Theory of Weightless Sagging Elasto-Flexible Cables

Abstract

In this Paper, a theory of single sagging planer weightless elasto-flexible cables is proposed. In reference to the instantaneous natural state, hypoelastic rate- type constitutive equations and third-order nonlinear differential equations of planer motion for massless cables with nodal masses are derived. New concepts like configurational complementary potential and contra-gradient principles are proposed. Typical dynamic response of these elastic cables with different sustained loads, axial rigidity and sag/span ratios is determined. Modal, subharmonic and internal resonances, jump and beat phenomena, etc., a re predicted. A new mode of damping of 'free' vibration of the system perturbed from its equilibrium state is identified. Significance of the proposed theory of weightless sagging elasto-flexible cables is discussed.

Keywords:
Weightless cables; configurational nonlinearity; rate- type hypoelastic constitutive equations; third order equations of motion; new damping mode