竖向地震诱发桥梁结构多次重撞击问题的研究
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摘要
随着近年来一些无法用传统观点解释的桥梁震害的发现,被低估的竖向地震动对工程结构可能造成的损害受到了越来越多的关注。竖向地震动可能引发桥跨结构和桥墩间的多次重撞击现象,造成接触面的损伤、桥跨弯矩超载以及桥墩底部混凝土破碎、钢筋屈曲等震害。由于桥梁结构间的多次重撞击问题涉及多变接触拓扑构形、波动效应和非线性效应等复杂情况,对其的理论和数值研究存在较大困难。本文提出并运用瞬态波特征函数展开法,研究了竖向地震作用下桥梁结构的多次弹性重撞击瞬态波响应问题。本文的主要研究工作包括：
(1)建立了竖向地震作用下双跨单墩桥梁结构间多次重撞击动力学模型,提出了应用瞬态波特征函数展开法解决多次重撞击问题的基本理论。通过接触面上的应力和位移边界条件,给出了交替进行的撞击过程和分离过程开始时间的判别方法。并采用撞击过程中的组合体瞬态内力法,给出了多次重撞击力的求解方法。
(2)针对人工简谐竖向地震波作用下的双跨连续刚构桥的瞬态波传播问题,应用瞬态波特征函数展开法推导了瞬态波响应理论解。研究了竖向地震激励引起的瞬态波的反射、相互作用和波碰撞等波传播现象。并通过选取不同的竖向地震烈度,对比研究了桥跨长度参数对桥墩和桥跨结构响应的影响。
(3)应用瞬态波特征函数展开法研究了人工简谐竖向地震波作用下双跨连续梁桥的多次重撞击问题,推导了交替发生的撞击接触过程和分离过程的瞬态波响应理论解。系统地研究了计算时间步长和波模态截断数对重撞击力的收敛性,描述了地震瞬态波和撞击激发的瞬态波在结构内的传播过程,并探讨了不同桥梁结构参数和地震周期对桥梁结构响应行为的影响。
(4)基于人工简谐竖向地震激励,通过对比研究相同结构参数的连续刚构桥和连续梁桥地震瞬态响应的计算结果,表明不同墩梁连接形式对桥梁结构响应有着显著的影响。对比分析了地震激励周期和桥梁结构参数对重撞击(接触)力、桥跨弯矩和桥墩轴力等响应的影响。
(5)提出了研究实际竖向地震波作用下连续梁桥多次重撞击问题的瞬态波特征函数方法。通过对地震波进行FFT分析,推导出由多个简谐波叠加而成的实际复杂竖向地震波作用下桥梁多次重撞击瞬态响应理论解。并研究了实际竖向地震波作用下,地震波的频谱特性和桥梁结构参数对桥梁多次重撞击瞬态响应的影响。
With the observations of bridge damages which can't be explained by the tradition views, it's found the effect of vertical earthquake is underestimated. So there are more attentions for possible structural failure due to vertical earthquake. Vertical earthquake may causes the multiple poundings between girders and piers, which lead to contact surface damage, girders moment overloaded, the concrete broken and the reinforcement buckling in the bottom of piers. However, since these are related to variable contact topology, wave effect and nonlinear effect, the theoretical and numerical studies on multiple-pounding are difficult. In this paper, the multiple elastic poundings responses under vertical earthquakes are solved using the expansion of transient wave functions in a series of eigenfunctions. The main researches are shown as followings:
(1) A basic theory of using the expansion of transient wave functions in a series of eigenfunctions is developed to account for multiple poundings dynamics of bridge structures based on a single-pier and two-span bridge model under vertical earthquake. The determination method for the start time of pounding phase and separation phase which appear alternately is presented. The multiple poundings force is obtained based on the transient internal force of contact surface of combined impact body.
(2) By the use of the artificial vertical earthquake in the form of a sinusoidal excitation, the theoretical solution of transient wave responses of continuous rigid frame bridge are derived from the expansion of transient wave functions in a series of eigenfunctions. The propagations of stress wave including reflection, reaction and wave impacts throughout the pier and the girders are studied. The effects of the vertical earthquake intensity and the length of girder are analyzed for the structures responses of bridges.
(3) By the use of the artificial sinusoidal earthquake, the multiple poundings problem of continuous bridge is studied. The transient responses of alternative phases of pounding and separation are derived from the present method. The pounding force is proved convergent for the time step length and the truncation of wave modes. The propagations of earthquake wave and the pounding-induced transient waves can be depicted. The effects of the vertical earthquake period and the bridge parameters are analyzed for the structures responses of bridges.
(4) By comparison of transient responses of continuous rigid frame bridge and continuous bridge with same structure parameters based on the artificial sinusoidal earthquake, it's shown the connection forms of girders and pier have obvious effects for bridge dynamics. Influences of the vertical earthquake period and the bridge parameters on pounding (contact) force, girders moment and pier axial force are studied.
(5) The method of studying multiple poundings problem of continuous bridge under real vertical earthquake is proposed. Real vertical earthquake can be equal to sinusoidal wave superposition throughout FFT analysis. The multiple poundings response is derived from using the expansion of transient wave functions in a series of eigenfunctions. Influences of the frequency spectrum characteristics of vertical earthquake and the bridge parameters are analyzed for the multiple poundings responses of bridges.
(1)建立了竖向地震作用下双跨单墩桥梁结构间多次重撞击动力学模型,提出了应用瞬态波特征函数展开法解决多次重撞击问题的基本理论。通过接触面上的应力和位移边界条件,给出了交替进行的撞击过程和分离过程开始时间的判别方法。并采用撞击过程中的组合体瞬态内力法,给出了多次重撞击力的求解方法。
(2)针对人工简谐竖向地震波作用下的双跨连续刚构桥的瞬态波传播问题,应用瞬态波特征函数展开法推导了瞬态波响应理论解。研究了竖向地震激励引起的瞬态波的反射、相互作用和波碰撞等波传播现象。并通过选取不同的竖向地震烈度,对比研究了桥跨长度参数对桥墩和桥跨结构响应的影响。
(3)应用瞬态波特征函数展开法研究了人工简谐竖向地震波作用下双跨连续梁桥的多次重撞击问题,推导了交替发生的撞击接触过程和分离过程的瞬态波响应理论解。系统地研究了计算时间步长和波模态截断数对重撞击力的收敛性,描述了地震瞬态波和撞击激发的瞬态波在结构内的传播过程,并探讨了不同桥梁结构参数和地震周期对桥梁结构响应行为的影响。
(4)基于人工简谐竖向地震激励,通过对比研究相同结构参数的连续刚构桥和连续梁桥地震瞬态响应的计算结果,表明不同墩梁连接形式对桥梁结构响应有着显著的影响。对比分析了地震激励周期和桥梁结构参数对重撞击(接触)力、桥跨弯矩和桥墩轴力等响应的影响。
(5)提出了研究实际竖向地震波作用下连续梁桥多次重撞击问题的瞬态波特征函数方法。通过对地震波进行FFT分析,推导出由多个简谐波叠加而成的实际复杂竖向地震波作用下桥梁多次重撞击瞬态响应理论解。并研究了实际竖向地震波作用下,地震波的频谱特性和桥梁结构参数对桥梁多次重撞击瞬态响应的影响。
With the observations of bridge damages which can't be explained by the tradition views, it's found the effect of vertical earthquake is underestimated. So there are more attentions for possible structural failure due to vertical earthquake. Vertical earthquake may causes the multiple poundings between girders and piers, which lead to contact surface damage, girders moment overloaded, the concrete broken and the reinforcement buckling in the bottom of piers. However, since these are related to variable contact topology, wave effect and nonlinear effect, the theoretical and numerical studies on multiple-pounding are difficult. In this paper, the multiple elastic poundings responses under vertical earthquakes are solved using the expansion of transient wave functions in a series of eigenfunctions. The main researches are shown as followings:
(1) A basic theory of using the expansion of transient wave functions in a series of eigenfunctions is developed to account for multiple poundings dynamics of bridge structures based on a single-pier and two-span bridge model under vertical earthquake. The determination method for the start time of pounding phase and separation phase which appear alternately is presented. The multiple poundings force is obtained based on the transient internal force of contact surface of combined impact body.
(2) By the use of the artificial vertical earthquake in the form of a sinusoidal excitation, the theoretical solution of transient wave responses of continuous rigid frame bridge are derived from the expansion of transient wave functions in a series of eigenfunctions. The propagations of stress wave including reflection, reaction and wave impacts throughout the pier and the girders are studied. The effects of the vertical earthquake intensity and the length of girder are analyzed for the structures responses of bridges.
(3) By the use of the artificial sinusoidal earthquake, the multiple poundings problem of continuous bridge is studied. The transient responses of alternative phases of pounding and separation are derived from the present method. The pounding force is proved convergent for the time step length and the truncation of wave modes. The propagations of earthquake wave and the pounding-induced transient waves can be depicted. The effects of the vertical earthquake period and the bridge parameters are analyzed for the structures responses of bridges.
(4) By comparison of transient responses of continuous rigid frame bridge and continuous bridge with same structure parameters based on the artificial sinusoidal earthquake, it's shown the connection forms of girders and pier have obvious effects for bridge dynamics. Influences of the vertical earthquake period and the bridge parameters on pounding (contact) force, girders moment and pier axial force are studied.
(5) The method of studying multiple poundings problem of continuous bridge under real vertical earthquake is proposed. Real vertical earthquake can be equal to sinusoidal wave superposition throughout FFT analysis. The multiple poundings response is derived from using the expansion of transient wave functions in a series of eigenfunctions. Influences of the frequency spectrum characteristics of vertical earthquake and the bridge parameters are analyzed for the multiple poundings responses of bridges.
引文
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