了Chang显式法（CEM）[1,2]和恒定平均加速度法[3]（AAM）来计算响应，结果如图1所示。因为从AAM获得的数值解是与从CEM获得的数据完全相同，为简洁起见，在此图中仅绘制了CEM的数据点。显然，对于CEM和AAM来说，在整个响应中都没有位移超调，而通常发现从CRM获得的位移响应有超调效果，并且随着Ω值的增加而变得明显。这表明，在一般的结构动力学问题中，总响应受低频模式支配，由于CRM的明显过冲效应，总响应可能被高频响应污染甚至破坏。

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