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[1] Chen Yong, Donald M. McFarland, Billie F. Spencer, et al. Improved complex modal superposition methodwith inclusion of overdamped modes [J]. Journal of Southeast University (English Edition), 2023, 39 (3): 213-224. [doi:10.3969/j.issn.1003-7985.2023.03.001]
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Improved complex modal superposition methodwith inclusion of overdamped modes()
考虑过阻尼模态参与的改进复模态叠加法
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
39
Issue:
2023 3
Page:
213-224
Research Field:
Civil Engineering
Publishing date:
2023-09-20

Info

Title:
Improved complex modal superposition methodwith inclusion of overdamped modes
考虑过阻尼模态参与的改进复模态叠加法
Author(s):
Chen Yong1, 2, Donald M. McFarland3, 4, Billie F. Spencer, Jr.2, Lawrence A. Bergman3
1College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310027, China
2Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana 61801, USA
3Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, Urbana 61801, USA
4College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou 310014, China
陈勇1, 2, Donald M. McFarland3, 4, Billie F. Spencer, Jr.2, Lawrence A. Bergman3
1浙江大学建筑工程学院, 杭州 310027; 2Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana 61801, USA; 3Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, Urbana 61801, USA; 4浙江工业大学机械工程学院, 杭州 310014
Keywords:
nonclassically damped system;  continuous system;  forced vibration;  complex mode superposition method;  overdamped mode;  dynamic response
非经典阻尼系统;  连续系统;  强迫振动;  复模态叠加法;  过阻尼模态;  动力响应
PACS:
TU311.3
DOI:
10.3969/j.issn.1003-7985.2023.03.001
Abstract:
To address the involvement of overdamped complex modes that appear in a nonproportionally damped system, an improved complex mode superposition(ICMS)theory is proposed for forced vibration analysis, which suggests the use of exact modes in pairs for CMS-based dynamic analysis of whether the modes are overdamped or not. A typical nonproportionally damped system, namely, a cantilever beam with attached multiple arbitrarily placed external dampers, is considered an example because the first mode of the system is likely to be overdamped with the increase in damping. First, the relationship between the response in a complex modal space and the actual dynamic response is elucidated, based on which complete theoretical ICMS approaches for attaining time-domain response, transfer functions, and variances are expounded in detail. By decomposing the governing equation into real and imaginary parts, the original equation of motion in the complex domain is represented by an augmented state-space equation with real-valued matrices, which considerably reduces the difficulties observed in computing the time-varying response using complex-valued matrices. Additionally, for external excitations that can be regarded as filtered white noise, an efficient method for evaluating the variance response is proposed, which effectively reduces the computational cost. The results from the application of the proposed CMS-based methods are compared with those obtained by an assumed-mode(AM)method and finite element analysis(FEA). It can be found that the current results are closer to those obtained by FEA than those by the AM method. Finally, the optimal damping and optimal position of the dampers are investigated using an enumeration method, which reveals that the use of multiple dampers with small damping demonstrates a better effect than that of a single damper with large damping.
为处理非比例阻尼系统可能出现的过阻尼模态, 提出了一种改进的复模态叠加强迫振动分析方法, 建议无论模态是否过阻尼, 复模态振动分析时应成对使用复模态.以一个连接任意布置外部阻尼器的悬臂梁典型非比例阻尼系统为例, 其第1阶模态会随阻尼系数的增加而过阻尼.在厘清复模态响应与实际动力响应关系的基础上阐述了采用改进复模态叠加法获得时域响应、传递函数和方差的完整理论方法.将方程分为实部和虚部, 使得原复数域运动方程成为基于实数矩阵的增广状态空间方程, 从而克服了采用复数矩阵计算时变响应的困难.此外, 针对基于白噪声滤波的外部激励, 提出了一种高效方差响应评估方法, 降低了计算资源消耗.结果表明, 相较于假设模态法, 复模态叠加法的结果更接近于有限元结果.基于遍历法研究最优阻尼器参数和位置时, 采用多个小阻尼阻尼器优于单个大阻尼阻尼器.

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Memo

Memo:
Biographies: Chen Yong(1974—), male, Ph.D., professor; Donald M. McFarland(corresponding author), male, doctor, professor, dmmcf@dmmcf.net.
Foundation items: National Science Foundation through TeraGrid Resources provided by the National Center for Supercomputing Applications(No. TG-MSS100016).
Citation: Chen Yong, Donald M. McFarland, Billie F. Spencer, Jr., et al. Improved complex modal superposition method with inclusion of overdamped modes[J].Journal of Southeast University(English Edition), 2023, 39(3):213-224.DOI:10.3969/j.issn.1003-7985.2023.03.001.
Last Update: 2023-09-20