【作者】 左晓宝；

【导师】 李爱群；

【作者基本信息】 东南大学 ， 防灾减灾工程及防护工程， 2005， 博士

【摘要】 斜拉索是斜拉桥等索支撑结构中重要的受力构件,随着斜拉桥跨度的逐渐增加,拉索也越来越长,轻而长的拉索的振动控制问题也日益突出。根据拉索的振动特性,寻找适合于拉索振动控制的方法和减振控制材料及装置是解决拉索振动控制的关键问题。本文以这一问题为研究背景,从形状记忆合金(SMA)材料的力学性能分析、SMA阻尼器的研制和SMA阻尼器—斜拉索系统振动与控制分析三个方面系统地开展了SMA阻尼器—斜拉索系统减振控制的理论分析与试验研究工作。本文的主要工作和成果如下:1、进行了等原子NiTi SMA丝处于超弹性状态下的力学性能试验,研究了环境温度、加载速率、应变幅值、循环次数等加载工况对SMA的相变应力、耗能能力、变形模量及残余应变等力学性能参数的影响规律,给出了各力学性能参数与相应的加载工况之间的关系。在此基础上,根据已有的几种SMA热力学本构模型,并结合SMA的应力诱发马氏体相变变化规律,建立了SMA的分段线性超弹性本构模型,该模型考虑了温度、应力及内变量(马氏体相变体积分数)等参数对SMA力学性能的影响,并简化了反映马氏体相变变化规律的相变方程。运用该模型模拟了超弹性SMA的拉伸行为,其结果与试验结果较为吻合。2、设计并制作了一种新型超弹性SMA阻尼器,通过试验研究了加载频率、位移幅值对该阻尼器的输出力、刚度和耗能等力学性能参数的影响;在试验研究和受力分析的基础上,建立了该阻尼器的力学计算模型,并就模型中的关键参数(阻尼器内滑条槽深与接触面摩擦系数、SMA丝的预应变及缠绕量、环境温度及位移幅值等)对阻尼器力学性能的影响规律进行了数值分析。试验和分析的结果表明,该阻尼器是一种位移相关性的变刚度复合摩擦阻尼器,具有输出控制力大、耗能能力强和刚度可变等特性。3、根据Hamilton原理,结合Galerkin法,建立了SMA阻尼器—拉索系统的非线性振动方程。以润扬大桥斜拉桥的J13索为例,通过数值仿真分析,探讨了斜拉索的三维非线性耦合振动特性,分析了SMA阻尼器及其参数(凹槽深度、接触面摩擦系数、SMA丝的绕制量、环境温度和安装位置等)对拉索减振效果的影响。分析结果表明,非线性耦合作用能激发或加剧拉索的三维振动反应,其程度取决于Irvine参数的大小,当Irvine参数很小时,非线性耦合作用的影响较小,可以忽略;安装SMA阻尼器后,拉索的振动受到明显的抑制作用,其中,SMA丝材的缠绕量和内、外滑条之间的摩擦系数是影响SMA阻尼器减振效果的主要参数。4、建立了基于LQR算法的SMA阻尼器—斜拉索系统振动的最优被动控制设计理论和方法,以合理地确定SMA阻尼器的有关参数,给出了SMA阻尼器参数优化设计的原理和步骤,并以J13索的振动控制为例,进行了SMA阻尼器的参数设计和相应的控制效果分析。5、以润扬大桥斜拉桥的缩尺模型为试验平台,进行了SMA阻尼器—斜拉索—桥面系统的减振试验,研究了SMA阻尼器对J13模型索在自由振动和桥面振动激励下的减振效果的影响,并探讨了桥面振动而导致的模型索与桥面之间所出现的耦合振动现象,最后,就拉索自由振动的试验结果与理论分析结果进行了对比,以验证上述理论分析的合理性。更多还原

【Abstract】 The cable is a very important member in the cable bridge, and its length is greatly increasing with the span of the bridge. The vibration control of a light and long cable is an attentive focus. How to search for a method fit for vibration control of cable and damping material and its device is a key question. Based on the question, a series of theoretic and experimental studies, which includes analysis of mechanical behaviors of superelastic shape memory alloy, design of shape memory alloy damper, analysis of vibration control of SMA damper-cable system, have been completed. The main contents and achievements in this paper are as follows.Experiments on the mechanical behaviors of many specimens of superelastic NiTi shape memory alloy (SMA) wires have been finished in this paper. Temperature, strain rate, strain amplitude and cyclic number were considered as loading conditions to investigate the effects of them on the mechanical parameters of SMA such as phase transformation stress, energy dissipation, effective stiffness and residual strain, and the relations between every mechanical parameters and its corresponding loading conditions is presented. Based on the above experimental results and the general SMA constitutive models, and depending on analysis of stress induced Martensite transformation characteristics of SMA, a simplified constitutive model, in which not only temperature, stress and internal variable’s effects on SMA’s behaviors are considered, but also the phase transformation equations reflected the changes of the Martensite transformation is simplified, has been set up. Using the model to simulate the tension behaviors of superelastic SMA, the results match well with experimental results.A new superelastic SMA damper is designed and manufactured. Experiments were taken to investigate the influence of loading frequencies and displacement amplitudes on the damper’s mechanical behaviors such as the stiffness, control force, dissipated energy. Based on the above experiments and the damper’s principle, the SMA damper’s calculating model has been established. The effects of the parameters of the damper such as the groove’depth and friction coefficient between contact surfaces, the prestrain and amount of SMA wires, environmental temperature and displacement amplitude, on its mechanical behaviors are analyzed. The results show that the SMA damper is a displacement-correlated, variable-stiffness’s, and friction type damper, and it has some advantageous properties such as large control force, high dissipated energy and variable stiffness.Based Hamilton principle and Galerkin method, the equations of nonlinear vibration of SMA damper-cable system have been set up. Taking cable J13 of the Run-yang cable-bridge as an example, by numerical simulation, the coupling behaviors of 3-D nonlinear vibration are discussed, and the effects of SMA damper and its parameters such as groove’depth, friction coefficient, amount of SMA wires, environmental temperature and the damper’s location on reducing cable’s vibration are analyzed. The results show that, the nonlinear coupling actions strengthen the vibration response of cable in 3-D directions, the level of which is determined by Irvine parameter, when a small Irvine parameter, the effects of the couplingis neglected. After setting up SMA damper in this system, the vibration of the cable is reduced obviously, and that the friction coefficient and amount of SMA wires are key factors influenced reducing cable’s vibration.In order to determine the reasonable parameters of SMA damper, the theories and methods of optimum passive control design of SMA damper-cable system have been set up based on LQR algorithm, and the principle and processes of the optimum design of SMA damper’s parameters is presented. In the end, the example of the vibration control of cable J13 is given to explain the methods of optimum design of SMA damper.Taking 1:60 model of the Run-Yang-cable-bridge as test platform, the experiments on vibration control of the system made up of SMA damper, cable and bridge deck are carried out to investigate the effects of SMA damper on reduction of cable’s vibration under free vibration and the parameter excitations induced by the deck vibration, and to discuss that the deck vibration cause the coupling vibration between the deck and the cable. In the end, the comparisons between the experimental and theoretical result of the responses of the cable under free vibration are done to verify the reasonability of above-mentioned theories.更多还原