周期径向荷载作用下圆弧格构拱动力稳定性分析
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摘要
基于结构弹性稳定理论,根据能量法推导出以位移为基本未知量的圆弧格构拱总势能,从Hamilton原理出发,建立了考虑剪切变形的圆弧格构拱的动力稳定微分方程。利用Galerkin方法将其转化为二阶常微分Mathieu型参数共振方程,求得周期解所包围的动力不稳定区域,探讨了圆弧格构拱发生参数共振的动力稳定性问题,分析了缀条面积、圆弧半径、圆心角等参数对圆弧格构拱动力稳定性的影响,为拱型结构动力分析与设计提供参考依据。
Based on the theory of elastic stability of structure,the total potential energy of circular lattice arch taking displacement as basic unknown variables was obtained according to energy method.The dynamic stability differential equation of circular lattice arch subjected to distributing radial periodic load was derived by applying the energy method and Hamilton principle.Galerkin's method was used to convert the partial differential equations into the ordinary differential Mathieu equations.The dynamic instability regions surrounded by periodic solutions were obtained.The dynamic stability problems of parametric vibration were discussed about circular lattice arch.The influences of sewed bars area,radius of circle and central angle etc.on the dynamic stabilities were discusseded.This provided a reference basis for dynamic analysis and design in structural engineering.
Based on the theory of elastic stability of structure,the total potential energy of circular lattice arch taking displacement as basic unknown variables was obtained according to energy method.The dynamic stability differential equation of circular lattice arch subjected to distributing radial periodic load was derived by applying the energy method and Hamilton principle.Galerkin's method was used to convert the partial differential equations into the ordinary differential Mathieu equations.The dynamic instability regions surrounded by periodic solutions were obtained.The dynamic stability problems of parametric vibration were discussed about circular lattice arch.The influences of sewed bars area,radius of circle and central angle etc.on the dynamic stabilities were discusseded.This provided a reference basis for dynamic analysis and design in structural engineering.
引文
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[2]Bi Q,Dai H H.Analysis of non-linear dynamics and bifurcations of a shallow arch subjected to periodic excitation with internal resonance[J].Journal of Sound and Vibration,2000,233(4):557-571.
[3]Tien W M,Namachchivaya N S,Bajaj A K.Non-linear dynamics of a shallow arch under periodic excitation-I.1:2 internal resonance[J].In-ternational Journal of Non-Linear Mechanics,1994,29(3):349-366.
[4]唐毅.剪切变形对大跨格构拱平面内整体稳定的影响[D].重庆:重庆大学,2005.
[5]王连华,易壮鹏,张辉.周期荷载作用下几何缺陷拱的动力稳定性[J].湖南大学学报,2007,34(11):16-19.
[6]易壮鹏,赵跃宇,朱克兆.几何缺陷浅拱的动力稳定性分析[J].计算力学学报,2008,25(6):932-938.
[7]郭彦林,郭宇飞,窦超.纯压圆弧形钢管桁架拱平面内稳定性能及设计方法[J].建筑结构学报,2010,31(8):45-53
[8]吴玉华,亓兴军,郭剑飞.拱结构动力稳定实用判别方法[J].地震工程与工程振动,2010,30(4):45-53
[2]Bi Q,Dai H H.Analysis of non-linear dynamics and bifurcations of a shallow arch subjected to periodic excitation with internal resonance[J].Journal of Sound and Vibration,2000,233(4):557-571.
[3]Tien W M,Namachchivaya N S,Bajaj A K.Non-linear dynamics of a shallow arch under periodic excitation-I.1:2 internal resonance[J].In-ternational Journal of Non-Linear Mechanics,1994,29(3):349-366.
[4]唐毅.剪切变形对大跨格构拱平面内整体稳定的影响[D].重庆:重庆大学,2005.
[5]王连华,易壮鹏,张辉.周期荷载作用下几何缺陷拱的动力稳定性[J].湖南大学学报,2007,34(11):16-19.
[6]易壮鹏,赵跃宇,朱克兆.几何缺陷浅拱的动力稳定性分析[J].计算力学学报,2008,25(6):932-938.
[7]郭彦林,郭宇飞,窦超.纯压圆弧形钢管桁架拱平面内稳定性能及设计方法[J].建筑结构学报,2010,31(8):45-53
[8]吴玉华,亓兴军,郭剑飞.拱结构动力稳定实用判别方法[J].地震工程与工程振动,2010,30(4):45-53
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