Experimental And Analytic Study Of Vibration Control Of Cable Based On Shape Memory Alloy Damper

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.