A Force Method Model for Dynamic Analysis of Flat-Sag Cable Structures
A new force method is proposed for analysing the dynamic behaviour of oscillating cables with small sags. The accepted dynamic model of such cables reduces to a partial differential equation (the equation of motion) and an integral equation (the compatibility equation). In the paper, D’Alembert’s travelling wave solution is applied to the partial differential equation (PDE). Substituting the solution into the compatibility and boundary conditions, the governing equation is obtained in terms of the dynamic tension increment. This equation has been named the force method dynamic equation (FMDE). In this way the infinite-degree-of-freedom dynamic system is effectively simplified to a system with only one unknown. Explicit solutions for both single-span and multi-span cable systems are derived. The natural frequencies obtained from the FMDE are shown to be identical to those deduced using the conventional displacement method (DM). Nonlinear governing equations are developed by considering the effect of quadratic and cubic displacement terms. Finally, two examples are presented to illustrate the accuracy of the proposed force method for single and multi-span cable systems subjected to harmonic forces.