|Title:||Wind-rain-induced vibration and control of stay cables in cable-stayed bridges|
|Subject:||Hong Kong Polytechnic University -- Dissertations|
Bridges, Cable-stayed -- Vibration
Bridges, Cable-stayed -- Aerodynamics
|Department:||Department of Civil and Structural Engineering|
|Pages:||1 v. (various pagings) : ill. (some col.) ; 30 cm|
|Abstract:||This thesis aims to develop a systematic theoretical framework, supported by field measurements and wind tunnel test results, to explore the mechanisms of wind-rain-induced cable vibration, to understand wind-rain-induced vibration behavior of prototype stay cables, and to assess the effectiveness of active stiffness control in mitigating wind-rain-induced vibration of prototype stay cables. The wind rain tunnel tests are performed to investigate the formation and position of water rivulet on the surface of inclined stationary cylinder immerged in a uniform wind field under different wind speeds and various cylinder inclinations, wind yaw angles, cylinder diameters, and water flow rates. The experimental results are then described and discussed in detail to enhance the understanding of the formation and position of the upper rivulet. The relationship between the rivulet position and the incident mean wind speed, obtained here, are used in the development of the theoretical framework. A single-degree-of-freedom (SDOF) analytical model, taking into account the interaction between wind, upper rivulet and cable, is developed to investigate the steady-state wind-rain-induced cable vibration. The circumferential oscillation of the upper rivulet is assumed to be harmonic and its amplitude is quantified using the measured results from wind rain tunnel tests. The developed SDOF analytical model is then verified through the comparisons between the analytical and measured results for some cable models tested in either a wind tunnel with fixed artificial rivulets or a wind-rain tunnel with moving rivulets. The mechanisms of wind-rain-induced cable vibration are also explored using this analytical model. It is found that the analytical model is able to capture main vibration features of inclined cylinders with moving rivulet, such as velocity- restricted vibration and amplitude-restricted vibration. The occurrence of velocity- and amplitude- restricted vibration is mainly because of alternating aerodynamic damping ratio and/or alternating excitation force due to the interaction between rivulet motion, cable motion and wind. The proposed analytical model can also predict the vibration of horizontal cylinder with fixed artificial rivulet. The SDOF model is extended to a two-degree-of-freedom (2DOF) analytical model to investigate both the transient period and the steady-state period of wind-rain-induced cable vibration and to predict the vibration amplitude and feature of the rivulet that is coupled with the motion of cylinder. In the 2DOF model, the rotating motion of the rivulet around the central axis of the cylinder is considered to couple with the transverse motion of the yawed and inclined cylinder. The interaction between the upper rivulet and the cylinder is described in terms of nonlinear damping force, linear restoring force, and inertia force. Since the equations of motion of the coupled rivulet and cylinder system are strongly nonlinear, the Runge-Kutta-Fehlberg method is applied to achieve the numerical solution of the nonlinear equations of motion of the system. The computed results from the 2DOF model are compared with wind-rain-tunnel measurement results to verify the 2DOF model. It turns out that the 2DOF model is able to capture main vibration features of inclined cylinder with moving rivulet. The detail studies on the possible mechanisms of wind-rain-induced cable vibration using the 2DOF model reveal that wind-rain-induced cable vibration depends on the mean wind speed and the static position of the upper rivulet. When mean wind speed is small, the aerodynamic damping ratio of the system is positive and the aerodynamic force due to the rivulet motion is small. Thus no significant wind-rain-induced cable vibration occurs. As mean wind speed increases to certain level, the aerodynamic damping ratio and/or aerodynamic force become alternating and the amplitude-restricted wind-rain-induced cable vibration occurs. When mean wind speed further increases, the aerodynamic damping ratio becomes positive again and the aerodynamic force becomes a harmonic excitation due to the rivulet motion. Wind-rain-induced cable vibration somewhat likes the vortex shedding induced cable vibration but the vibration amplitude is much smaller than that associated with the alternating aerodynamic damping and force. The computed results from the 2DOF model are finally compared with those predicted by the SDOF model, from which the applicability of the SDOF model can be clarified. The following study explores the possibility of applying the 2DOF model for wind-rain-induced vibration of inclined cylinder to wind-rain-induced vibration of prototype stay cables. The equation of motion of a prototype inclined sag cable under the excitation from the simultaneous occurrence of wind and rain is derived, in which the wind speed varying along the height of the cable is taken into consideration to simulate the real site condition. The equation of motion is established using the Lagrange's formulation in conjunction with the modal superposition method. The 4th-order Runge-Kutta method with variable time-step is employed to find the solution of the equation of motion. The field measurement results of wind-rain-induced prototype sag cables obtained by other researchers are then used to validate the proposed model. Finally, the mechanism of wind-rain-induced prototype sag cable vibration is explored and extensive parametric studies are performed to find the effects of main parameters on wind-rain-induced prototype cable vibration. An active control algorithm using the active stiffness control method is established to suppress wind-rain-induced vibration of prototype stay cables. The control algorithm demands the support motion based on the displacement and velocity response of the cable at its critical position. The governing equations of motion of wind-rain-induced vibration control of prototype stay cables with active stiffness control algorithm are first derived. The 4th -order Runge-Kutta method is then introduced to find numerical solutions of the problem. The effectiveness of the control method established for wind-rain-induced cable vibration is assessed subsequently. The proposed control method can reduce the displacement response amplitude of wind-rain-induced vibration of the prototype cable within the effective wind speed range if the control factor is selected properly. The proposed control scheme for wind-rain-induced cable vibration mitigation needs only small support motion with a little power supply demand. Finally, the extensive parameter studies are carried out to investigate the features of wind-rain-induced stay cable vibration with active control and their results can be used as a design guideline.|
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