简支桥梁体系纵向频率解析计算
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摘要
针对简支梁桥体系的纵漂振动特性计算,提出了悬臂梁顶部用弹簧联接集中质量计算体系的动力特性解析计算公式,推导了考虑轴力和不考虑轴力影响的计算方程,分析了体系基频计算中参数的相关性.通过将解析法结果与有限元法计算结果进行对比可知,该计算模型能准确地模拟简支桥梁体系的质量、刚度分布和受力特点,且解析法具有严格理论基础,可以快速、准确计算结构体系的动力特性;解析法计算结果与有限元法计算误差很小,每阶频率的误差都比较稳定,随着计算频率阶数的增加而增加;轴力会降低结构频率,其影响对体系一阶频率很小,而对二阶以上频率和振型影响较大.
The system that cantilevered beam carring a tip mass with a spring is established for computation of dynamic characters the simply supported bridge system.The equations which ignore the influence of axis force and not are deducted.With these equations the relativity in frequency computation is analyzed.Comparison of the results with the analytical method and FEM show the model can simulate the stiffness,mass distribution and mechanical characteristics exactly,and the analytical method can solve the dynamic problem dynamic characteristic rapidly with high accuracy.There is small difference between the results with two methods.The frequency difference is steady,and it is increased with the frequency number increased.The axial force can decrease the frequency,but the influence is slight for the first mode frequency and large for the second mode and above obviously.
The system that cantilevered beam carring a tip mass with a spring is established for computation of dynamic characters the simply supported bridge system.The equations which ignore the influence of axis force and not are deducted.With these equations the relativity in frequency computation is analyzed.Comparison of the results with the analytical method and FEM show the model can simulate the stiffness,mass distribution and mechanical characteristics exactly,and the analytical method can solve the dynamic problem dynamic characteristic rapidly with high accuracy.There is small difference between the results with two methods.The frequency difference is steady,and it is increased with the frequency number increased.The axial force can decrease the frequency,but the influence is slight for the first mode frequency and large for the second mode and above obviously.
引文
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[9]范立础,聂利英,李建中.地震作用下板式橡胶支座滑动的动力性能分析[J].中国公路学报,2003,16(4):30-35.FAN Li-chu,NIE Li-ying,LI Jian-zhong.Dynamiccharacter istic analys is of laminated rubber bearing slid-ing under earthquake[J].China Journal of Highway andTransport,2003,16(4):30-35.
[2]袁万城,闫冬.斜拉桥纵飘频率简化计算方法[J].同济大学学报(自然科学版),2005,33(11):1423-1427.YUAN Wan-cheng,YAN Dong.Simplified clculationalmethod of floating frequency for cable-stayed bridges[J].Journal of Tongji University(Natural Science),2005,33(11):1423-1427.
[3]JTJ004-89.公路工程抗震设计规范[S].北京:人民交通出版社,1990.
[4]范立础.桥梁抗震[M].上海:同济大学出版社,1997.
[5]ROSSIT C A,LAURA P A A.Free vibrations of a can-tilever beam with a spring-mass system attached to thefree end[J].Ocean Engineering,2001,28:933-939.
[6]GURGOZE M.On the eigenfrequencies of a cantilever beamwith attached tip mass and a spring mass system[J].Jour-nal of Sound and Vibration,1996,190:149-162.
[7]MICKENS R E.A combined equivalent linearization andaveraging perturbation method for non-linear oscillatorequations[J].Journal of Sound and Vibration,2003,264:1195-1200.
[8]VIRGIN L N,SANTILLAN S T,HOLLAND D B.Effect of gravity on the vibration of vertical cantilevers[J].Mechanics Research Communications,2007,34:312-317.
[9]范立础,聂利英,李建中.地震作用下板式橡胶支座滑动的动力性能分析[J].中国公路学报,2003,16(4):30-35.FAN Li-chu,NIE Li-ying,LI Jian-zhong.Dynamiccharacter istic analys is of laminated rubber bearing slid-ing under earthquake[J].China Journal of Highway andTransport,2003,16(4):30-35.
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