阻尼器对悬索桥吊索减振效果的数值研究

发布时间：2018-01-03 13:27

本文关键词：阻尼器对悬索桥吊索减振效果的数值研究　出处：《湖南大学》2015年硕士论文　论文类型：学位论文

【摘要】：随着悬索桥的跨度不断增大,其吊索的长度也不断增长。由于吊索属于细长结构,其阻尼小、质量轻、频率低的特点,极易在风荷载、桥面或主缆的激励作用下发生大幅振动。本文采用数值方法研究阻尼器对悬索桥吊索振动的控制效果,主要内容如下:(1)采用数值方法,以单根吊索为研究对象,研究了阻尼器支架刚度、阻尼器刚度和吊索弯曲刚度对悬索桥吊索减振效果的影响。首先,推导了支架-阻尼器-吊索系统的运动偏微分方程。其次,采用有限差分方法对支架-阻尼器-吊索系统的运动微分方程进行数值离散求解,与已有的结果验证了方法的可靠性,研究了阻尼器支架刚度、阻尼器刚度和吊索弯曲刚度对无量纲阻尼比曲线、可实现的最优阻尼比及其对应的最优阻尼系数等的影响,研究了阻尼器支架模态质量的影响,并与相关文献结果进行比较。研究结果表明,随着阻尼器支架刚度的减小,能实现的最优阻尼比减小,对应的最优阻尼系数也减小,会影响阻尼器效率,且各阶模态的无量纲阻尼比曲线不一致,阻尼器支架的模态质量对阻尼器效率影响很小;随着阻尼器刚度的增大,能实现的最优阻尼比减小,对应的最优阻尼系数则增大,也会影响阻尼器效率;随着吊索弯曲刚度的减小,能实现的最优阻尼比先减小后增大,对应的最优阻尼系数增大,但是实际悬索桥的吊索弯曲刚度很小,对阻尼器效率的影响可忽略。(2)采用数值方法,以平行双吊索为研究对象,研究了双吊索之间安装阻尼器对双吊索系统动力特性的影响。首先,推导了双吊索-阻尼器系统的运动偏微分方程。其次,采用有限差分方法对双吊索-阻尼器系统的运动微分方程进行数值离散求解,研究了双吊索之间安装单个和多个阻尼器情况下,对结构频率、振型和模态阻尼比的影响。研究结果表明:平行双吊索之间安装阻尼器仅能对双吊索反向振型提供模态阻尼,对双吊索同向振型不能提高模态阻尼;在双吊索之间安装阻尼器,能够改变结构振型的排列次序,提高单根吊索的振动频率,对于吊索的振动控制有利,当阻尼器阻尼系数无穷大时,相当于刚性分隔器的作用。(3)以四根吊索为研究对象,吊索之间以刚性分隔器连接,在吊索端部安装双阻尼器,以控制吊索的扭转振动。采用ANSYS有限元软件平台,建立了安装刚性分隔器的四根吊索模型,研究了阻尼器对四吊索-分隔器系统扭转振动的控制效果。研究了四吊索-分隔器-阻尼器系统的扭转模态无量纲阻尼比曲线,研究了阻尼器支架刚度和阻尼器刚度对扭转模态无量纲阻尼比曲线、可实现的最优阻尼比及其对应的最优阻尼系数等的影响,结果表明:阻尼器自身刚度和阻尼器支架刚度都会使系统扭转模态阻尼比减小,其无量纲阻尼比曲线与单根吊索-阻尼器系统的无量纲阻尼比曲线相同。
[Abstract]:With the increasing span of suspension bridge, the length of sling is also increasing. Because the slings belong to slender structure, its damping is small, light weight, low frequency, so it is easy to wind load. Large vibration occurs under excitation of bridge deck or main cable. In this paper, numerical method is used to study the control effect of suspension cable vibration of suspension bridge by damper. The main contents are as follows: 1) numerical method. The effects of damper support stiffness, damper stiffness and sling bending stiffness on the vibration reduction of suspension bridge are studied with single sling as the research object. The partial differential equations of motion of the brace-damper-sling system are derived. Secondly, the finite difference method is used to solve the differential equations of motion of the brace-damper-sling system. The reliability of the method is verified by the existing results. The stiffness of the damper bracket, the damper stiffness and the curve of the sling bending stiffness to the dimensionless damping ratio are studied. The effect of the realizable optimal damping ratio and its corresponding optimal damping coefficient on the modal mass of the damper bracket is studied and compared with the results of related literatures. With the decrease of the stiffness of the damper, the optimal damping ratio and the corresponding optimal damping coefficient are reduced, which will affect the efficiency of the damper, and the dimensionless damping ratio curve of the different modes is not consistent. The modal mass of the damper bracket has little effect on the damper efficiency. With the increase of damper stiffness, the optimal damping ratio decreases and the corresponding optimal damping coefficient increases, which also affects the efficiency of the damper. With the decrease of the bending stiffness of sling, the optimal damping ratio decreases first and then increases, the corresponding optimal damping coefficient increases, but the actual suspension bridge sling bending stiffness is very small. The effect of dampers on the efficiency of double slings is negligible. (2) A numerical method is used to study the effect of dampers on the dynamic characteristics of double sling systems by taking parallel double slings as the object of study. The partial differential equations of motion of double sling dampers are derived. Secondly, the differential equations of motion of double slings dampers are solved numerically by finite difference method. In the case of single and multiple dampers mounted between two slings, the frequency of the structure is studied. The results show that the damper installed between parallel double slings can only provide modal damping for the reverse mode of double slings, but can not increase the modal damping for the same mode of double slings. The installation of dampers between the two slings can change the arrangement order of the structural modes and increase the vibration frequency of the single sling, which is beneficial to the vibration control of the sling, when the damping coefficient of the dampers is infinite. Equivalent to the role of rigid separator. 3) take the four sling as the object of study, the slings are connected by rigid separator, and double dampers are installed at the end of the sling. In order to control the torsional vibration of the sling, four sling models with rigid separator are established by using the ANSYS finite element software platform. The effect of damper on torsional vibration of four-sling separator system is studied, and the dimensionless damping ratio curve of four-sling separator damper system is studied. The effects of the stiffness of the damper bracket and the damper stiffness on the dimensionless damping ratio curve of torsional mode, the optimal damping ratio and the corresponding optimal damping coefficient are studied. The results show that both the stiffness of the damper and the stiffness of the damper bracket can reduce the damping ratio of the torsional mode, and the dimensionless damping ratio curve is the same as the dimensionless damping ratio curve of the single sling-damper system.
【学位授予单位】：湖南大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：U441.3;U448.25

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