隔震结构系统线性粘弹性液体阻尼器非平稳响应分析法

李创第,柏大炼,葛新广,刘鹏

振动与冲击 ›› 2019, Vol. 38 ›› Issue (2) : 234-246.

PDF(1678 KB)
PDF(1678 KB)
振动与冲击 ›› 2019, Vol. 38 ›› Issue (2) : 234-246.
论文

隔震结构系统线性粘弹性液体阻尼器非平稳响应分析法

  • 李创第,柏大炼,葛新广,刘鹏
作者信息 +

Non stationary response analysis of  isolated structures with linear viscoelastic liquid dampers

  • LI Chuangdi,BAI Dalian,GE Xinguang,LIU Peng
Author information +
文章历史 +

摘要

为建立线性粘弹性阻尼器抗震动力可靠度分析法和基于反应谱的模态叠加抗震设计法,对隔震系统线性粘弹性液体阻尼器时域瞬态响应的模态叠加解析解和非平稳随机地震响应分析法进行了系统研究。首先,采用最一般的线性粘弹性阻尼器的积分型分析模型,用非对称微分积分方程组实现设置线性粘弹性液体阻尼器的隔震结构系统的时域非扩阶建模;然后,采用传递矩阵法,直接获得隔震结构系统及其一般线性粘弹性液体阻尼器在任意激励和非零初始条件下时域瞬态响应的非扩阶模态叠加解析解;最后,应用此解析解和快速虚拟激励法,建立隔震系统及其线性粘弹性液体阻尼器在均匀与非均匀调幅滤过白噪声非平稳地震激励下的非平稳响应分析法。所获得的时域瞬态响应解析解以及所建立的一般非平稳随机地震响应分析法,将为建立整体隔震系统各构件抗震动力可靠度和基于反应谱的模态叠加抗震设计法提供分析路径。

Abstract

In order to establish an analytical method for seismic dynamic reliability analysis and a modal superposition seismic design method based on response spectrums for viscoelastically damped linear structures,the modal superposition solutions of transient responses and the analytical method for non stationary random seismic responses of isolated structures with linear viscoelastic liquid dampers were studied systematically.Using the general integral analytical model for linear viscoelastic dampers,the non-symmetric integral-differential dynamic response equations for the structures were established.By using the transfer matrix method,the modal superposition solutions in original structural space for the transient responses of the isolated structures and its general linear viscolastic liquid dampers under arbitrary exterior forcing loadings and non-zero initial conditions were obtained.By virtue of these analytical solutions and the fast pseudo excitation method,a non stationary response analytical method for isolated structures with linear viscoelastic liquid dampers under uniform or non-uniform amplitude modulated filtered white noise seismic excitation was established.The obtained transient response solutions and the established general non stationary response analytical method can provide a path for establishing the analytical method for seismic dynamic reliability analysis and the modal superposition seismic design method based on response spectrums of the components of isolated structures.

关键词

隔震结构 / 粘弹性液体阻尼器 / 模态叠加 / 瞬态响应 / 非平稳响应

Key words

 isolated structure / viscoelastic liquid damper / modal superposition / transient response / non stationary response

引用本文

导出引用
李创第,柏大炼,葛新广,刘鹏. 隔震结构系统线性粘弹性液体阻尼器非平稳响应分析法[J]. 振动与冲击, 2019, 38(2): 234-246
LI Chuangdi,BAI Dalian,GE Xinguang,LIU Peng. Non stationary response analysis of  isolated structures with linear viscoelastic liquid dampers[J]. Journal of Vibration and Shock, 2019, 38(2): 234-246

参考文献

[1] Christopoulos C, Filiatrault A, Bertero V V. Principles of passive supplemental damping and seismic isolation[M]. Iuss press, 2006.
[2] GB 50011-2010建筑抗震设计规范[S]. 北京: 中国建筑工业出版社, 2010.
 GB 50011-2010 Code for seismic design of buildings[S]. Beijing: China Construction Industry Press, 2010. (in Chinese)
[3] Koh C G, Kelly J M. Application of fractional derivatives to seismic analysis of base-isolated models[J]. Earthquake engineering and structural dynamics, 1990, 19(2): 229-241.
[4] Hwang J S, Ku S W. Analytical modeling of high damping rubber bearings[J]. Journal of Structural Engineering, 1997, 123(8): 1029-1036.
[5] Makris N, Constantinou M C, Dargush G F. Analytical Model of Viscoelastic Fluid Dampers[J]. Journal of Structural Engineering, 1993, 119(11): 3310-3325.
[6] 卢立恒, 徐赵东, 潘毅, 等. 多维地震激励下工程结构隔减震技术研究进展[J]. 土木工程学报, 2013, 46(1): 1-6.
 Lu Liheng, Xu Zhaodong, Pan Yi, et al. State of structural isolation and mitigation technology under multi-dimensional excitations[J]. China Civil Engineering Journal, 2013, 46(1): 1-6. (in Chinese)
[7] Kaul S. Maxwell–Voigt and Maxwell Ladder Models for Multi-Degree-of-Freedom Elastomeric Isolation Systems[J]. Journal of Vibration and Acoustics, 2015, 137(2): 021021.
[8] Barone G, Paola M D, Iacono F L, et al. Viscoelastic bearings with fractional constitutive law for fractional tuned mass dampers[J]. Journal of Sound and Vibration, 2015, 344: 18-27.
[9] Shaska K, Ibrahim R A, Gibson R F. Influence of excitation amplitude on the characteristics of nonlinear butyl rubber isolators[J]. Nonlinear Dynamics, 2007, 47(1-3): 83-104.
[10] Xie L, Cao M, Funaki N, et al. Performance Study of an Eight-story Steel Building Equipped with Oil Dampers Damaged During the 2011 Great East Japan Earthquake Part 1: Structural Identification and Damage Reasoning[J]. Journal of Asian Architecture and Building Engineering, 2015, 14(1): 181-188.
[11] JGJ297-2013建筑消能减震技术规程[S]. 北京: 中国建筑工业出版社, 2013.
 JGJ297-2013 Technical specification for building energy dissipation[S]. Beijing: China Construction Industry Press, 2013. (in Chinese)
[12] 国家自然科学基金委员会工程与材料科学部.学科发展战略研究报告-建筑、环境与土木工程Ⅱ(土木工程卷): 工程结构的振动控制理论及其应用(瞿伟廉,吴斌,李爱群执笔) [M]. 北京: 科学出版社, 2006: 456-475.
 National Natural Science Foundation of Engineering and Materials Science Department. Discipinary development strategy research report-Structure, Environmental and Civil Engineering (Civil Engineering Volume): Vibration control engineering structure theory and its applications ( Qu Weilian, Wu bin, Li Aiqun authored )[M]. Beijing: Science Press, 2006: 456-475. (in Chinese)
[13] Soong T T, Dargush G F. Passive energy dissipation systems in structural engineering[M]. Wiley, 1997.
[14] 周云. 粘弹性阻尼减震结构设计[M]. 武汉: 武汉理工大学出版社, 2006.
 Zhou Yun. Viscoelastic damping structure design[M]. Wuhan: Wuhan University of Technology Press,2006. (in Chinese)
[15] 李宏男. 结构振动与控制[M]. 北京: 中国建筑工业出版社, 2005.
 Li Hongnan. Structural vibration and control[M]. Beijing: China Construction Industry Press, 2005. (in Chinese)
[16] Johnson C D, Kienholz D A. Finite element prediction of damping in structures with constrained viscoelastic layers[J]. AIAA journal, 1982, 20(9): 1284-1290.
[17] Ou J P, Long X, Li Q S. Seismic response analysis of structures with velocity-dependent dampers[J]. Journal of Constructional Steel Research, 2007, 63(5): 628-638.
[18] Park S W. Analytical modeling of viscoelastic dampers for structural and vibration control[J]. International Journal of Solids and Structures, 2001, 38: 8065-8092.
[19] Singh M P, Chang T S. Seismic Analysis of Structures with Viscoelastic Dampers[J]. Journal of Engineering Mechanics, 2009, 135(6): 571-580.
[20] Zhang J, Zheng G T. The Biot Model and Its Application in Viscoelastic Composite Structures[J]. Journal of Vibration and Acoustics, 2007, 129(5): 533-540.
[21] Bagley R L, Torvik P J. Fractional calculus-A different approach to the analysis of viscoelastically damped structures[J]. AIAA Journal(ISSN 0001-1452), 1983, 21(5): 741-748.
[22] Lewandowski R, Chorążyczewski B. Identification of the parameters of the Kelvin–Voigt and the Maxwell fractional models used to modeling of viscoelastic dampers[J]. Computers and structures, 2010, 88(1): 1-17.
[23] Rossikhin Y A, Shitikova M V. Application of fractional calculus for dynamic problems of solid mechanics: novel trends and recent results[J]. Applied Mechanics Reviews, 2010, 63(1): 1-52.
[24] Woodhouse J. Linear damping models for structural vibration[J]. Journal of Sound and Vibration, 1998, 215(3): 547-569.
[25] Christensen R M, Freund L B. Theory of Viscoelasticity[M]. Academic Press, 1982.
[26] 张义同. 热粘弹性理论[M]. 天津: 天津大学出版社, 2002.
 Zhang Yitong. Thermo viscoelasticity theory[M]. Tianjin: Tianjin University Press, 2002. (in Chinese)
[27] Palmeri A. Correlation coefficients for structures with viscoelastic dampers[J]. Engineering Structures, 2006, 28(8): 1197-1208.
[28] Golla D F, Hughes P C. Dynamics of Viscoelastic Structures: A Time-Domain Finite Element Formulation[J]. Journal of Applied Mechanics, 1985, 52(4): 897-906.
[29] Xiao R, Sun H, Chen W. An equivalence between generalized Maxwell model and fractional Zener model[J]. Mechanics of Materials, 2016, 100: 148-153.
[30] Chang T S, Singh M P. Mechanical Model Parameters for Viscoelastic Dampers[J]. Journal of Engineering Mechanics, 2009, 135(6): 581-584.
[31] Zambrano A, José, Inaudi A, et al. Modal Coupling and Accuracy of Modal Strain Energy Method[J]. Journal of Engineering Mechanics, 1996, 122(7): 603-612.
[32] Palmeri A, Ricciardelli F, Luca A D, et al. State Space Formulation for Linear Viscoelastic Dynamic Systems with Memory[J]. Journal of Engineering Mechanics, 2003, 129(7): 715-724.
[33] Singh M P, Verma N P, Moreschi L M. Seismic Analysis and Design with Maxwell Dampers[J]. Journal of Engineering Mechanics, 2003, 129(3): 273-282.
[34] 张天舒, 方同. 弹性-粘弹性复合结构系统的随机响应分析[J]. 工程力学, 2001, 18(5): 71-76.
 Zhang Tianshu, Fang Tong. The random response analysis of elasyic-viscoelastic combined systems[J]. Engineering Mechanics, 2001, 18(5): 71-76. (in Chinese)
[35] 李创第, 李暾, 尉宵腾, 等. Maxwell 阻尼耗能结构非平稳地震响应解析分析[J]. 振动与冲击, 2016, 35(19):172-180.
 Li Chuangdi, Li Tun, Wei Xiaoteng, et al. Response analysis of energy disspation structures with Maxwell dampers under non-stationary seismic excitation[J]. Journal of Vibration and Shock, 2016, 35(19): 172-180. (in Chinese)
[36] Gluck N, Reinhorn A M, Gluck J, et al. Design of Supplemental Dampers for Control of Structures[J]. Journal of Structural Engineering, 1996, 122(12): 1394-1399.
[37] Council B S S. Prestandard and commentary for the seismic rehabilitation of buildings[J]. Report FEMA-356, Washington, DC, 2000.
[38] Fu Y, Kasai K. Comparative Study of Frames Using Viscoelastic and Viscous Dampers[J]. Journal of Structural Engineering, 1998, 124(5): 513-522.
[39] 常业军, 苏毅, 程文瀼, 等. 工程结构粘弹性消能支撑型式及设计参数的研究[J]. 地震工程与工程振动, 2007, 27(1):136-140.
 Chang Yejun, Su Yi, ChengW enrang, et al. Study on brace types and design parameters of engineering structures using viscoelastic dampers[J]. Earthquake engineering and Engineering Vibration, 2007, 27(1): 136-140.  (in Chinese)
[40] Liang Z, Lee G C, Dargush G F, et al. Structural damping: applications in seismic response modification[M]. CRC press, 2011.
[41] 林家浩, 张亚辉. 随机振动的虚拟激励法[M]. 北京: 科学出版社, 2004.
 Lin Jiahao, Zhang Yahui. Virtual excitation method for random vibration[M]. Beijing: Science Press, 2004. (in Chinese)
[42] 徐瑞, 苏成. 结构非平稳随机响应分析的快速虚拟激励法[J]. 计算力学学报, 2010, 27(05): 822-827.
 Xu Rui, Su Cheng. Fast pseudo-excitation method in structural non-stationary stochastic response analysis[J]. Chinese Journal of computational mechanics, 2010, 27 (05): 822-827.  (in Chinese)
[43] 苏成, 徐瑞. 非平稳激励下结构随机振动时域分析法[J]. 工程力学, 2010, 27(12): 77-83.
 Su Cheng, Xu Rui. Random vibration analysis of structured subjected to non-stationary excitations by time domain  method[J]. Engineering Mechanics, 2010, 27 (12): 77-83.  (in Chinese)
[44] Su C, Huang H, Ma H. Fast Equivalent Linearization Method for Nonlinear Structures under Nonstationary Random Excitations[J]. Journal of Engineering Mechanics, 2016, 142(8): 04016049.
[45] 李创第, 李暾, 葛新广, 等. 一般线性粘弹性阻尼器耗能结构瞬态响应的非正交振型叠加精确解[J]. 工程力学, 2015(11): 140-149.
 Li Chuangdi , Li Tun , Ge Xinguang , et al. Exact non-orthogonal modal superposition solutions of transient response of MDOF dissipation structures with general linear viscoelastic dampers[J]. Engineering Mechanics, 2015(11): 140-149. (in Chinese)
[46] Priestley M B. Power spectral analysis of non-stationary random processes[J]. Journal of Sound and Vibration, 1967, 6(1): 86-97.
[47] 欧进萍. 结构随机振动[M]. 北京: 高等教育出版社, 1998.
 Ou Jinping. Structural random vibration [M]. Beijing: Higher Education Press, 1998.
[48] Shinozuka M, Sato Y. Simulation of Nonstationary Random Process[J]. Journal of the Engineering Mechanics Division, 1967, 93(1): 11-40.
[49] Spanos P T D, Solomos G P. Markov approximation to transient vibration[J]. Journal of Engineering Mechanics, 1983, 109(4): 1134-1150.

PDF(1678 KB)

Accesses

Citation

Detail

段落导航
相关文章

/