复杂变截面塔式结构振动基频实用算法研究
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摘要
在Rayleigh能量法和Southwell频率合成法的基础上,以满足边界条件的静挠度函数为位移函数,推导出了底部固定、顶端带有附加质量的变截面塔式结构自振基频解析计算公式。结构的振动基频可表示成由各变形元和惯性元组成的子系统频率的合成。如果塔身截面变化复杂,可以将塔身沿高度方向划分成数个单元,以分段求和取代积分。计算实例表明,该实用算法与有限元建模计算结果很接近。通过钢塔模型的振动台试验,进一步证明了该算法具有较高的精度。该方法不仅适用于底部固定以及顶端带有附加质量的钢塔结构,也适用于其它材料、截面复杂的输电塔、电视塔、桥墩等高耸工程结构。
Based on the combination of Rayleigh and Southwell's methods,the fundamental frequencies of structures could be denoted by a composition of frequencies of several subsystems,which consists of deformation component and inertia component,thus the approximate algorithm could be built to calculate the fundamental frequency of tower structure in which the bottom is fixed and there is an additional mass on the top.If the tower body varies complicatedly,it could be divided into several elements along height direction,so the integration would be replaced by segmentation sum.In order to verify the algorithm mentioned in this paper,the vibration test of a steel tower is carried out on the shaking table to measure its fundamental frequency.The test result is close to the approximate algorithm,which shows high precision of this algorithm.This algorithm is not only suitable for the tower with fixed bottom or with an additional mass on its top,but also suitable for other high buildings with complicated section,chimneys and so on.
Based on the combination of Rayleigh and Southwell's methods,the fundamental frequencies of structures could be denoted by a composition of frequencies of several subsystems,which consists of deformation component and inertia component,thus the approximate algorithm could be built to calculate the fundamental frequency of tower structure in which the bottom is fixed and there is an additional mass on the top.If the tower body varies complicatedly,it could be divided into several elements along height direction,so the integration would be replaced by segmentation sum.In order to verify the algorithm mentioned in this paper,the vibration test of a steel tower is carried out on the shaking table to measure its fundamental frequency.The test result is close to the approximate algorithm,which shows high precision of this algorithm.This algorithm is not only suitable for the tower with fixed bottom or with an additional mass on its top,but also suitable for other high buildings with complicated section,chimneys and so on.
引文
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[5]Li Q S,Wu J R,Xu Jianyun.Longitudinal vibration of multi-step non-uniform structures with lumped masses and spring supports[J].AppliedAcoustics,2002,63:333-350.
[6]Li Q S,Fang J Q,Jeary AP.Free vibration analysis of cantilevered tall structures under various axial loads[J].Engineering Structures,2000,22:525-534.
[7]Naguleswaran S.Vibration of an Euler-Bernoulli beam on elastic end supports and with up to three step changes in cross-section[J].Interna-tional Journal of Mechanical Sciences,2002,44:2541-2555.
[8]梁枢果,朱继华,王力争.大跨越输电塔-线体系动力特性分析[J].地震工程与工程振动,2003,23(6):63-69.
[9]谢官模,王超.大跨度悬索桥竖向振动基频的实用近似计算公式[J].固体力学学报,2009,29:200-203.
[10]Auciello N M.On the transverse vibrations of non-uniform beams with axial loads and elastically restrained ends[J].International Journal of Me-chanical Sciences,2001,43:193-208.
[11]王俊,汪凤泉.变截面桥墩复合振动基频近似算法[J].东南大学学报:自然科学版,2005,25(4):580-583.
[2]Bazeos N,Hatxigeorigiou G D,Hondros ID,et al.Static,seismic and stability analyses of a prototype wind turbine steel tower[J].EngineeringStructure,2002,24(8):1015-1025.
[3]Dutta P K,Ghosh AK,Agarwal B L.Dynamic response of structures subjected to tornado loads by FEM[J].Journal of Wind Engineering and In-dustrial Aerodynamics,2002,90(1):55-69.
[4]李宏男,白海峰.输电塔线体系的风(雨)致振动响应与稳定性研究[J].土木工程学报,2008,41(11):31-38.
[5]Li Q S,Wu J R,Xu Jianyun.Longitudinal vibration of multi-step non-uniform structures with lumped masses and spring supports[J].AppliedAcoustics,2002,63:333-350.
[6]Li Q S,Fang J Q,Jeary AP.Free vibration analysis of cantilevered tall structures under various axial loads[J].Engineering Structures,2000,22:525-534.
[7]Naguleswaran S.Vibration of an Euler-Bernoulli beam on elastic end supports and with up to three step changes in cross-section[J].Interna-tional Journal of Mechanical Sciences,2002,44:2541-2555.
[8]梁枢果,朱继华,王力争.大跨越输电塔-线体系动力特性分析[J].地震工程与工程振动,2003,23(6):63-69.
[9]谢官模,王超.大跨度悬索桥竖向振动基频的实用近似计算公式[J].固体力学学报,2009,29:200-203.
[10]Auciello N M.On the transverse vibrations of non-uniform beams with axial loads and elastically restrained ends[J].International Journal of Me-chanical Sciences,2001,43:193-208.
[11]王俊,汪凤泉.变截面桥墩复合振动基频近似算法[J].东南大学学报:自然科学版,2005,25(4):580-583.
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