Hybrid pseudo-force/Laplace transform method for non-linear transient response of a suspended cable

A hybrid numerical scheme involving the combination of the Laplace transform technique and the pseudo-force method is proposed to analyze the non-linear transient response of a suspended cable subjected to arbitrary dynamic loading. A theoretical model of the cable with multi-degree-of-freedom is first obtained through discretization of the partial differential equations by finite difference approximation. The non-linear governing equations take into account the effects of quadratic and cubic geometric non-linearities. The proposed method deals with the non-linear effects as pseudo-forces and then establishes an iterative solution scheme in the alternating Laplace/time domain by means of fast numerical Laplace transform. This method eschews a time-stepping process and therefore is computationally efficient. It also readily deals with the viscoelastic damping with frequency-dependent model parameters and the hysteresis damping in terms of complex stiffness models. Numerical examples are presented to evaluate the dynamic responses of suspended cables under a concentrated sinusoidal force and a distributed random excitation, and to identify the non-linear response properties by comparison with the linear vibration. The validity and accuracy of the proposed method is also verified by comparing the results with those obtained by using the direct time integration.