桥梁高墩结构的运动稳定性及影响因素分析
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摘要
随着现代科学技术日新月异的发展,桥梁跨径越来越大,桥墩越来越高,结构受力空间性增强,同时,桥梁中的桥墩结构越来越多的采用高强材料和薄壁结构,使得桥墩稳定问题日益突出,特别是现代超高墩桥梁的桥墩部分长细比越来越大,分析其稳定性显得尤为重要。
对桥墩结构稳定性的研究,当前通行的方法是取最不利状态进行分析,例如计算最大悬臂施工状态下的稳定系数,这是一种静力分析的方法,相对而言,动力分析尚处于理论为主的阶段。
本文首先导出了桥墩结构在轴向荷载作用下的运动平衡方程,然后以李雅普诺夫运动稳定性理论为基础,在不同的边界条件下选取不同的试函数来模拟变形曲线,推导了运动稳定区和不稳定区的界限,分析材料常数、截面形式和边界条件对其的影响。
尝试改进原有弱参数激励的限制,寻求新的求解参激问题的方法：先沿用传统方法,在弱参数激励的前提下进行分析,得到相应的近似解和过渡曲线。然后,突破参数激励幅值的限值,通过表达式转换得到另一个小参数替换前者,确定任意激励幅值下的稳定区和不稳定区。并将传统方法和改进方法的计算结果进行对比,证实了改进方法有可取之处。
继而,引入非线性项,建立非线性微分方程。考虑轴向荷载产生的轴向变形影响,忽略高阶小项,运用加权残值法进行转换,得到一般形式的运动方程。用多尺度法进行定性分析,分别讨论了基本参数共振和主参数共振下的非线性问题,两者都将出现Hopf分岔。
实例分析时,选取某高墩特大桥为研究对象进行线性和非线性的分析。将规范规定的荷载合理的转化为动载,对不同模型根据时长分别确定载荷步,以基本参数共振和主参数共振时的动力响应来对比相关因素的影响程度。特别是针对成桥状态,将墩底的边界条件转换为不同的支撑刚度进行数字试验,分别进行线性和非线性的分析,得出了有益于工程设计的结论。
The stability of bridge structure is one of the main problems in the safety and economy. It has the same importance with the strength. With the rapid development of modern science and technology, more and more high strength materials and thin wall structures are used in the piers. Therefore the stability of bridge structure is becoming increasingly prominent. Especially the pier structure slenderness ratio of modern very high-pier bridge is being larger and larger, so analysis of its stability is particularly important.
For the stability of pier structure, the current popular method is to focus on the most unfavorable state, for example, to calculate stability coefficient under cantilever construction state. This is a static analysis method. Relatively, dynamic analysis is still in the theory stage.
This paper first derives the dynamic equilibrium equation of pier structure under axial loads, then based on the Lyapunov stability theory, according to different boundary conditions, chooses different trial functions to imitate the deformation curve, deduces the boundary of stable and unstable regions, and analyses the influence of material constants, section forms and boundary conditions. Then the nonlinear terms are introduced, and the multi-scale method is used for qualitative analysis. The nonlinear problem of fundamental parametric resonance and principal parametric resonance are discussed respectively, and both will lead to the Hopf bifurcation.
In addition, this paper tries to break the original weak parametric excitation limitation, and looks for new methods to solve the parametric excitation problem. With the traditional method, using small parameter, the approximate solution and the transition curve are obtained. Then, to replace small parametric excitation amplitude with another small parameter by equation transformation, the stable and unstable regions under arbitrary excitation amplitude can be determined. Moreover, compared the calculation results of the traditional method and the improved method, the advantage of the improved method is advisable.
At the case study, taking the current first high pier bridge in Asia—Hezhang super large bridge as an example, whose piers are195m high, different from the static analysis in the existing literature data, this paper transforms reasonably loads from the code to dynamic loads, compares the influence of the related factors according to the dynamic response of fundamental parametric resonance and principal parametric resonance. Especially aiming at finished bridge state, converting the boundary conditions of pier bottom to different support stiffness in digital test, analysing respectively the linear and nonlinear problems, some useful conclusions for engineering design are obtained.
对桥墩结构稳定性的研究,当前通行的方法是取最不利状态进行分析,例如计算最大悬臂施工状态下的稳定系数,这是一种静力分析的方法,相对而言,动力分析尚处于理论为主的阶段。
本文首先导出了桥墩结构在轴向荷载作用下的运动平衡方程,然后以李雅普诺夫运动稳定性理论为基础,在不同的边界条件下选取不同的试函数来模拟变形曲线,推导了运动稳定区和不稳定区的界限,分析材料常数、截面形式和边界条件对其的影响。
尝试改进原有弱参数激励的限制,寻求新的求解参激问题的方法：先沿用传统方法,在弱参数激励的前提下进行分析,得到相应的近似解和过渡曲线。然后,突破参数激励幅值的限值,通过表达式转换得到另一个小参数替换前者,确定任意激励幅值下的稳定区和不稳定区。并将传统方法和改进方法的计算结果进行对比,证实了改进方法有可取之处。
继而,引入非线性项,建立非线性微分方程。考虑轴向荷载产生的轴向变形影响,忽略高阶小项,运用加权残值法进行转换,得到一般形式的运动方程。用多尺度法进行定性分析,分别讨论了基本参数共振和主参数共振下的非线性问题,两者都将出现Hopf分岔。
实例分析时,选取某高墩特大桥为研究对象进行线性和非线性的分析。将规范规定的荷载合理的转化为动载,对不同模型根据时长分别确定载荷步,以基本参数共振和主参数共振时的动力响应来对比相关因素的影响程度。特别是针对成桥状态,将墩底的边界条件转换为不同的支撑刚度进行数字试验,分别进行线性和非线性的分析,得出了有益于工程设计的结论。
The stability of bridge structure is one of the main problems in the safety and economy. It has the same importance with the strength. With the rapid development of modern science and technology, more and more high strength materials and thin wall structures are used in the piers. Therefore the stability of bridge structure is becoming increasingly prominent. Especially the pier structure slenderness ratio of modern very high-pier bridge is being larger and larger, so analysis of its stability is particularly important.
For the stability of pier structure, the current popular method is to focus on the most unfavorable state, for example, to calculate stability coefficient under cantilever construction state. This is a static analysis method. Relatively, dynamic analysis is still in the theory stage.
This paper first derives the dynamic equilibrium equation of pier structure under axial loads, then based on the Lyapunov stability theory, according to different boundary conditions, chooses different trial functions to imitate the deformation curve, deduces the boundary of stable and unstable regions, and analyses the influence of material constants, section forms and boundary conditions. Then the nonlinear terms are introduced, and the multi-scale method is used for qualitative analysis. The nonlinear problem of fundamental parametric resonance and principal parametric resonance are discussed respectively, and both will lead to the Hopf bifurcation.
In addition, this paper tries to break the original weak parametric excitation limitation, and looks for new methods to solve the parametric excitation problem. With the traditional method, using small parameter, the approximate solution and the transition curve are obtained. Then, to replace small parametric excitation amplitude with another small parameter by equation transformation, the stable and unstable regions under arbitrary excitation amplitude can be determined. Moreover, compared the calculation results of the traditional method and the improved method, the advantage of the improved method is advisable.
At the case study, taking the current first high pier bridge in Asia—Hezhang super large bridge as an example, whose piers are195m high, different from the static analysis in the existing literature data, this paper transforms reasonably loads from the code to dynamic loads, compares the influence of the related factors according to the dynamic response of fundamental parametric resonance and principal parametric resonance. Especially aiming at finished bridge state, converting the boundary conditions of pier bottom to different support stiffness in digital test, analysing respectively the linear and nonlinear problems, some useful conclusions for engineering design are obtained.
引文
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