Approximate Series Solutions for Nonlinear Free Vibration of Suspended Cables

Abstract EN

This paper presents approximate series solutions for nonlinear free vibration of suspended cables via the Lindstedt-Poincare method and homotopy analysis method, respectively.

Firstly, taking into account the geometric nonlinearity of the suspended cable as well as the quasi-static assumption, a mathematical model is presented.

Secondly, two analytical methods are introduced to obtain the approximate series solutions in the case of nonlinear free vibration.

Moreover, small and large sag-to-span ratios and initial conditions are chosen to study the nonlinear dynamic responses by these two analytical methods.

The numerical results indicate that frequency amplitude relationships obtained with different analytical approaches exhibit some quantitative and qualitative differences in the cases of motions, mode shapes, and particular sag-to-span ratios.

Finally, a detailed comparison of the differences in the displacement fields and cable axial total tensions is made.