The dynamic stiffness analysis of extensible inclined taut cables

The linear dynamic behaviors of an extensible sagging inclined cable are investigated. An improved dynamic stiffness matrix for a cable element is derived. The coupling between the tangential and normal displacements, the weight component parallel to the cable chord and the viscous damping are taken into account. All dynamic stiffness coefficients are derived from more general asymptotic solution of the motion equation in the natural vibration. Example calculations are discussed to demonstrate the efficiency of the current method. Since the dynamic stiffness matrix has direct relation with the natural frequency of vibration, it can be used to calculate the natural frequencies and mode shapes of the prestressed cable network and cable-stayed structures through a summation process the same as the conventional finite element method.