Research on the characteristics of transverse dynamic stiffness of an inclined shallow cable

Based on the governing equation of inclined cable segment vibration, an equilibrium equation formulated in dynamic stiffness is built to describe the force balance status at arbitrary location along cable where transverse force is applied. A closed-form solution to transverse dynamic stiffness matrix corresponding to two degrees-of-freedom and dynamic stiffness corresponding to one degree-of-freedom is proposed herein, which considers the effects of sag, flexural rigidity, clamped boundary condition, and inclined angle of real inclined cable simultaneously. A real cable damper system vibration test is used to verify the rationality and credibility of the proposed closed-form solution. The effects of cable parameters above mentioned on the dynamic stiffness of cable are investigated by using this approach. It shows that, by the influence of these factors, the cable transverse dynamic stiffness takes on complicated behaviors. Due to the marked errors or even wrong results induced, it is unreasonable to evaluate the cable transverse dynamic stiffness both by the approach of taut string theory and by treating the inclined angle to horizontal attitude.