钢框架的瑞利阻尼与模态阻尼矩阵叠加以及高模态贡献评估

IF 1.7 4区 工程技术 Q3 ENGINEERING, CIVIL
Mario D. Llanes-Tizoc, Federico Valenzuela-Beltrán, Edén Bojórquez, Juan Bojórquez, José R. Gaxiola-Camacho, Jesus M. Leal-Graciano, Robespierre Chavez-López, Alfredo Reyes-Salazar
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引用次数: 0

摘要

在钢结构建筑的抗震分析中,通常采用瑞利阻尼来建立阻尼矩阵 (CR),其中初始刚度 (Ki) 和总质量 (ML) 矩阵以及前两个侧向振动模式通常都会用到。此外,在非线性动力平衡方程中使用 ML 也是一种普遍做法。同样,与旋转和关节垂直位移(JR-VD)相关的较高模态对响应的贡献通常也被忽略。本研究探讨了与这些做法相关的一些问题,将使用 CR 得出的结果与使用模态阻尼矩阵叠加(MDMS)程序等更精确模型得出的阻尼矩阵(CM)的结果进行对比,并将 ML 得出的响应与一致质量矩阵(MC)的响应进行对比。我们使用了三种钢结构建筑模型,分别为低层、中层和高层建筑。如果采用 CR,与 MDMS 程序得出的结果相比,轴向荷载、弯矩、漂移和层间剪力平均分别被低估了 42%、23%、22% 和 20%;水平阻尼力被高估了 232%。对于轴向荷载,JR-VD 模式的贡献率可达 41%,对于弯矩、层间剪力和漂移,JR-VD 模式的贡献率可达 20%。如果使用 ML 和 Ki,与 MC 和切线刚度矩阵 (Kt) 相比,轴向荷载的平均高估率高达 80%;相反,弯矩和层间剪力的低估率分别高达 24% 和 16%。因此,应使用 CM、Kt 和 MC 矩阵;不应忽视 JR-VD 模式的贡献;如果使用 CR,为提高精度,必须考虑模式 1 和大于模式 2 的模式,以获得瑞利阻尼矩阵。否则可能导致非保守设计。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Rayleigh Damping vs. Modal Damping Matrix Superposition for Steel Frames and Evaluation of Higher-Mode Contribution

Rayleigh Damping vs. Modal Damping Matrix Superposition for Steel Frames and Evaluation of Higher-Mode Contribution

Rayleigh damping is usually adopted in seismic analysis of steel buildings to develop the damping matrix (CR), where the initial stiffness (Ki) and the lumped mass (ML) matrices, and the first two lateral vibration modes are often used. Additionally, it is a widespread practice to use ML in the nonlinear dynamic equilibrium equation. Similarly, the contributions to the response of higher modes related to rotations and vertical displacement of joints (JR-VD) are generally ignored. In this study, some issues related to these practices are addressed, contrasting the results obtained through the use of CR with those of a damping matrix (CM) obtained with a more accurate model as that of modal damping matrix superposition (MDMS) procedure, and by comparing the responses derived from ML with those of the consistent mass matrix (MC). Three steel building models are used, which are considered low, medium and high height. If CR is adopted, axial loads, bending moments, drifts, and interstory shears are underestimated, on average, by up to 42%, 23%, 22% and 20%, respectively, compared to the results obtained with the MDMS procedure; the horizontal damping forces are overestimated by up to 232%. The contribution of the JR-VD modes can be up 41% for axial loads and up to 20% for bending moments, interstory shears and drifts. If ML and Ki are used, average overestimations of up to 80% are observed for axial loads with respect to those of MC and the tangent stiffness matrix (Kt); bending moments and interstory shears, in contrast, can be underestimated by up to 24% and 16%, respectively. Hence, the CM, Kt and MC matrices should be used; the contributions of the JR-VD modes should not be overlooked; and if CR is used, to increase the accuracy, mode 1 and a mode greater than the second must be considered to obtain the Rayleigh damping matrix. Failure to do so may result in non-conservative designs.

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来源期刊
CiteScore
3.30
自引率
11.80%
发文量
203
期刊介绍: The aim of the Iranian Journal of Science and Technology is to foster the growth of scientific research among Iranian engineers and scientists and to provide a medium by means of which the fruits of these researches may be brought to the attention of the world’s civil Engineering communities. This transaction focuses on all aspects of Civil Engineering and will accept the original research contributions (previously unpublished) from all areas of established engineering disciplines. The papers may be theoretical, experimental or both. The journal publishes original papers within the broad field of civil engineering which include, but are not limited to, the following: -Structural engineering- Earthquake engineering- Concrete engineering- Construction management- Steel structures- Engineering mechanics- Water resources engineering- Hydraulic engineering- Hydraulic structures- Environmental engineering- Soil mechanics- Foundation engineering- Geotechnical engineering- Transportation engineering- Surveying and geomatics.
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