考虑非黏性阻尼的黏弹性DDA解法

doi:10.13722/j.cnki.jrme.2016.0582

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摘要

将非黏性阻尼引入到DDA方法中，用以分析非黏性阻尼对于非连续黏弹性结构的影响。首先，将非黏性阻尼引入到块体系统的运动方程中，发现微分形式运动方程难以求解的问题。其次，通过黏弹性结构的力与位移的关系以及Newmark积分方案，推导得到具有对称系数矩阵的含有非黏性阻尼的等价DDA运动方程。最后，结合具体算例，分别分析在恒力作用下和谐振激励作用下的块体位移响应，通过比较DDA计算值和理论值，验证提出的含有非黏性阻尼的黏弹性结构DDA解法的正确性。研究结果表明该考虑非黏性阻尼的DDA方法是一种高效的处理黏弹性问题的解法，这为分析黏弹性结构的非连续变形提供了新思路。

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	赵健1
	肖明1
	杨阳2
	陈俊涛1
	李冬冬1

关键词 ：数值分析, 非黏性阻尼, 黏弹性, DDA

Abstract：

The non-viscous damping is introduced into the DDA method in this article for analysing the influence of non-viscous damping on discontinuous viscoelastic structure. Firstly，the non-viscous damping is introduced into the motion equations of block system，and the difficulty of solving the differential motion equations was found. Secondly，with the relationship between force and displacement and the Newmark integration algorithm，the equivalent DDA motion equations considering non-viscous damping with the symmetrical coefficient matrix was derived. Finally，with specific examples，the block displacement response under constant force or resonant excitation was analyzed，and through comparing DDA calculated value and theoretical value，the correctness of the viscoelastic DDA solution considering non-viscous damping proposed in the article was verified. Thus，the DDA solution considering non-viscous damping is a highly effective method to deal with viscoelastic problem，and it provides a new idea for analysing the discontinuous deformation of viscoelastic structure.

Key words： numerical analysis non-viscous damping viscoelasticity DDA

引用本文:

赵健1，肖明1，杨阳2，陈俊涛1，李冬冬1. 考虑非黏性阻尼的黏弹性DDA解法[J]. 岩石力学与工程学报, 2017, 36(S2): 3799-3807.
ZHAO Jian1，XIAO Ming1，YANG Yang2，CHEN Juntao1，LI Dongdong1. Viscoelastic DDA solution considering non-viscous damping. , 2017, 36(S2): 3799-3807.

链接本文:

https://rockmech.whrsm.ac.cn/CN/10.13722/j.cnki.jrme.2016.0582 或 https://rockmech.whrsm.ac.cn/CN/Y2017/V36/IS2/3799

[1] SHI G H. Discontinuous deformation analysis—A new numerical model for the statics and dynamics of block systems[Ph. D. Thesis][D]. Berkeley：Department of Civil Engineering，University of California，1988.

[2] 王华宁，仲政. 黏弹性岩体中支护圆形洞室施工过程的解析分析[J]. 应用力学学报，2012，29(1)：1–8.(WANG Huaning，ZHONG Zheng. Analytical analysis of supporting circular tunnel construction in viscoelastic rock mass[J]. Chinese Journal of Applied Mechanics，2012，29(1)：1–8.(in Chinese))

[3] 薛琳，杨志法. 关于符合马克斯威尔，鲍埃丁–汤姆逊和H-K 模型的黏弹性岩体的位移反分析原理[J]. 青岛理工大学学报，1988，(1)：82–91.(XUE Lin，YANG Zhifa. The principle of back- analysis from displacements for viscoelastic rock mass represented by Maxwell，Poyting-Thomson and H-K body[J]. Journal of Qingdao Institute of Architecture and Engineering，1988，(1)：82–91.(in Chinese))

[4] 刘学增，朱合华. 考虑动态施工过程的岩土介质横观各向同性黏弹性反分析及其工程应用[J]. 岩土工程学报，2002，24(1)：89–92. (LIU Xuezeng，ZHU Hehua. Back analysis on staged construction in transversely isotropic viscoelastic soil and its application to geotechnical engineering[J]. Chinese Journal of Geotechnical Engineering，2002，24(1)：89–92.(in Chinese))

[5] 付晓东，盛谦，张勇慧. 非连续变形分析方法中的阻尼问题研究[J]. 岩土力学，2015，36(7)：2 057–2 062.(FU Xiaodong，SHENG Qian，ZHANG Yonghui. Damping problem in discontinuous deformation analysis method[J]. Rock and Soil Mechanics，2015，36(7)：2 057–2 062.(in Chinese))

[6] 姜清辉，周创兵，漆祖芳. 基于Newmark积分方案的DDA方法[J]. 岩石力学与工程学报，2009，28(增1)：2 778–2 783.(JIANG Qinghui，ZHOU Chuangbing，QI Zufang. Discontinuous deformation analysis method based on Newmark integration algorithm[J]. Chinese Journal of Rock Mechanics and Engineering，2009，28(增1)：2 778–2 783.(in Chinese))

[7] 刘永茜，杨军. 一种改进步长自调的非连续变形分析法[J]. 岩土力学，2011，32(8)：2 544–2 548.(LIU Yongqian，YANG Jun. An improved DDA method with adaptive step size[J]. Rock and Soil Mechanics，2011，32(8)：2 544–2 548.(in Chinese))

[8] 沈洪宇，段忠东. 非黏滞阻尼系统阻尼系数识别的拉普拉斯域方法[J]. 振动与冲击，2010，29(1)：94–99.(SHEN Hongyu，DUAN Zhongdong. Damping coefficient identification of a non-viscous damping model in Laplace domain[J]. Journal of Vibration and Shock，2010，29(1)：94–99.(in Chinese))

[9] 沈洪宇. 卷积型阻尼模型参数识别与结构响应的理论与试验研究[博士学位论文][D]. 哈尔滨：哈尔滨工业大学，2010.(SHEN Hongyu. Theoretical and experimental research on parameter identification and time-history analysis of a convolutionary damped system[Ph. D. Thesis][D]. Harbin：Harbin Institute of Technology，2010.(in Chinese))

[10] 潘玉华，王元丰. 基于微分求积法求解非黏滞阻尼系统的时程响应[J]. 计算力学学报，2011，28(4)：517–522.( PAN Yuhua，WANG Yuanfeng. Time-history analysis of non-viscously damped systems based on the differential quadrature method[J]. Chinese Journal of Computational Mechanics，2011，28(4)：517–522.(in Chinese))

[11] 潘玉华. 指数型阻尼模型及其在钢筋混凝土结构动力分析中的应用[博士学位论文][D]. 北京：北京交通大学，2013.(PAN Yuhua. Exponential Damping Model and Its Applications to Dynamic Analysis of Reinforced Concrete Structures[Ph. D. Thesis][D]. Beijing：Beijing Jiaotong University，2013.(in Chinese))

[12] 高淑华，赵阳，李淑娟. 黏弹性结构动力学分析的等效黏性阻尼算法[J]. 振动与冲击，2005，24(1)：18–21.(GAO Shuhua，ZHAO Yang，LI Shuhua. Equivalent visco-damping method for the dynamic response analysis of visco-elastic structure[J]. Journal of Vibration and Shock，2005，24(1)：18–21.(in Chinese))

[13] 李青麒. 软岩蠕变参数的曲线拟合计算方法[J]. 岩石力学与工程学报，1998，17(5)：559–564.(LI Qingqi. Curve fitting method for creep parameter of soft rock[J]. Chinese Journal of Rock Mechanics and Engineering，1998，17(5)：559–564.(in Chinese))

[14] 周火明，丁秀丽，盛谦. 三峡工程地下电站开挖的黏弹性数值模拟及稳定性评价[J]. 长江科学院院报，2002，19(1)：31–34.(ZHOU Huoming，DING Xiuli，SHENG Qian. Viscoelastic numerical simulation and stability evaluation on excavation process of underground power station of TGP[J]. Journal of Yangtze River Scientific Research Institute，2002，19(1)：31–34.(in Chinese))

[15] 欧阳鬯. 黏弹塑性理论[M]// 长沙：湖南科学技术出版社，1986：26–27.(OUYANG Chang. Elastic-viscoplastic theory[M]. Changsha：Hunan Science and Technology Press，1986：26–27.(in Chinese))

[16] 高淑华. 含黏弹性阻尼结构的动力分析[硕士学位论文][D]. 上海：复旦大学，2001.(GAO Shuhua. Dynamic analysis of structure considering viscoelastic damping[M. S. Thesis][D]. Shanghai：Fudan University，2001.(in Chinese))

[17] CLOUGH R W，PENZIEN J，GRIFFIN D S. Dynamics of structures[J]. Journal of Applied Mechanics，2014，44(2)：366.

[18] 付晓东，盛谦，张勇慧. 非连续变形分析方法中的阻尼问题研究[J]. 岩土力学，2015，36(7)：2 057–2 062.(FU Xiaodong，SHENG Qian，ZHANG Yonghui. Damping problem in discontinuous deformation analysis method[J]. Rock and Soil Mechanics，2015，36(7)：2 057–2 062.(in Chinese))

[19] ADHIKARI S，WOODHOUSE J. Quantification of non-viscous damping in discrete linear systems[J]. Journal of Sound and Vibration，2003，260(3)：499–518.

[20] ADHIKARI S，WOODHOUSE J. Identification of damping：part 2， non-viscous damping[J]. Journal of Sound and Vibration，2001，243(1)：63–88.

[21] 姜清辉，周创兵. 岩土工程不连续变形分析计算中的若干问题[J]. 岩石力学与工程学报，2007，26(10)：2 014–2 025.(JIANG Qinghui，ZHOU Chuangbing. Some issues in discontinuous deformation analysis for geotechnical engineering[J]. Chinese Journal of Rock Mechanics and Engineering，2007，26(10)：2 014–2 025.(in Chinese))

[22] CHOPRA A K，NAEIM F. Dynamics of structures—theory and applications to earthquake engineering，third edition[J]. Earthquake Spectra，2001，17(3)：549–550.