Nonlinear dynamic analysis of galloping of a single iced conductor with four degrees of freedom based on curved beam theory

Based on the nonlinear strain-displacement relationship of spatial curved beam theory, a finite element model for galloping analysis of iced transmission lines is established, which involves three translational degrees of freedom (DOF) and one rotational degree of freedom for each node. Considering the aerodynamic nonlinearity and the geometric nonlinearity of large amplitude motions of the iced transmission line, the nonlinear dynamic finite element equation is presented by using the virtual work principle. The equation is transformed into the sub-space according to the mode superposition method and a time integration algorithm is also performed in the sub-space. Then, the element independence and modal convergence are researched. Finally, the influence of aerodynamic forces on structural frequency is analyzed. The numerical results show that aerodynamic forces will greatly affect the torsional frequency of the transmission line, which accurately reflects the dynamic characteristics of transmission lines. Furthermore, the galloping calculation of the transmission line has reliable accuracy by using 4-DOF (per node) elements for the iced conductor. On the other hand, the model can predict the actual galloping response of the transmission line, which is convenient for the implementation of subsequent control design.