索网-阻尼器系统自振特性研究

Study on Natural Vibration Characteristics of Cable Network-Damper System

斜拉桥中多根斜拉索与辅助索、阻尼器连接形成多层索网-阻尼器系统,可有效实现斜拉索减振。为深入了解该系统的真实动力行为,揭示辅助索、阻尼器作用的相互影响规律,文中提出了多层索网-阻尼器系统模型,将辅助索简化为线性弹簧单元,通过理论推导得到系统的复特征方程,进而求解出系统各阶自振频率、阻尼比,并提出了局部振动模态参数以表征系统不同模态的局部振动程度及系统中的能量分布规律,辅助判断系统振动的整体性;借助实验及有限元仿真分析方法验证了理论公式的正确性;研究了辅助索从柔到刚变化过程中三层索网-单阻尼器系统振型、频率、局部振动模态参数及阻尼比的变化规律,分析了辅助索刚度、阻尼器位置变化对系统阻尼比的影响。研究结果表明:多层索网-阻尼器系统的形成具有减小拉索振幅、提高系统阻尼比的效果;辅助索刚度变化和设置索端阻尼器都会使系统的多阶振型发生相应的变化,阻尼器索端锚固位置变化也会引起个别阶振型的变化,阻尼比与阻尼器所在索段振型振幅密切相关,与辅助索刚度变化密切相关;并非所有模态阻尼比都会从索端阻尼器的设置中获益。总体来说,阻尼器在索端锚固点距离桥面越远,对阻尼器发挥作用愈有利;辅助索刚度越大,系统的整体性越好,频率越高,各拉索之间的相互约束更强。

In cable-stayed bridges,multiple stay cables are connected with cross-ties and dampers to form a multilevel cable network-damper system,which can effectively reduce the vibration of stay cables.In order to deeply understand the real dynamic behavior of the system and grasp the interaction law of cross-ties and dampers,this paper proposes a model of multilevel cable network-damper system,which simplifies the cross-ties into linear spring elements,and obtains the complex characteristic equation of the system through theoretical derivation.Next,the natural frequency and damping ratio of each order of the system are solved,and local mode parameter is proposed to characterize the local vibration degree of different modes as well as the energy distribution rules of the system,and,furthermore,auxiliary estimate the vibration consistent of the system.Then,the proposed theoretical formulation is verified by the experiment and finite element simulation.Fnially,the changes of vibration mode,frequency,local mode parameter and damping ratio of the triple-layer cable network-single damper system during the change of cross-ties from flexible to rigid are investigated,and the effects of the cross-tie stiffness and damper position on the damping ratio of the system are analyzed.The results show that the multilevel cable networks-damper system decreases the amplitude of the cables and increases damping ratio of the system;that the stiffness change of the cross-tie and the set of damper at the cable end may both lead to corresponding change of multi-order system mode shape;that the change of anchoring position of the damper at the cable end may also cause individual mode shape change.;that the damping ratio is closely related to the amplitude of the section where the damper is located and to the stiffness change of the cross-tie;and that not all mode damping ratios benefit from the damper set at the cable end.In general,the farther the damper is from the bridge deck at the cable-end anchor point,the more favorable it is for the damper to play;the greater the stiffness of the auxiliary cable,the better the integrity of the vibration system;the higher the frequency,the stronger the mutual constraint between the cables.