Analysis Of Nonlinear Vibration Behaviors And Wind-Excited Responses For Suspension Cables

Owing to many unique properties of their own such as light self-weight, large flexibility and low damping ratio, suspension cables often suffer large displacements but small strains each under normal work conditions. Cables are also sensitive to dynamic loading with low frequencies such as wind loading. The deformation and vibration analysis of cables under common loads is therefore a complex nonlinear problem as geometric non-linearity is generally involved.In this thesis a new numerical method - the finite volume method is developed to achieve the static and dynamic large-deflection response analysis for suspension cables. The finite-volume division scheme is first established along the length of the cable and the deformation of each volume is defined using the common engineering strain concept. Based on this strain definition the strain energy of the cable is determined. The final finite-volume discretization equations are derived using the Lagrange principle. Meanwhile the global nodal force vectors, mass matrix and tangent stiffness matrix of the cable are also obtained. The Dynamical Relaxition Method is adopted for solution of the obtained discretized equations in static forming problems.Based on the above formulation large-deflection static analysis is first carried out. The in-plane large displacements of a typical suspension cable under the given vertical load are analyzed. The obtained numerical results are compared with results got by the other methods and good agreement is found. This demonstrates the accuracy and validity of the proposed method. Then the dynamic behavior analysis and harmonically excited transient response analysis are conducted. The nonlinear discretized dynamic equations were achieved in MATLAB. As an example the main cable of the Tsing Ma suspension bridge is considered. The modal frequencies and shapes are determined. Finally the wind-induced dynamic responses of suspension cables are discussed and a typical numerical example is presented. In this dynamic analysis the fluctuating wind-load function modeled from a certain wind speed spectrum is taken as the dynamic loading. Through discussion and comparison of some numerical results with the corresponding tested results, it demonstrates that the proposed finite volume method can accurately and effectively predict the static large-deflection deformation behavior and wind-induced vibration behavior. The method is also of high computational efficiency.