形状记忆合金振动系统分析与计算
|
摘要
目前,非线性动力学理论在自然科学、生命科学、社会科学等领域的应用越来越得到重视。特别是在工程领域,基于非线性动力学分析的设计逐步引起人们的重视。
形状记忆合金(SMA)是一类应用前景广阔的智能材料。通过SMA预变形,可以使形状记忆合金产生不同形状的回复力-位移关系曲线,这些曲线形状分别为矩型,三角旗,蝴蝶结,双旗帜型。双旗帜型(Flag-Shaped)的滞回模型更加典型,并且能反映预应力钢结构节点和磁流变阻尼器的力位移特性。作为非线性动力学设计初步探讨,本文研究双旗帜型(Flag-Shaped)的滞回模型特性对动力学行为的影响。
本文建立了形状记忆合金减振器的力学模型,用平均法导出系统的幅频响应方程,用约束分岔奇异性理论计算了转迁集和分岔图。针对滞后模型分段线性的特点,用统一的绝对值函数求和形式来描述滞后特性的各种可能路径,显著减少了路径切换的种类,降低了逻辑判断的难度,简化了程序编制的复杂性。利用编制的matlab数值程序,计算了系统的多种幅频响应分岔图,通过与理论结果对比发现:在参数刚度k数值较小的情况下,数值计算得到数据与理论分析得到的幅频曲线有较高的吻合程度;在参数刚度k数值比较大的情况下,数值计算得到数据与理论分析得到的幅频曲线吻合较差。
最后对形状记忆合金减振器的减振效果进行分析。形状记忆合金的加入,使系统避开线性系统共振区高峰值,并使得系统的最大幅值得到抑制。上述研究对形状记忆合金减振器设计有一定的指导意义。
Nowadays, nonlinear dynamics theory is more and more important in the natural sciences, life sciences, social sciences and other fields of application. Especially in the engineering field, the design based on nonlinear dynamic analysis gradually attracts people's attention.
Shape memory alloy (SMA) is a kind of intelligent material with promising future in application. With the pre-deformation of shape memory alloy (SMA), it could produce different response force - displacement curves. The shape of these curves are rectangle, triangle, bowknot, and flag-shaped. The Flag-Shaped hysteretic model is more typical, and can also reflect the force-displacement characteristics of the prestressed steel nodes and the magneto-rheological damper. As a preliminary study of the design on nonlinear dynamic analysis, this paper mainly studies the influence of the Flag-Shaped hysteresis on the dynamic behavior.
This paper builds the model of a mass-spring system with the shape memory alloy damper. Obtaining amplitude-frequency equation by using the averaging method, and calculate the transition sets and bifurcation diagrams by the theory of singular bifurcation. In order to simplify the complication of the programming, an unified form of absolute value function is introduced to express all the possible routes of the hysteretic model. By comparison with the theoretical results, it is shown that the amplitude-frequency curves based on numerical calculation agree well with those obtained by theoretical analysis for small stiffness parameters,
Finally, the effects of shape memory alloy damper on the vibration reduction are investigated. The results show that the damper reduces the vibration amplitude of the system.
形状记忆合金(SMA)是一类应用前景广阔的智能材料。通过SMA预变形,可以使形状记忆合金产生不同形状的回复力-位移关系曲线,这些曲线形状分别为矩型,三角旗,蝴蝶结,双旗帜型。双旗帜型(Flag-Shaped)的滞回模型更加典型,并且能反映预应力钢结构节点和磁流变阻尼器的力位移特性。作为非线性动力学设计初步探讨,本文研究双旗帜型(Flag-Shaped)的滞回模型特性对动力学行为的影响。
本文建立了形状记忆合金减振器的力学模型,用平均法导出系统的幅频响应方程,用约束分岔奇异性理论计算了转迁集和分岔图。针对滞后模型分段线性的特点,用统一的绝对值函数求和形式来描述滞后特性的各种可能路径,显著减少了路径切换的种类,降低了逻辑判断的难度,简化了程序编制的复杂性。利用编制的matlab数值程序,计算了系统的多种幅频响应分岔图,通过与理论结果对比发现:在参数刚度k数值较小的情况下,数值计算得到数据与理论分析得到的幅频曲线有较高的吻合程度;在参数刚度k数值比较大的情况下,数值计算得到数据与理论分析得到的幅频曲线吻合较差。
最后对形状记忆合金减振器的减振效果进行分析。形状记忆合金的加入,使系统避开线性系统共振区高峰值,并使得系统的最大幅值得到抑制。上述研究对形状记忆合金减振器设计有一定的指导意义。
Nowadays, nonlinear dynamics theory is more and more important in the natural sciences, life sciences, social sciences and other fields of application. Especially in the engineering field, the design based on nonlinear dynamic analysis gradually attracts people's attention.
Shape memory alloy (SMA) is a kind of intelligent material with promising future in application. With the pre-deformation of shape memory alloy (SMA), it could produce different response force - displacement curves. The shape of these curves are rectangle, triangle, bowknot, and flag-shaped. The Flag-Shaped hysteretic model is more typical, and can also reflect the force-displacement characteristics of the prestressed steel nodes and the magneto-rheological damper. As a preliminary study of the design on nonlinear dynamic analysis, this paper mainly studies the influence of the Flag-Shaped hysteresis on the dynamic behavior.
This paper builds the model of a mass-spring system with the shape memory alloy damper. Obtaining amplitude-frequency equation by using the averaging method, and calculate the transition sets and bifurcation diagrams by the theory of singular bifurcation. In order to simplify the complication of the programming, an unified form of absolute value function is introduced to express all the possible routes of the hysteretic model. By comparison with the theoretical results, it is shown that the amplitude-frequency curves based on numerical calculation agree well with those obtained by theoretical analysis for small stiffness parameters,
Finally, the effects of shape memory alloy damper on the vibration reduction are investigated. The results show that the damper reduces the vibration amplitude of the system.
引文
[1]陈予恕,非线性振动,天津,天津科技出版社,1983
[2]陈予恕,现代工程非线性动力学的现状与展望,力学与实践,1995,17(6):11~19
[3]任勇生,SMA及其在振动主被动控制中的应用,力学进展, 1999, 29(1) : 19~33
[4]巩建鸣,户伏寿昭,循环加载下TiNi形状记忆合金超弹性变形行为,南京工业大学学报(自然科学版),2002,24(1):252~256
[5]巩建鸣,户伏寿昭,高田和幸等,循环加载条件下TiNi形状记忆合金超弹性变形特性分析与模拟,航空材料科学,2002,22(4):62~72
[6]任勇生,SMA及其在振动主被动控制中的应用,力学进展, 1999, 29(1) : 19~33
[7] Tanaka K. A thermo mechanical sketch of shape memory effect; one dimensional tensile behavior Res Mechanica ,1986 ,18 :251~263
[8] Liang C and Rogers C A, One Dimensional memory martial institutive Relations for Shape Memory Materials Journal of Intelligent Material Systems and Structures, 1990, 1:207~234
[9] Saadat S, Salichs J, et al. An overview of vibration and seismic application of NiTi shape memory alloy Smart Materials and Structures 2002, 11:218~229
[10]贺志荣,Tini形状记忆合金的工程应用研究现状和展望,材料导报,2005,19(4):50~53
[11]Nims, D. K., Richter, P. J., and Bacham, R. E. Use of energydissipating restraint for seismic hazard mitigation, Earthquake Spectra, 9(3), 467~489
[12]Caughey, T. K. ,Sinusoidal excitation of a system with bilinear hysteresis, Appl. Mech., 27(4):640~643
[13]赵永峰,童根树,双折线弹塑性滞回模型的结构影响系数,工程力学,2008,25(1):61~69
[14]周云,金属耗能减震结构设计,武汉:武汉理工大学出版社,2006
[15]欧进萍,结构振动控制-主动、半主动和智能控制,北京:科学出版社,2003
[16]李人厚,智能控制理论和方法,西安:西安电子科技大学出版社,1999
[17]Han YL et. al1Structural vibration control by shape memory alloy damper,Earthquake Engineering and Structural Dynamics.12003, 32:483~49 [18杨勇,章梓茂,改进型高层钢框架节点非线性有限元分析,北方交通大学学报,2003,27(4):52~56
[19]禹慧,陈俊岭,钢框架预应力节点的介绍与分析,结构工程师,2005,21(4):61~65
[20]李小林,张雨烨,形状记忆合金超弹性的Preisach滞回模型,科教前沿,2008,7:45~46
[21]张雨烨,阎石,Song Gangbing,马宁,基于Preisach理论形状记忆合金电阻-应变滞回模型,2008,27(8):146~148
[22]杨飏,欧进萍,可调滞回模型的电流变隔震装置理论分析,东北大学学报,2007,28(4):584~588
[23]孙清,伍晓红,胡志义,周进雄,张陵,磁流变阻尼器性能试验及其非线性力学模型,工程力学,2007,24(4):183~187
[24]王唯,夏品奇,一种改进的磁流变阻尼器模型及其对振动主动控制的应用,力学季刊,2008,29(2):194~198
[25]M.A.Qidwai ,D.C.Lagoudas. Numerical implementation of a shape memory alloy thermo mechanical constitutive model using return mapping algorithms, International Journal For Numerical Methods In Engineering, 2000,47:1123~1168
[26]Dimitris C. Lagoudas,Luciano G. Machado,Magdalini Z. Lagoudas. Nonlinear vibration of a one-degree of freedom shape memory alloy oscillator: anumerical -experimental investigation structures, Structural Dynamics & Materials conference april, 18~21. Austin, TX, USA
[27]Capecchi, D., and Vestroni, F, Steady-state dynamic analysis of hysteretic systems, Eng. Mech., 111(12), 1515~1531
[28]Christopoulos, C., Filiatrault, A., and Folz, B. ,Seismic response of self-centering hysteretic SDOF systems, Earthquake Eng.Struct.Dyn., 31, 1131~1150
[29]Christopoulos, C., Filiatrault, A., Uang, C.-M., and Folz, B. , Post tensioned energy dissipating connections for moment-resisting steel frames, Struct. Eng., 128(9), 1111~1120
[30]Wilde K, Gardoni P, fujino Y. Base Isolation system with shape memory alloy device for elevated highwaybridges,Engineering Structures 2000, 22:222~291
[31]Graesser E J, Cozarelli F A. Shape memory alloys as a new materials for a seismic isolation,Eng Mech ASCE ,1991 ,117 (11) :2590~26081
[32]Peter W C. Experimental and analytical studies of shape memory alloy dampers for structural control ,SPIE2445, 1995: 241~251
[33]郑阿奇,MATLAB实用教程,北京:电子工业出版社,2004
[34]Edward B.Magrab,MATLAB原理与工程应用,北京:电子工业出版社,2002
[35]张学敏,MATLAB基础及应用,北京:中国电力出版社,2009
[36]马昌凤,林伟川,现代数值计算方法MATLAB版,北京:科学出版社,2008
[37]景振毅,张泽兵,董霖,MATLAB 7.0实用宝典,北京:中国铁道出版社,2009
[38]褚洪生,杜增吉,阎金华等,MATLAB 7.2优化设计实例指导教程,北京:机械工业出版社2007
[39]张德喜,周予生,MATLAB语言程序设计教程,北京:中国铁道出版社2006
[40]许波,刘征,MATLAB工程数学应用,北京:电子工业出版社,2000
[2]陈予恕,现代工程非线性动力学的现状与展望,力学与实践,1995,17(6):11~19
[3]任勇生,SMA及其在振动主被动控制中的应用,力学进展, 1999, 29(1) : 19~33
[4]巩建鸣,户伏寿昭,循环加载下TiNi形状记忆合金超弹性变形行为,南京工业大学学报(自然科学版),2002,24(1):252~256
[5]巩建鸣,户伏寿昭,高田和幸等,循环加载条件下TiNi形状记忆合金超弹性变形特性分析与模拟,航空材料科学,2002,22(4):62~72
[6]任勇生,SMA及其在振动主被动控制中的应用,力学进展, 1999, 29(1) : 19~33
[7] Tanaka K. A thermo mechanical sketch of shape memory effect; one dimensional tensile behavior Res Mechanica ,1986 ,18 :251~263
[8] Liang C and Rogers C A, One Dimensional memory martial institutive Relations for Shape Memory Materials Journal of Intelligent Material Systems and Structures, 1990, 1:207~234
[9] Saadat S, Salichs J, et al. An overview of vibration and seismic application of NiTi shape memory alloy Smart Materials and Structures 2002, 11:218~229
[10]贺志荣,Tini形状记忆合金的工程应用研究现状和展望,材料导报,2005,19(4):50~53
[11]Nims, D. K., Richter, P. J., and Bacham, R. E. Use of energydissipating restraint for seismic hazard mitigation, Earthquake Spectra, 9(3), 467~489
[12]Caughey, T. K. ,Sinusoidal excitation of a system with bilinear hysteresis, Appl. Mech., 27(4):640~643
[13]赵永峰,童根树,双折线弹塑性滞回模型的结构影响系数,工程力学,2008,25(1):61~69
[14]周云,金属耗能减震结构设计,武汉:武汉理工大学出版社,2006
[15]欧进萍,结构振动控制-主动、半主动和智能控制,北京:科学出版社,2003
[16]李人厚,智能控制理论和方法,西安:西安电子科技大学出版社,1999
[17]Han YL et. al1Structural vibration control by shape memory alloy damper,Earthquake Engineering and Structural Dynamics.12003, 32:483~49 [18杨勇,章梓茂,改进型高层钢框架节点非线性有限元分析,北方交通大学学报,2003,27(4):52~56
[19]禹慧,陈俊岭,钢框架预应力节点的介绍与分析,结构工程师,2005,21(4):61~65
[20]李小林,张雨烨,形状记忆合金超弹性的Preisach滞回模型,科教前沿,2008,7:45~46
[21]张雨烨,阎石,Song Gangbing,马宁,基于Preisach理论形状记忆合金电阻-应变滞回模型,2008,27(8):146~148
[22]杨飏,欧进萍,可调滞回模型的电流变隔震装置理论分析,东北大学学报,2007,28(4):584~588
[23]孙清,伍晓红,胡志义,周进雄,张陵,磁流变阻尼器性能试验及其非线性力学模型,工程力学,2007,24(4):183~187
[24]王唯,夏品奇,一种改进的磁流变阻尼器模型及其对振动主动控制的应用,力学季刊,2008,29(2):194~198
[25]M.A.Qidwai ,D.C.Lagoudas. Numerical implementation of a shape memory alloy thermo mechanical constitutive model using return mapping algorithms, International Journal For Numerical Methods In Engineering, 2000,47:1123~1168
[26]Dimitris C. Lagoudas,Luciano G. Machado,Magdalini Z. Lagoudas. Nonlinear vibration of a one-degree of freedom shape memory alloy oscillator: anumerical -experimental investigation structures, Structural Dynamics & Materials conference april, 18~21. Austin, TX, USA
[27]Capecchi, D., and Vestroni, F, Steady-state dynamic analysis of hysteretic systems, Eng. Mech., 111(12), 1515~1531
[28]Christopoulos, C., Filiatrault, A., and Folz, B. ,Seismic response of self-centering hysteretic SDOF systems, Earthquake Eng.Struct.Dyn., 31, 1131~1150
[29]Christopoulos, C., Filiatrault, A., Uang, C.-M., and Folz, B. , Post tensioned energy dissipating connections for moment-resisting steel frames, Struct. Eng., 128(9), 1111~1120
[30]Wilde K, Gardoni P, fujino Y. Base Isolation system with shape memory alloy device for elevated highwaybridges,Engineering Structures 2000, 22:222~291
[31]Graesser E J, Cozarelli F A. Shape memory alloys as a new materials for a seismic isolation,Eng Mech ASCE ,1991 ,117 (11) :2590~26081
[32]Peter W C. Experimental and analytical studies of shape memory alloy dampers for structural control ,SPIE2445, 1995: 241~251
[33]郑阿奇,MATLAB实用教程,北京:电子工业出版社,2004
[34]Edward B.Magrab,MATLAB原理与工程应用,北京:电子工业出版社,2002
[35]张学敏,MATLAB基础及应用,北京:中国电力出版社,2009
[36]马昌凤,林伟川,现代数值计算方法MATLAB版,北京:科学出版社,2008
[37]景振毅,张泽兵,董霖,MATLAB 7.0实用宝典,北京:中国铁道出版社,2009
[38]褚洪生,杜增吉,阎金华等,MATLAB 7.2优化设计实例指导教程,北京:机械工业出版社2007
[39]张德喜,周予生,MATLAB语言程序设计教程,北京:中国铁道出版社2006
[40]许波,刘征,MATLAB工程数学应用,北京:电子工业出版社,2000