Journal of Shanghai Jiao Tong University

Journal of Shanghai Jiaotong University >

2021 , Vol. 55 >Issue 6: 672 - 680

DOI: https://doi.org/10.16183/j.cnki.jsjtu.2020.031

Time-Domain Calculation Method of an Equivalent Viscous Damping Model Based on Complex Damping Model

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  • 1. School of Civil Engineering, Chongqing University, Chongqing 400045, China
    2. Key Laboratory of New Technology for Construction of Cities in Mountain Area of the Ministry of Education, Chongqing University, Chongqing 400045, China
    3. School of Traffic and Engineering, Shenzhen Institute of Information Technology, Shenzhen 518172, Guangdong, China

Received date: 2020-01-27

  Online published: 2021-06-08

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Abstract

The damping matrix of the complex damping model is easy to be constructed, which only depends on the material loss factor and the structural stiffness matrix. However, the complex damping model has some shortcomings, such as time-domain divergence and causality. Structural inherent characteristics are constant, so that the equivalent relationship between material loss factor and structural damping ratio is deduced and the viscous damping model which is equivalent to complex damping model is obtained. The proposed damping model overcomes the shortcoming of the complex damping model. Besides, the convenience that the complex damping model is directly dependent on material loss factor is retained. According to the equivalent relationship between the material loss factor and structural modal damping ratio, the real mode superposition method based on the proposed damping model is suggested for the proportional damping system. For the non-proportional damping system, according to the equivalent relationship between the material loss factor and modal damping ratio of the substructure, the complex mode superposition method based on the proposed damping model is proposed by the aid of Rayleigh damping and the state space method. The example analysis proves the feasibility and correctness of the proposed method.

Key words： complex damping; viscous damping; equivalent; loss factor; modal damping ratio

Cite this article

SUN Panxu, YANG Hong, ZHAO Zhiming, LIU Qinglin . Time-Domain Calculation Method of an Equivalent Viscous Damping Model Based on Complex Damping Model[J]. Journal of Shanghai Jiaotong University, 2021 , 55(6) : 672 -680 . DOI: 10.16183/j.cnki.jsjtu.2020.031

References

[1] 吴泽玉, 王东炜, 李玉河. 复阻尼结构动力方程的增维精细积分法[J]. 振动与冲击, 2017, 36(2):107-110.
[1] WU Zeyu, WANG Dongwei, LI Yuhe. Magnified dimension precise integration method for the dynamic equations of complex damped structures[J]. Journal of Vibration and Shock, 2017, 36(2):107-110.
[2] 张辉东, 王元丰. 空间网壳结构的节点-构件阻尼模型研究[J]. 土木工程学报, 2015, 48(2):54-62.
[2] ZHANG Huidong, WANG Yuanfeng. Investigation of a joint-member damping model for single-layer latticed domes[J]. China Civil Engineering Journal, 2015, 48(2):54-62.
[3] 曹树谦, 张文德, 萧龙翔. 振动结构模态分析: 理论、实验与应用[M]. 天津: 天津大学出版社, 2001.
[3] CAO Shuqian, ZHANG Wende, XIAO Longxiang. Modal analysis of vibrational structure: Theory, experiment and application[M]. Tianjin: Tianjin University Press, 2001.
[4] BERT C W. Material damping: An introductory review of mathematic measures and experimental technique[J]. Journal of Sound and Vibration, 1973, 29(2):129-153.
[5] 朱敏, 朱镜清. 逐步积分法求解复阻尼结构运动方程的稳定性问题[J]. 地震工程与工程振动, 2001, 21(4):59-62.
[5] ZHU Min, ZHU Jingqing. Studies on stability of step-by-step methods under complex damping conditions[J]. Earthquake Engineering and Engineering Vibration, 2001, 21(4):59-62.
[6] NAKAMURA N. Practical causal hysteretic damping[J]. Earthquake Engineering & Structural Dynamics, 2007, 36(5):597-617.
[7] YANG F Y, ZHI X D, FAN F. Effect of complex damping on seismic responses of a reticulated dome and shaking table test validation[J]. Thin-Walled Structures, 2019, 134:407-418.
[8] REGGIO A, ANGELIS M. Modelling and identification of structures with rate-independent linear damping[J]. Meccanica, 2015, 50(3):617-632.
[9] WANG J. Rayleigh coefficients for series infrastructure systems with multiple damping properties[J]. Journal of Vibration and Control, 2015, 21(6):1234-1248.
[10] 李暾, 谢海文, 李创第, 等. 基于谱矩的单自由度复阻尼结构的等效阻尼分析[J]. 广西科技大学学报, 2019, 30(4):6-14.
[10] LI Tun, XIE Haiwen, LI Chuangdi, et al. Equivalent damping of single-degree-of-freedom complex damping structures based on spectral moment[J]. Journal of Guangxi University of Science and Technology, 2019, 30(4):6-14.
[11] 梁超锋. 混凝土材料与结构阻尼测试、增强与表达[D]. 哈尔滨: 哈尔滨工业大学, 2005.
[11] LIANG Chaofeng. Concrete material and structural damping test, enhancement and expression[D]. Harbin: Harbin Institute of Technology, 2005.
[12] 梁超锋, 欧进萍. 结构阻尼与材料阻尼的关系[J]. 地震工程与工程振动, 2006, 26(1):49-55.
[12] LIANG Chaofeng, OU Jinping. Relationship between structural damping and material damping[J]. Earthquake Engineering and Engineering Vibration, 2006, 26(1):49-55.
[13] 孙攀旭, 杨红, 吴加峰, 等. 基于频率相关黏性阻尼模型的复模态叠加法[J]. 力学学报, 2018, 50(5):1185-1197.
[13] SUN Panxu, YANG Hong, WU Jiafeng, et al. Complex mode superposition method based on frequency dependent viscous damping model[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(5):1185-1197.
[14] 孙攀旭, 杨红, 刘庆林. 基于复阻尼模型的改进时域计算方法[J]. 湖南大学学报(自然科学版), 2019, 46(11):122-130.
[14] SUN Panxu, YANG Hong, LIU Qinglin. Improved time domain calculation method based on complex damping model[J]. Journal of Hunan University (Natural Sciences) , 2019, 46(11):122-130.
[15] CLOUGH R W, PENZIEN J. Dynamics of structures[M]. 3nd ed. Berkeley, California: Computer and Structures, Inc, 2003.
[16] 欧进萍, 王光远. 结构随机振动[M]. 北京: 高等教育出版社, 1998.
[16] OU Jinping, WANG Guangyuan. Random vibration of structures[M]. Beijing: Higher Education Press, 1998.
[17] 陈华霆, 谭平, 彭凌云, 等. 基于隔震结构Benchmark模型的复振型叠加反应谱方法[J]. 振动与冲击, 2017, 36(23):157-163.
[17] CHEN Huating, TAN Ping, PENG Lingyun, et al. Complex modal shapes superposition response spectrum approach based on vibration isolation structure benchmark model[J]. Journal of Vibration and Shock, 2017, 36(23):157-163.
[18] 陈华霆, 谭平, 彭凌云, 等. 复振型叠加方法合理振型数量的确定[J]. 建筑结构学报, 2020, 41(2):157-165.
[18] CHEN Huating, TAN Ping, PENG Lingyun, et al. Determination of reasonable mode number for complex modal superposition approach[J]. Journal of Building Structures, 2020, 41(2):157-165.
[19] DE DOMENICO D, RICCIARDI G. Dynamic response of non-classically damped structures via reduced-order complex modal analysis: Two novel truncation measures[J]. Journal of Sound and Vibration, 2019, 452:169-190.
[20] 何钟怡. 复本构理论中的对偶原则[J]. 固体力学学报, 1994, 15(2):177-180.
[20] HE Zhongyi. The dual principle in theory of complex constitutive equations[J]. Acta Mechanica Solida Sinica, 1994, 15(2):177-180.
[21] 朱镜清. 关于复阻尼理论的两个基本问题[J]. 固体力学学报, 1992, 13(2):113-118.
[21] ZHU Jingqing. On the two basic problems of complex damping theory[J]. Acta Mechanica Solida Sinica, 1992, 13(2):113-118.
[22] 廖振鹏. 工程波动理论导论[M]. 北京: 科学出版社, 2002.
[22] LIAO Zhenpeng. Introduction to wave motion theories in engineering[M]. Beijing: Science Press, 2002.
[23] LAGE Y, CACHÃO H, REIS L, et al. A damage parameter for HCF and VHCF based on hysteretic damping[J]. International Journal of Fatigue, 2014, 62:2-9.
[24] 潘玉华, 王元丰. 复阻尼结构动力方程的高斯精细时程积分法[J]. 工程力学, 2012, 29(2):16-20.
[24] PAN Yuhua, WANG Yuanfeng. Gauss precise time-integration of complex damping vibration systems[J]. Engineering Mechanics, 2012, 29(2):16-20.
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