大跨斜拉桥拉索局部振动特性及其影响研究
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摘要
近年来,随着斜拉桥跨径的不断增大,斜拉索结构的局部振动特性及索-桥耦合振动特性正逐步成为大跨斜拉桥设计过程中的一个新的研究课题。在国内外学者研究的基础上,本文系统的研究了拉索端部塔、梁位移激励下平面内拉索局部振动特性;空间三维坐标系下拉索面内、外耦合振动特性;随机激励下拉索振动的面内、面外均方根响应特性及考虑拉索局部振动特性的斜拉桥地震时程响应特性。具体主要工作包括以下几个方面:
(1)研究了平面内拉索承受塔端、梁端谐波位移激励下的非线性振动特性。推导了完整的斜拉桥拉索平面内同时承受梁端和塔端真实激励下的振动微分方程,增加定义了拉索振动模型中的自振频率修正系数,拉索振动初始静平衡特性参数,并修正了拉索振动的强迫振动项和参数振动项系数,分析了拉索激励参数及其物理参数等因素对拉索振动特性的影响。其次,推导并统一了斜拉桥拉索平面内振动过程中松弛和无松弛状态下的斜拉桥拉索承受梁端位移激励下的单变量双控制耦合振动微分方程组。采用Runge-Kutta分段逐步时程积分方法求解该方程组,得出了拉索振动过程中的松弛和非松弛状态交替变化的全过程。
(2)研究了空间倾斜拉索承受塔端或梁端谐波位移激励下的非线性振动特性。推导并统一了斜拉索端部任意方向位移激励下综合考虑拉索振动松弛与非松弛状态的三维空间单变量双控制非线性耦合振动微分方程组;取不同拉索端部激励方向角及激励频率值,分析了拉索面内外耦合振动响应特性及面外自激振动特性,求解了耦合振动幅值与拉索面内外固有频率及激励频率的关系以及自激振动产生的最小临界激励幅值;最后,根据搜索求解相应参数下拉索振动的相平面图、Poincare截面图、最大Lyapunov指数谱图,分析和证实了拉索振动的混沌特性。
(3)研究了斜拉索面内承受端部轴向零均值高斯白噪声位移激励下的随机振动特性及拉索两端不动时承受横桥向零均值高斯白噪声随机激励下斜拉索振动特性。推导了基于伊藤方程标准形的斜拉桥拉索平面内索端承受轴向随机位移激励下的随机非线性振动微分方程。分别利用高斯截断法、随机线性化法、Falsone改进随机线性化法推出了拉索振动状态向量的二阶矩均方微分方程。推导了横桥向随机风载激励下的拉索空间三维非线性随机振动平衡微分方程,采用等价随机线性化法推出了14维拉索面内、面外横向振动状态向量一阶均方微分方程组,利用Runge-Kutta数值积分法求解该方程组的均方根响应特性。最后,基于Schorling稳定性理论,采用Lyaponov指数判断系统在随机激励下的稳定特性。
(4)对鄂东大桥全桥及拉索局部振动动力特性进行了详细的分析,结合前述推导的拉索振动一阶自振频率理论计算方程,并建立考虑拉索局部振动有限元模型(MECS)和不考虑拉索局部振动有限元模型(OECS)两种计算模型,分析了拉索自振频率及全桥结构自振频率的关系,判断了拉索可能发生大幅局部振动的拉索编号及频率匹配关系,选取具有代表性的Z16、Z30号拉索为研究对象,运用第三章的计算公式,分析了拉索的局部振动特性,并近似计算了指定激励幅值下抑制全桥斜拉索发生参数振动所需的最小模态阻尼比。
(5)研究了考虑斜拉索局部振动影响下的大跨斜拉桥抗震性能。以鄂东大桥为实例,结合ANSYS重启动功能及参量瞬变命令,编制了基于真实初始静平衡状态下及斜拉索Ernst等效弹性模量(E_(ep))时效改变下的地震非线性时程响应通用求解程序,对比分析了罕遇地震作用下拉索E_(ep)的时变和非时变效应对斜拉桥地震响应的影响规律。通过输入两种振幅一致但频谱特性各异的地震动激励,研究了不同频率匹配关系时考虑拉索局部振动而产生的“附加阻尼”效应及“振动放大”效应。
Recently,as the main span of cable-stayed bridges increase continuously,the really local vibration features of inclined cables and coupled oscillation characteristics of the cable and the bridge are more and more becoming to be a new significant topic research in the design process of cable-stayed bridges.Based on the investigation both of domestic and international scholars,this paper researched systematically in the in-plane cable local vibration characteristics,the coupled analysis of out-of-plane oscillation and in-plane vibration of stayed-cables in spatial three-dimensional coordinates,the responses of Root Mean Square(RMS) property both in in-plane and out-of-plane under random excitations, and seismic time-history response of cable-stayed bridges with local cable vibration. Concretely,the researches in this paper include the following five aspects:
(1) The inner nonlinear vibration behavior of cables subjected the the excitations at either beam or tower end was investigated.The inner oscillatory differential equation which considered the excitations at both beam and tower end was deduced,the modificatory coefficient of natural frequency and the parameters indicated initial equilibrium state in the cable vibration model was added defined,the forced vibration items and parametrical vibration items were modified,and the vibration characteristic relations with those ingredients such as physical parameters and excitation parameters are analyzed.Secondly,the inner single argument and double control coupling oscillatory differential equations in loosening and non-loosening state which considered the excitations at beam are deduced and uniformed,and the Runge-Kutta subsection integration method is applied to solve those equations,the whole alternate variation processes between loosening and non-loosening state are obtained.
(2) Non-Linear vibration behavior of spatial inclined cables subjected to harmonic and arbitrary orientation displacement excitation at beam end or tower end is carried out,the three-dimensional non-linear coupling control oscillatory differential equations in loosening and non-loosening state which considered the arbitrary orientation excitations are deduced and uniformed.With different excitation orientation angles and frequences, the coupled oscillation analysis both in-plane and out-of-plane of an inclined cable is carried out,the relationship of vibration amplitude with matching ratio of natural frequencies of cable and excitation frequency is analyzed.Subsequently,the out-of-plane self-excited vibration is investigated and the minimum excitation amplitude arising self-excited vibration is obtained.Finally,with the figure of phase plane,Poincare section and the maximal Lyapunov exponent spectrum,the existence of chaotic motions in certain parameters are proved.
(3) Non-Linear stochastic vibration behavior of inclined cables subjected to a Gaussian zero mean stationary white noise process displacement excitation at beam end or tower end and In-plane self-excited stochastic vibration behavior of inclined cables subjected to a Gaussian zero mean stationary white noise process excitation in transverse bridge orientation are carried out.The inner oscillatory differential equations which based on It(?) differential standard type are deduced.Gaussian closure method,stochastic linearization method and Falsone's innovated stochastic linearization method are applied to derive the second order mean square moment equations.The three-dimensional non-linear coupling control oscillatory differential equations of inclined cables are deduced,equivalent stochastic linearization method is applied to derive the 14 first-order nonlinear differential equations of state vectors of inclined cables,and the Runge-Kutta integration method is utilized to obtain the RMS response characteristics.The Lyaponov exponent is applied to investigate the stability property of the auto-parametric vibration under random excitations.
(4) The dynamical behavior of global bridge model and local cable model of E DONG Bridge are analyzed in detail,combined with the analytical solution of the first order natural frequency of inclined cables considering the influences of sag effect and the initial equilibrium state in the above aspect,the models both considering local cable vibration(MECS) and ignore local oscillatory(OECS) are established.Subsequently,the relationship between the natural frequency of inclined cables and the global bridge is analyzed,and the serial number of cables which may present large amplitude vibration and the corresponding frequency relationship are estimated.In the end,the local vibration characteristics of selected representational cables of Z16 and Z30 is calculated applying the formulary in chapter 3,and the minimal modal damping ratios under distinct amplitude excitation are solved approximately.
(5) Seismic time-history response of cable-stayed bridges with local cable vibration is investigated,taking E DONG Bridge for example,combined with the restart function and parameter transient variation commands in ANSYS,a general program to solve the geometrical nonlinear seismic time-history response was established based on the state of truly initial static equilibrium and time-varying effects with E_(ep) of cables,the solution was compared with the results under the time-invariant E_(ep) of cables calculated by the initial cable tension.By inputting two kinds of excitation earthquake with identical amplitudes but different spectral properties in the cable-stayed bridge model considering local cable vibrations,the additional damping effect and vibration amplificatory effect with different matching relationship of the frequencies were analyzed.
(1)研究了平面内拉索承受塔端、梁端谐波位移激励下的非线性振动特性。推导了完整的斜拉桥拉索平面内同时承受梁端和塔端真实激励下的振动微分方程,增加定义了拉索振动模型中的自振频率修正系数,拉索振动初始静平衡特性参数,并修正了拉索振动的强迫振动项和参数振动项系数,分析了拉索激励参数及其物理参数等因素对拉索振动特性的影响。其次,推导并统一了斜拉桥拉索平面内振动过程中松弛和无松弛状态下的斜拉桥拉索承受梁端位移激励下的单变量双控制耦合振动微分方程组。采用Runge-Kutta分段逐步时程积分方法求解该方程组,得出了拉索振动过程中的松弛和非松弛状态交替变化的全过程。
(2)研究了空间倾斜拉索承受塔端或梁端谐波位移激励下的非线性振动特性。推导并统一了斜拉索端部任意方向位移激励下综合考虑拉索振动松弛与非松弛状态的三维空间单变量双控制非线性耦合振动微分方程组;取不同拉索端部激励方向角及激励频率值,分析了拉索面内外耦合振动响应特性及面外自激振动特性,求解了耦合振动幅值与拉索面内外固有频率及激励频率的关系以及自激振动产生的最小临界激励幅值;最后,根据搜索求解相应参数下拉索振动的相平面图、Poincare截面图、最大Lyapunov指数谱图,分析和证实了拉索振动的混沌特性。
(3)研究了斜拉索面内承受端部轴向零均值高斯白噪声位移激励下的随机振动特性及拉索两端不动时承受横桥向零均值高斯白噪声随机激励下斜拉索振动特性。推导了基于伊藤方程标准形的斜拉桥拉索平面内索端承受轴向随机位移激励下的随机非线性振动微分方程。分别利用高斯截断法、随机线性化法、Falsone改进随机线性化法推出了拉索振动状态向量的二阶矩均方微分方程。推导了横桥向随机风载激励下的拉索空间三维非线性随机振动平衡微分方程,采用等价随机线性化法推出了14维拉索面内、面外横向振动状态向量一阶均方微分方程组,利用Runge-Kutta数值积分法求解该方程组的均方根响应特性。最后,基于Schorling稳定性理论,采用Lyaponov指数判断系统在随机激励下的稳定特性。
(4)对鄂东大桥全桥及拉索局部振动动力特性进行了详细的分析,结合前述推导的拉索振动一阶自振频率理论计算方程,并建立考虑拉索局部振动有限元模型(MECS)和不考虑拉索局部振动有限元模型(OECS)两种计算模型,分析了拉索自振频率及全桥结构自振频率的关系,判断了拉索可能发生大幅局部振动的拉索编号及频率匹配关系,选取具有代表性的Z16、Z30号拉索为研究对象,运用第三章的计算公式,分析了拉索的局部振动特性,并近似计算了指定激励幅值下抑制全桥斜拉索发生参数振动所需的最小模态阻尼比。
(5)研究了考虑斜拉索局部振动影响下的大跨斜拉桥抗震性能。以鄂东大桥为实例,结合ANSYS重启动功能及参量瞬变命令,编制了基于真实初始静平衡状态下及斜拉索Ernst等效弹性模量(E_(ep))时效改变下的地震非线性时程响应通用求解程序,对比分析了罕遇地震作用下拉索E_(ep)的时变和非时变效应对斜拉桥地震响应的影响规律。通过输入两种振幅一致但频谱特性各异的地震动激励,研究了不同频率匹配关系时考虑拉索局部振动而产生的“附加阻尼”效应及“振动放大”效应。
Recently,as the main span of cable-stayed bridges increase continuously,the really local vibration features of inclined cables and coupled oscillation characteristics of the cable and the bridge are more and more becoming to be a new significant topic research in the design process of cable-stayed bridges.Based on the investigation both of domestic and international scholars,this paper researched systematically in the in-plane cable local vibration characteristics,the coupled analysis of out-of-plane oscillation and in-plane vibration of stayed-cables in spatial three-dimensional coordinates,the responses of Root Mean Square(RMS) property both in in-plane and out-of-plane under random excitations, and seismic time-history response of cable-stayed bridges with local cable vibration. Concretely,the researches in this paper include the following five aspects:
(1) The inner nonlinear vibration behavior of cables subjected the the excitations at either beam or tower end was investigated.The inner oscillatory differential equation which considered the excitations at both beam and tower end was deduced,the modificatory coefficient of natural frequency and the parameters indicated initial equilibrium state in the cable vibration model was added defined,the forced vibration items and parametrical vibration items were modified,and the vibration characteristic relations with those ingredients such as physical parameters and excitation parameters are analyzed.Secondly,the inner single argument and double control coupling oscillatory differential equations in loosening and non-loosening state which considered the excitations at beam are deduced and uniformed,and the Runge-Kutta subsection integration method is applied to solve those equations,the whole alternate variation processes between loosening and non-loosening state are obtained.
(2) Non-Linear vibration behavior of spatial inclined cables subjected to harmonic and arbitrary orientation displacement excitation at beam end or tower end is carried out,the three-dimensional non-linear coupling control oscillatory differential equations in loosening and non-loosening state which considered the arbitrary orientation excitations are deduced and uniformed.With different excitation orientation angles and frequences, the coupled oscillation analysis both in-plane and out-of-plane of an inclined cable is carried out,the relationship of vibration amplitude with matching ratio of natural frequencies of cable and excitation frequency is analyzed.Subsequently,the out-of-plane self-excited vibration is investigated and the minimum excitation amplitude arising self-excited vibration is obtained.Finally,with the figure of phase plane,Poincare section and the maximal Lyapunov exponent spectrum,the existence of chaotic motions in certain parameters are proved.
(3) Non-Linear stochastic vibration behavior of inclined cables subjected to a Gaussian zero mean stationary white noise process displacement excitation at beam end or tower end and In-plane self-excited stochastic vibration behavior of inclined cables subjected to a Gaussian zero mean stationary white noise process excitation in transverse bridge orientation are carried out.The inner oscillatory differential equations which based on It(?) differential standard type are deduced.Gaussian closure method,stochastic linearization method and Falsone's innovated stochastic linearization method are applied to derive the second order mean square moment equations.The three-dimensional non-linear coupling control oscillatory differential equations of inclined cables are deduced,equivalent stochastic linearization method is applied to derive the 14 first-order nonlinear differential equations of state vectors of inclined cables,and the Runge-Kutta integration method is utilized to obtain the RMS response characteristics.The Lyaponov exponent is applied to investigate the stability property of the auto-parametric vibration under random excitations.
(4) The dynamical behavior of global bridge model and local cable model of E DONG Bridge are analyzed in detail,combined with the analytical solution of the first order natural frequency of inclined cables considering the influences of sag effect and the initial equilibrium state in the above aspect,the models both considering local cable vibration(MECS) and ignore local oscillatory(OECS) are established.Subsequently,the relationship between the natural frequency of inclined cables and the global bridge is analyzed,and the serial number of cables which may present large amplitude vibration and the corresponding frequency relationship are estimated.In the end,the local vibration characteristics of selected representational cables of Z16 and Z30 is calculated applying the formulary in chapter 3,and the minimal modal damping ratios under distinct amplitude excitation are solved approximately.
(5) Seismic time-history response of cable-stayed bridges with local cable vibration is investigated,taking E DONG Bridge for example,combined with the restart function and parameter transient variation commands in ANSYS,a general program to solve the geometrical nonlinear seismic time-history response was established based on the state of truly initial static equilibrium and time-varying effects with E_(ep) of cables,the solution was compared with the results under the time-invariant E_(ep) of cables calculated by the initial cable tension.By inputting two kinds of excitation earthquake with identical amplitudes but different spectral properties in the cable-stayed bridge model considering local cable vibrations,the additional damping effect and vibration amplificatory effect with different matching relationship of the frequencies were analyzed.
引文
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