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浙江大学学报(工学版)  2017, Vol. 51 Issue (7): 1284-1290    DOI: 10.3785/j.issn.1008-973X.2017.07.003
土木工程     
瑞利阻尼物理本质及参数对动力响应的影响
胡成宝1,2, 王云岗3, 凌道盛1,2,4
1. 浙江大学 岩土工程研究所, 浙江 杭州 310058;
2. 浙江大学 软弱土与环境土工教育部重点实验室, 浙江 杭州 310058;
3. 浙江大学城市学院 工程学院, 浙江 杭州 310015;
4. 浙江大学宁波理工学院 土木建筑工程学院, 浙江 宁波 315100
Physical essence and influence of model parameters on dynamic response of Rayleigh damping
HU Cheng-bao1,2, WANG Yun-gang3, LING Dao-sheng1,2,4
1. Institute of Geotechnical Engineering, Zhejiang University, Hangzhou 310058, China;
2. MOE Key Laboratory of Soft Soils and Geoenvironmental Engineering, Zhejiang University, Hangzhou 310058, China;
3. School of Engineering, Zhejiang University City College, Hangzhou 310015, China;
4. School of Civil Engineering and Architecture, Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China
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摘要:

为了研究瑞利阻尼模型的物理意义及模型参数对动力响应的影响,基于虚功方程推导瑞利阻尼的质量相关部分和刚度相关部分,利用解析和数值方法对比分析不同瑞利阻尼系数下的一维黏弹性杆件的动力响应.结果表明,瑞利阻尼质量相关部分反映了外部环境因素对振动体系的能量耗散作用;刚度相关部分反映了材料对动力响应的阻滞作用,表现为应力不仅与应变有关,而且与应变率相关.一维黏弹性振动响应解析解和有限元数值解对比分析表明,常规有限单元软件应力计算时,没有考虑应变率的贡献,导致计算应力和实际应力存在差异,计算应力不满足力边界条件.有限元应力计算误差随着瑞利阻尼系数和激励频率的增加而提高.

Abstract:

The influences of the physical meaning and model parameters of the Rayleigh damping model on the dynamic response were analyzed. The mass-related and stiffness-related items of Rayleigh damping model were derived based on the virtual work equation. The vibration response of one-dimensional viscoelastic rod with different Rayleigh damping coefficient was analyzed comparatively via analytical and numerical methods. The energy dissipation phenomenon caused by external environments can be reflected by mass-related section, while material's blocking effects on dynamic response can be reflected by stiffness-related item. The blocking effects mentioned above indicate that strain rate should be included in stress calculation except the strain item. Analytical and numerical methods were employed to analyze the vibration response of one-dimensional viscoelasticity. The comparison results show that numerical solutions differ with analytical ones in stress calculation, and the former without considering the contribution of strain rate to stress calculation can't meet the force boundary condition. The errors of stress calculated by the finite element method increase with the rise of Rayleigh damping coefficient and the exciting frequency.

收稿日期: 2016-06-03 出版日期: 2017-07-08
CLC:  TU435  
基金资助:

国家“973”重点基础研究发展规划资助项目(2014CB047005);国家自然科学基金资助项目(51578502,51278451);国家重点研发计划资助项目(2016YFC0800200);浙江省自然科学基金面上项目(LY12E08011)

通讯作者: 凌道盛,男,教授.ORCID:0000-0002-0604-1175.     E-mail: dsling@zju.edu.cn
作者简介: 胡成宝(1990—),男,博士生,从事土动力学的研究.ORCID:0000-0002-4908-8790.E-mail:11412027@zju.edu.cn
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引用本文:

胡成宝, 王云岗, 凌道盛. 瑞利阻尼物理本质及参数对动力响应的影响[J]. 浙江大学学报(工学版), 2017, 51(7): 1284-1290.

HU Cheng-bao, WANG Yun-gang, LING Dao-sheng. Physical essence and influence of model parameters on dynamic response of Rayleigh damping. JOURNAL OF ZHEJIANG UNIVERSITY (ENGINEERING SCIENCE), 2017, 51(7): 1284-1290.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2017.07.003        http://www.zjujournals.com/eng/CN/Y2017/V51/I7/1284

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