TMD等强度悬臂梁实际应用时的频率精确分析
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摘要
为了确定实际应用中调谐质量阻尼器(TMD)刚度单元的梯形悬臂梁参数,建立了梯形悬臂梁频率的精确计算公式,计算了梯形等强度悬臂梁与三角形等强度悬臂梁频率的误差,利用梯形悬臂梁频率计算公式确定了TMD等强度悬臂梁的设计步骤与程序,给出了工程示例,并使用仿真软件ANSYS进行了验证。结果表明:悬臂梁自由端的宽度小于固定端宽度的12.65%时,梯形等强度悬臂梁与三角形等强度悬臂梁的频率相对误差小于5%;所用程序可以用于确定满足频率精度要求的TMD等强度悬臂梁的参数,对工程实际有较大指导意义。
In order to determine the parameters of trapezoidal cantilever beam of stiffness element of tuned mass damper(TMD)in practical cases,the exact analytic solution of frequency of trapezoidal cantilever beam was deduced.The error of frequency between triangular equal strength cantilever beam and trapezoidal equal strength cantilever beam was calculated.The design procedure and program of equal strength cantilever beam of TMD using the formula of frequency of trapezoidal cantilever beam was defined.A typical example in engineering field was given and the results were checked with simulation software ANSYS.The results show that when the width of free end is less than 12.65% of the width of fixed end,the error of frequency between them is less than 5%.The designed program can be applied to determine parameters of equal strength cantilever beams of TMD when the accuracy requirements of frequency are met,and it is of great value when applied to the practical cases of engineering.
In order to determine the parameters of trapezoidal cantilever beam of stiffness element of tuned mass damper(TMD)in practical cases,the exact analytic solution of frequency of trapezoidal cantilever beam was deduced.The error of frequency between triangular equal strength cantilever beam and trapezoidal equal strength cantilever beam was calculated.The design procedure and program of equal strength cantilever beam of TMD using the formula of frequency of trapezoidal cantilever beam was defined.A typical example in engineering field was given and the results were checked with simulation software ANSYS.The results show that when the width of free end is less than 12.65% of the width of fixed end,the error of frequency between them is less than 5%.The designed program can be applied to determine parameters of equal strength cantilever beams of TMD when the accuracy requirements of frequency are met,and it is of great value when applied to the practical cases of engineering.
引文
[1]李春祥,刘艳霞,王肇民.质量阻尼器的发展[J].力学进展,2003,33(2):194-206.LI Chun-xiang,LIU Yan-xia,WANG Zhao-min.A Review on Mass Dampers[J].Advances in Mechanics,2003,33(2):194-206.
[2]顾明,陈甦人,项海帆,等.用于杨浦大桥抖振控制的MTMD研究[J].振动工程学报,1998,11(1):1-8.GU Ming,CHEN Su-ren,XIANG Hai-fan,et al.Buffeting Control of the Yangpu Bridge Using Multiple Tuned Mass Dampers[J].Journal of Vibration Engineering,1998,11(1):1-8.
[3]刘勋,施卫星,陈希.单摆式TMD简介及其减振性能分析[J].结构工程师,2012,28(6):66-71.LIU Xun,SHI Wei-xing,CHEN Xi.Introduction and Analysis of the Pendulum-type Tuned Mass Damper[J].Structural Engineers,2012,28(6):66-71.
[4]雷旭,牛华伟,陈政清,等.大跨度钢拱桥吊杆减振的新型电涡流TMD开发与应用[J].中国公路学报,2015,28(4):60-68.LEI Xu,NIU Hua-wei,CHEN Zheng-qing,et al.Development and Application of a New-type Eddy Current TMD for Vibration Control of Hangers of Longspan Steel Arch Bridges[J].China Journal of Highway and Transport,2015,28(4):60-68.
[5]夏云.基于ANSYS的矩形截面等强度悬臂梁的设计[J].中国西部科技,2010,9(23):26-27,32.XIA Yun.Design the Rectangle Equal Strength Cantilever Based on ANSYS[J].Science and Technology of West China,2010,9(23):26-27,32.
[6]张针粒,李世其,朱文革.一类整星隔振器的等强度设计方法[J].振动工程学报,2012,25(4):418-425.ZHANG Zhen-li,LI Shi-qi,ZHU Wen-ge.Equal Strength Design Method for a Kind of Whole-spacecraft Isolator[J].Journal of Vibration Engineering,2012,25(4):418-425.
[7]耿云贵.等强度悬臂梁实验装置的设计和应用[J].焦作矿业学院学报,1987(2):200-206.GENG Yun-gui.Application and Design of Cantilever Beam with Equalized Strength for Testing Equipment[J].Journal of Jiaozuo Mining Institute,1987(2):200-206.
[8]孙华,刘波,周海滨,等.一种基于等强度梁的光纤光栅高频振动传感器[J].传感技术学报,2009,22(9):1270-1275.SUN Hua,LIU Bo,ZHOU Hai-bin,et al.A Novel FBG High Frequency Vibration Sensor Based on Equi-intensity Cantilever Beam[J].Chinese Journal of Sensors and Actuators,2009,22(9):1270-1275.
[9]王雷,刘爱莲,李英娜,等.光纤光栅在等强度悬臂梁均匀应变区的转换与有限元分析[J].光学技术,2015,41(3):221-224.WANG Lei,LIU Ai-lian,LI Ying-na,et al.The Change of Fiber Bragg Grating in Uniform Strain Zones and Finite Element Analysis[J].Optical Technique,2015,41(3):221-224.
[10]邱艳宇,赵跃堂,张虹.等强度悬臂梁自振频率计算与实验研究[J].实验科学与技术,2014,12(2):26-28.QIU Yan-yu,ZHAO Yue-tang,ZHANG Hong.Calculation and Experiment of Natural Frequency of Equal Strength Beam[J].Experiment Science and Technology,2014,12(2):26-28.
[11]王文熙.桥梁TMD系统的参数优化与设计[D].长沙:湖南大学,2014.WANG Wen-xi.Parametric Optimization and Design of Bridge TMD System[D].Changsha:Hunan University,2014.
[2]顾明,陈甦人,项海帆,等.用于杨浦大桥抖振控制的MTMD研究[J].振动工程学报,1998,11(1):1-8.GU Ming,CHEN Su-ren,XIANG Hai-fan,et al.Buffeting Control of the Yangpu Bridge Using Multiple Tuned Mass Dampers[J].Journal of Vibration Engineering,1998,11(1):1-8.
[3]刘勋,施卫星,陈希.单摆式TMD简介及其减振性能分析[J].结构工程师,2012,28(6):66-71.LIU Xun,SHI Wei-xing,CHEN Xi.Introduction and Analysis of the Pendulum-type Tuned Mass Damper[J].Structural Engineers,2012,28(6):66-71.
[4]雷旭,牛华伟,陈政清,等.大跨度钢拱桥吊杆减振的新型电涡流TMD开发与应用[J].中国公路学报,2015,28(4):60-68.LEI Xu,NIU Hua-wei,CHEN Zheng-qing,et al.Development and Application of a New-type Eddy Current TMD for Vibration Control of Hangers of Longspan Steel Arch Bridges[J].China Journal of Highway and Transport,2015,28(4):60-68.
[5]夏云.基于ANSYS的矩形截面等强度悬臂梁的设计[J].中国西部科技,2010,9(23):26-27,32.XIA Yun.Design the Rectangle Equal Strength Cantilever Based on ANSYS[J].Science and Technology of West China,2010,9(23):26-27,32.
[6]张针粒,李世其,朱文革.一类整星隔振器的等强度设计方法[J].振动工程学报,2012,25(4):418-425.ZHANG Zhen-li,LI Shi-qi,ZHU Wen-ge.Equal Strength Design Method for a Kind of Whole-spacecraft Isolator[J].Journal of Vibration Engineering,2012,25(4):418-425.
[7]耿云贵.等强度悬臂梁实验装置的设计和应用[J].焦作矿业学院学报,1987(2):200-206.GENG Yun-gui.Application and Design of Cantilever Beam with Equalized Strength for Testing Equipment[J].Journal of Jiaozuo Mining Institute,1987(2):200-206.
[8]孙华,刘波,周海滨,等.一种基于等强度梁的光纤光栅高频振动传感器[J].传感技术学报,2009,22(9):1270-1275.SUN Hua,LIU Bo,ZHOU Hai-bin,et al.A Novel FBG High Frequency Vibration Sensor Based on Equi-intensity Cantilever Beam[J].Chinese Journal of Sensors and Actuators,2009,22(9):1270-1275.
[9]王雷,刘爱莲,李英娜,等.光纤光栅在等强度悬臂梁均匀应变区的转换与有限元分析[J].光学技术,2015,41(3):221-224.WANG Lei,LIU Ai-lian,LI Ying-na,et al.The Change of Fiber Bragg Grating in Uniform Strain Zones and Finite Element Analysis[J].Optical Technique,2015,41(3):221-224.
[10]邱艳宇,赵跃堂,张虹.等强度悬臂梁自振频率计算与实验研究[J].实验科学与技术,2014,12(2):26-28.QIU Yan-yu,ZHAO Yue-tang,ZHANG Hong.Calculation and Experiment of Natural Frequency of Equal Strength Beam[J].Experiment Science and Technology,2014,12(2):26-28.
[11]王文熙.桥梁TMD系统的参数优化与设计[D].长沙:湖南大学,2014.WANG Wen-xi.Parametric Optimization and Design of Bridge TMD System[D].Changsha:Hunan University,2014.