Analysis Of Nonlinear Vibration Behaviors By Finite Volume Method For Cable-Nets Structure

Owing to many unique properties of their own such as light self-weight, large flexibility and high damping ratio, net cables often suffer large displacements and small strains even under normal work conditions. Net cables are also sensitive to dynamic loading with low frequencies such as wind loading. The deformation and vibration analysis of net cables under common loads is therefore a complex nonlinear problem as geometric non-linearity is generally involved.In this dissertation a new numerical method — the finite volume method is developed to achieve the large-deflection static and dynamic characteristic analysis for net cables. The finite-volume division scheme is first established along the length of the cables and the deformation of each volume is defined using the common engineering strain concept. Based on this strain definition the strain energy of the net 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 net cable are also obtained. The Dynamical Relaxation 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 net cable under the given vertical load are analyzed. The obtained numerical results are compared with the results obtained by the other methods and good agreement is found. This demonstrates the accuracy and validity of the proposed method. Then the dynamic behavior analysis is conducted. The nonlinear discretized dynamic equations were solved with the aid of MATLAB software. As an example a typical diamond net cable is considered. The modal frequencies and shapes are determined. Through discussion and comparison of the numerical results with the corresponding results obtained by the other methods, it demonstrates that the proposed finite volume method can accurately and effectively predict the static and dynamic large-deflection deformation behaviors. The method is also of high computational efficiency.