基于集中柔度模型电流变体-砂浆悬臂梁固有频率的理论分析
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摘要
直接将电流变体密封后埋置在砂浆梁中制成智能复合悬臂结构,采用瞬态激振的方法测定其在不同电场强度下固有频率,对频率随电场强度的变化规律进行了实验研究.结果表明电场强度对第一、二阶频率影响比较大,对第三阶频率影响很小,而且电流变片埋置位置对复合梁的整体振动特性的影响比较大.在此基础上,利用一种基于集中柔度模型的分析裂纹梁动态响应的新方法对这种复合结构进行了数值分析.通过定义等效裂纹深度,建立了电流变体-砂浆复合悬臂梁的振动模型,得到计算复合悬臂梁频率的特征方程,并根据实验数据确定模型的参数,最后用于模拟含电流变体的砂浆悬臂梁随电场强度变化时固有频率的演化规律.研究结果显示,该模型的解析解与实验值吻合得较好,对前三阶频率模拟的效果较为理想,说明该模型可用于含电流变体砂浆复合悬臂梁的振动分析,为电流变体在实际工程结构振动控制领域的应用奠定了理论基础和实验依据.
The natural frequency response of electrorheological(ER) fluid-filled composite mortar beams with cantilevered boundary condition was investigated through hammering test.The experimental results show that there are changes in natural frequencies when the composite beam was subjected to an electric field.The increment in the first and second order frequencies of ER based adaptive beam increases monotonically with the applied electric field strength.However,the influence of electric field upon the third order frequency is not significant in magnitude.Then an analytical investigation was performed to model the dynamic behavior of the ER material based adaptive beams using concentrated compliance method.A theoretical model for adaptive beam structures with cantilevered boundary condition was developed to calculate the eigenfrequencies by defining an equivalent depth of a crack on the beam.Combined with the Euler-Bernoulli theories of beam,the present model was applied to derive the characteristic equation of the cantilever beam.Based on this characteristic equation,the relation between the natural frequencies of the beam and the applied electric field strength was predicted by minimizing the difference between the analytical and experimental frequencies only with the first three natural frequencies of the test.Qualitative agreement between the experimental data and the predicted values indicates that the proposed model accurately predicts the effect of the applied electric field strength on the dynamic characteristics of the ER based beam.This research sets up the experimental and theoretical basis for the application of ER fluid to the field of vibration control in engineering practice.
The natural frequency response of electrorheological(ER) fluid-filled composite mortar beams with cantilevered boundary condition was investigated through hammering test.The experimental results show that there are changes in natural frequencies when the composite beam was subjected to an electric field.The increment in the first and second order frequencies of ER based adaptive beam increases monotonically with the applied electric field strength.However,the influence of electric field upon the third order frequency is not significant in magnitude.Then an analytical investigation was performed to model the dynamic behavior of the ER material based adaptive beams using concentrated compliance method.A theoretical model for adaptive beam structures with cantilevered boundary condition was developed to calculate the eigenfrequencies by defining an equivalent depth of a crack on the beam.Combined with the Euler-Bernoulli theories of beam,the present model was applied to derive the characteristic equation of the cantilever beam.Based on this characteristic equation,the relation between the natural frequencies of the beam and the applied electric field strength was predicted by minimizing the difference between the analytical and experimental frequencies only with the first three natural frequencies of the test.Qualitative agreement between the experimental data and the predicted values indicates that the proposed model accurately predicts the effect of the applied electric field strength on the dynamic characteristics of the ER based beam.This research sets up the experimental and theoretical basis for the application of ER fluid to the field of vibration control in engineering practice.
引文
[1]Makris N,Scott AB,Mabel J.Analysis and design of ER damper for seismic protection of structures[J].ASCE,Journalof Engineering Mechanics,1996,122(10):1003-1011
[2]Makris N,Scott A B,Douglas P T.Electrorheological damper with annular ducts for seismic protection application[J].Smart Materials and Structures,1996,5(5):551-564
[3]瞿伟廉,项海帆.ER智能材料在结构振动控制中的应用[J].地震工程与工程振动,1998,18(3):49-55Qu Weilian,Xiang Haifan.Application of ER intelligent material to structural control[J].Journal of EarthquakeEngineering and Engineering Vibration,1998,18(3):49-55
[4]瞿伟廉,徐幼麟.ER/MR智能阻尼器对空间网壳结构地震反应的半主动控制[J].地震工程与工程振动,2001,21(4):24-31Qu Weilian,Xu Youlin.Semi-active control for earthquake responses of reticulated shells with ER/MR smart dampers[J].Journal of Earthquake Engineering and Engineering Vibration,2001,21(4):24-31
[5]刘彦菊,冷劲松,王殿富.含电流变体智能复合材料梁的振动响应分析[J].纤维复合材料,1999,16(2):33-36Liu Yanju,Leng Jinsong,Wang Dianfu.Analysis of dynamic responses of vibration for sandwich beam with embeddedER fluid[J].Fiber Composites,1999,16(2):33-36
[6]杨万忠,冷劲松,刘彦菊,等.含ER流体板结构的振动特性研究[J].实验力学,1999,14(1):41-46Yang Wanzhong,Leng Jinsong,Liu Yanjiu,et al.Investigation on the vibration characteristics of some plated structurescontraining ERF layer[J].Journal of Experimental Mechanics,1999,14(1):41-46
[7]Sprecher A F,Choi Y,Conrad H.Mechanical behaviour of ER fluid-filled composites in forced oscillation[A].US/Japan Conference on Adaptive Structures[C].New York:Technomic Publ Co Inc,1999:560-579
[8]Choi S B.Vibration control of a flexible structure using ER dampers[J].Journal of Dynamic Systems Measurement andControl-Transactions of the ASME,1999,121(1):134-138
[9]逯静洲,李庆斌.含电流变体的复合砂浆梁振动特性实验研究[J].地震工程与工程振动,2004,24(6):97-102Lu Jingzhou,Li Qingbin.Dynamic performance of cantilever mortar beams with Electrorheological fluid filled in a centralcrack[J].Journal of Earthquake Engineering and Engineering Vibration,2004,24(6):97-102
[10]逯静洲,李庆斌.电流变体-砂浆复合梁结构的振动特性研究[J].地震工程与工程振动,2005,25(1):54-57Lu Jingzhou,Li Qingbin.Vibration performance of electrorheological fluid-mortar cantilever beams[J].Journal ofEarthquake Engineering and Engineering Vibration,2005,25(1):54-57
[11]Lu jingzhou,Li Qingbin.Dynamic performance of cantilevermortar beams with embedded electrorheological fluids[C].IMAC XXIII Conference&Exposition on Structural Dynamics.Florida USA,Orlando,2005
[12]逯静洲,李庆斌,张文翠.含电流变体砂浆复合悬臂梁结构的振动分析[J].清华大学学报,2004,44(9):1235-1239Lu Jingzhou,Li Qingbin,Zhang Wencui.Free vibration analysis of a cantilever mortar beam with electrorheological fluidin a central crack[J].Journal of Tsinghua University(Science and Technology),2004,44(9):1235-1239
[13]逯静洲,李庆斌,曲淑英.含电流变体砂浆复合梁结构振动固有频率的理论研究[J].振动与冲击,2006,25(4):114-118Lu Jingzhou,Li Qingbin,Qu Shuying.Theoretical study on natural frequencies of a cantilever mortar beam withembedded electrorheological fluid[J].Journal of Vibration and Shock,2006,25(4):114-118
[14]Chondros TG,Dimarogonas A D.Identification of cracks in welded joints of complex structures[J].Journal of Soundand Vibration,1980,69(4):531-538
[15]沈亚鹏,唐照千.裂纹对悬臂梁板振动频谱的影响[J].固体力学学报,1982,(2):247-251Shen Yapeng,Tang Zhaoqian.Effects of cracks on frequency spectra of vibration of cantilever beams and plates[J].ActaMechanica Solida Sinica,1982,(2):247-251
[16]Dimarogonas A D,Paipetis S A.Analytical methods in rotor dynamics[M].London:Applied Science Publishers,1983
[2]Makris N,Scott A B,Douglas P T.Electrorheological damper with annular ducts for seismic protection application[J].Smart Materials and Structures,1996,5(5):551-564
[3]瞿伟廉,项海帆.ER智能材料在结构振动控制中的应用[J].地震工程与工程振动,1998,18(3):49-55Qu Weilian,Xiang Haifan.Application of ER intelligent material to structural control[J].Journal of EarthquakeEngineering and Engineering Vibration,1998,18(3):49-55
[4]瞿伟廉,徐幼麟.ER/MR智能阻尼器对空间网壳结构地震反应的半主动控制[J].地震工程与工程振动,2001,21(4):24-31Qu Weilian,Xu Youlin.Semi-active control for earthquake responses of reticulated shells with ER/MR smart dampers[J].Journal of Earthquake Engineering and Engineering Vibration,2001,21(4):24-31
[5]刘彦菊,冷劲松,王殿富.含电流变体智能复合材料梁的振动响应分析[J].纤维复合材料,1999,16(2):33-36Liu Yanju,Leng Jinsong,Wang Dianfu.Analysis of dynamic responses of vibration for sandwich beam with embeddedER fluid[J].Fiber Composites,1999,16(2):33-36
[6]杨万忠,冷劲松,刘彦菊,等.含ER流体板结构的振动特性研究[J].实验力学,1999,14(1):41-46Yang Wanzhong,Leng Jinsong,Liu Yanjiu,et al.Investigation on the vibration characteristics of some plated structurescontraining ERF layer[J].Journal of Experimental Mechanics,1999,14(1):41-46
[7]Sprecher A F,Choi Y,Conrad H.Mechanical behaviour of ER fluid-filled composites in forced oscillation[A].US/Japan Conference on Adaptive Structures[C].New York:Technomic Publ Co Inc,1999:560-579
[8]Choi S B.Vibration control of a flexible structure using ER dampers[J].Journal of Dynamic Systems Measurement andControl-Transactions of the ASME,1999,121(1):134-138
[9]逯静洲,李庆斌.含电流变体的复合砂浆梁振动特性实验研究[J].地震工程与工程振动,2004,24(6):97-102Lu Jingzhou,Li Qingbin.Dynamic performance of cantilever mortar beams with Electrorheological fluid filled in a centralcrack[J].Journal of Earthquake Engineering and Engineering Vibration,2004,24(6):97-102
[10]逯静洲,李庆斌.电流变体-砂浆复合梁结构的振动特性研究[J].地震工程与工程振动,2005,25(1):54-57Lu Jingzhou,Li Qingbin.Vibration performance of electrorheological fluid-mortar cantilever beams[J].Journal ofEarthquake Engineering and Engineering Vibration,2005,25(1):54-57
[11]Lu jingzhou,Li Qingbin.Dynamic performance of cantilevermortar beams with embedded electrorheological fluids[C].IMAC XXIII Conference&Exposition on Structural Dynamics.Florida USA,Orlando,2005
[12]逯静洲,李庆斌,张文翠.含电流变体砂浆复合悬臂梁结构的振动分析[J].清华大学学报,2004,44(9):1235-1239Lu Jingzhou,Li Qingbin,Zhang Wencui.Free vibration analysis of a cantilever mortar beam with electrorheological fluidin a central crack[J].Journal of Tsinghua University(Science and Technology),2004,44(9):1235-1239
[13]逯静洲,李庆斌,曲淑英.含电流变体砂浆复合梁结构振动固有频率的理论研究[J].振动与冲击,2006,25(4):114-118Lu Jingzhou,Li Qingbin,Qu Shuying.Theoretical study on natural frequencies of a cantilever mortar beam withembedded electrorheological fluid[J].Journal of Vibration and Shock,2006,25(4):114-118
[14]Chondros TG,Dimarogonas A D.Identification of cracks in welded joints of complex structures[J].Journal of Soundand Vibration,1980,69(4):531-538
[15]沈亚鹏,唐照千.裂纹对悬臂梁板振动频谱的影响[J].固体力学学报,1982,(2):247-251Shen Yapeng,Tang Zhaoqian.Effects of cracks on frequency spectra of vibration of cantilever beams and plates[J].ActaMechanica Solida Sinica,1982,(2):247-251
[16]Dimarogonas A D,Paipetis S A.Analytical methods in rotor dynamics[M].London:Applied Science Publishers,1983
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