组合梁等效阻尼比的两种计算方法及对比研究
|
摘要
为了确定钢-混凝土组合梁等效阻尼比的合理取值,提出组合梁各阶振型等效阻尼比的两种计算方法。基于复阻尼理论和各阶振型单个振动周期内阻尼耗能相等的原则,推导了组合梁各阶振型的等效阻尼比,在形式上为组合梁两种材料的阻尼比关于刚度的加权平均。基于共振状态下结构响应与阻尼比之间的关系,对组合梁各部分材料赋予Rayleigh阻尼和整体等效阻尼比,根据各阶模态变形情况施加对应简谐荷载激励,得到两种情况下组合梁的共振幅值,由此推导出组合梁的等效振型阻尼比。按照以上两种方法,对一根钢-混凝土组合梁进行数值计算,并对计算结果进行分析比较。结果表明:前者基于能量原理,较为合理地反映了组合梁的振动耗能特性,可以应用于不考虑界面滑移耗能时,组合梁各阶振型阻尼比的计算;后者求解思路较明确,但其基本假定与实际情况存在差异,且在计算中激励方式不易确定,故基于能量法的分析方法更有优势;阻尼的取值对组合梁动力响应的影响较大。
To simplify the dynamic analysis of composite beams,two calculation methods for equivalent damping ratios of the various vibration modes were presented.Based on complex damping theory and the principle of the equality of energy dissipation in single vibration cycle of each vibration mode,equivalent damping ratio was derived through the first method.It has the form of the weighted average of the damping ratios based on stiffness of the two elements of composite beams.Based on the relationship between structural response and damping ratios in resonance conditions,another expression of equivalent damping ratio was derived through the second method.Based on the two proposed calculation methods,numerical analysis was conducted and the results were compared.The conclusions of this paper are listed as follows: Based on the principle of energy,the first method reflects the characteristics of energy consumption of vibration reasonably.It could be used for the calculation of equivalent damping ratios of the various vibration modes when the slip on the interface of the composite beam could be neglected.The solution idea of the second method is clear,but divergences between its basic assumption and the actual situation and flaw in its incentive method exist.So,in terms of accuracy and applicability,the first method is more advantageous.In addition,the damping values have great impact on the dynamic response of composite beams.
To simplify the dynamic analysis of composite beams,two calculation methods for equivalent damping ratios of the various vibration modes were presented.Based on complex damping theory and the principle of the equality of energy dissipation in single vibration cycle of each vibration mode,equivalent damping ratio was derived through the first method.It has the form of the weighted average of the damping ratios based on stiffness of the two elements of composite beams.Based on the relationship between structural response and damping ratios in resonance conditions,another expression of equivalent damping ratio was derived through the second method.Based on the two proposed calculation methods,numerical analysis was conducted and the results were compared.The conclusions of this paper are listed as follows: Based on the principle of energy,the first method reflects the characteristics of energy consumption of vibration reasonably.It could be used for the calculation of equivalent damping ratios of the various vibration modes when the slip on the interface of the composite beam could be neglected.The solution idea of the second method is clear,but divergences between its basic assumption and the actual situation and flaw in its incentive method exist.So,in terms of accuracy and applicability,the first method is more advantageous.In addition,the damping values have great impact on the dynamic response of composite beams.
引文
[1]楼梦麟,雍国柱,李建元.阻尼特性对组合结构地震反应的影响[J].建筑科学与工程学报,2007,24(2):24-29.(LOU Menglin,YONG Guozhu,LI Jianyuan.Influence of damping characteristics on seismic responses of composite structures[J].Journal of Architecture and Civil Engineering,2007,24(2):24-29.(in Chinese))
[2]薛彦涛,韦承基,孙仁范,等.采用不同材料加层时结构阻尼比计算方法:应变能法[J].工程抗震与加固改造,2008,30(2):91-95.(XUE Yantao,WEI Chengji,SUN Renfan,et al.Calculation method for damping ratio of different story added structures:strain energy method[J].Earthquake Resistant Engineering and Retrofitting,2008,30(2):91-95.(in Chinese))
[3]任红伟,刘保东,李波.基于复频率的波纹钢腹板组合箱梁桥等效阻尼比计算[J].公路交通科技,2012,29(2):73-76.(REN Hongwei,LIU Baodong,LI Bo.Calculation of equivalent damping ratio of composite box gird bridge with corrugated steel webs based on complex frequency[J].Journal of Highway and Transportation Research and Development,2012,29(2):73-76.(in Chinese))
[4]克拉夫R W,彭津J.结构动力学[M].2版.王光远,译.北京:高等教育出版社,2006:112-138.
[5]俞瑞芳,周锡元.非比例阻尼弹性结构地震反应强迫解耦方法的理论背景和数值检验[J].工业建筑,2005,35(2):52-56.(YU Ruifang,ZHOU Xiyuan.Theoretical and numerical research on forced uncoupling method for seismic response of non-classically damped linear system[J].Industrial Construction,2005,35(2):52-56.(in Chinese))
[6]桂国庆,何玉敖.非比例阻尼结构体系近似解耦分析中的误差研究[J].工程力学,1994,11(4):40-45.(GUI Guoqing,HE Yuao.Study on errors of approximate decoupling analysis for non-proportionally damped structural systems[J].Engineering Mechanics,1994,11(4):40-45.(in Chinese))
[7]周锡元,董娣,苏幼坡.非正交阻尼线性振动系统的复振型地震响应叠加分析方法[J].土木工程学报,2003,36(5):30-36.(Zhou Xiyuan,Dong Di,Su Youpo.New method for linear systems with nonclassically damping under ground motion[J].China Civil Engineering Journal,2003,36(5):30-36.(in Chinese))
[8]朱镜清,朱敏.复阻尼多自由度系统动力分析的模态叠加法[J].地震工程与工程振动,2004,24(1):56-58.(ZHU Jingqing,ZHU Min.Two mode superposition methods for dynamic analysis of MDOF systems with complex damping characteristics[J].Earthquake Engineering and Engineering Vibration,2004,24(1):56-58.(in Chinese))
[9]王孝军,霍正存,马山明.钢混混合桥梁结构等效阻尼比的推算[J].公路工程,2009,34(1):81-83.(WANG Xiaojun,HUO Zhengcun,MA Shanming.Deduction of equivalent modal damping ratio for the composite bridge structure of steel-reinforced concrete[J].Highway Engineering,2009,34(1):81-83.(in Chinese))
[10]黄本才.组合结构振动的等效阻尼比[J].上海力学,1998,19(2):141-145.(HUANG Bencai.Equivalent modal damping ratios of vibration in composite structures[J].Shanghai Journal of Mechanics,1998,19(2):141-145.(in Chinese))
[11]段绍伟,向湘林,沈蒲生.复杂阻尼结构阻尼模型研究[J].振动与冲击,2011,30(2):73-76.(DUAN Shaowei,XIANG Xianglin,SHEN Pusheng.Damping model of a complex structure[J].Journal of Vibration and Shock,2011,30(2):73-76.(in Chinese))
[2]薛彦涛,韦承基,孙仁范,等.采用不同材料加层时结构阻尼比计算方法:应变能法[J].工程抗震与加固改造,2008,30(2):91-95.(XUE Yantao,WEI Chengji,SUN Renfan,et al.Calculation method for damping ratio of different story added structures:strain energy method[J].Earthquake Resistant Engineering and Retrofitting,2008,30(2):91-95.(in Chinese))
[3]任红伟,刘保东,李波.基于复频率的波纹钢腹板组合箱梁桥等效阻尼比计算[J].公路交通科技,2012,29(2):73-76.(REN Hongwei,LIU Baodong,LI Bo.Calculation of equivalent damping ratio of composite box gird bridge with corrugated steel webs based on complex frequency[J].Journal of Highway and Transportation Research and Development,2012,29(2):73-76.(in Chinese))
[4]克拉夫R W,彭津J.结构动力学[M].2版.王光远,译.北京:高等教育出版社,2006:112-138.
[5]俞瑞芳,周锡元.非比例阻尼弹性结构地震反应强迫解耦方法的理论背景和数值检验[J].工业建筑,2005,35(2):52-56.(YU Ruifang,ZHOU Xiyuan.Theoretical and numerical research on forced uncoupling method for seismic response of non-classically damped linear system[J].Industrial Construction,2005,35(2):52-56.(in Chinese))
[6]桂国庆,何玉敖.非比例阻尼结构体系近似解耦分析中的误差研究[J].工程力学,1994,11(4):40-45.(GUI Guoqing,HE Yuao.Study on errors of approximate decoupling analysis for non-proportionally damped structural systems[J].Engineering Mechanics,1994,11(4):40-45.(in Chinese))
[7]周锡元,董娣,苏幼坡.非正交阻尼线性振动系统的复振型地震响应叠加分析方法[J].土木工程学报,2003,36(5):30-36.(Zhou Xiyuan,Dong Di,Su Youpo.New method for linear systems with nonclassically damping under ground motion[J].China Civil Engineering Journal,2003,36(5):30-36.(in Chinese))
[8]朱镜清,朱敏.复阻尼多自由度系统动力分析的模态叠加法[J].地震工程与工程振动,2004,24(1):56-58.(ZHU Jingqing,ZHU Min.Two mode superposition methods for dynamic analysis of MDOF systems with complex damping characteristics[J].Earthquake Engineering and Engineering Vibration,2004,24(1):56-58.(in Chinese))
[9]王孝军,霍正存,马山明.钢混混合桥梁结构等效阻尼比的推算[J].公路工程,2009,34(1):81-83.(WANG Xiaojun,HUO Zhengcun,MA Shanming.Deduction of equivalent modal damping ratio for the composite bridge structure of steel-reinforced concrete[J].Highway Engineering,2009,34(1):81-83.(in Chinese))
[10]黄本才.组合结构振动的等效阻尼比[J].上海力学,1998,19(2):141-145.(HUANG Bencai.Equivalent modal damping ratios of vibration in composite structures[J].Shanghai Journal of Mechanics,1998,19(2):141-145.(in Chinese))
[11]段绍伟,向湘林,沈蒲生.复杂阻尼结构阻尼模型研究[J].振动与冲击,2011,30(2):73-76.(DUAN Shaowei,XIANG Xianglin,SHEN Pusheng.Damping model of a complex structure[J].Journal of Vibration and Shock,2011,30(2):73-76.(in Chinese))
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心