Modelling and transient planar dynamics of suspended cables with moving mass

Abstract

In this study, the 3D nonlinear equations of motion of the suspended cable with moving mass are obtained via the Hamilton principle, and its transient linear planar dynamics is investigated. Considering the quasi-static assumption, the condensed planar model accounting for the effect of the moving mass is derived, and it is then discretized by choosing the static deflection and sine series as shape functions. It is shown that this expansion shows good convergence features. The Newmark method is used to investigate the transient response. The effects of the inertia force, mass, sag and velocity of the moving mass on the transient dynamics of the suspended cable are systematically investigated. Finally, the horizontal tension of the suspended cable and the case of sequentially moving masses are examined. (C) 2010 Elsevier Ltd. All rights reserved

A Contrast on Conductor Galloping Amplitude Calculated by Three Mathematical Models with Different DOFs

“…In the displacement expansion, the use of the eigenfunctions is often the best choice in the aspects of convergence and accuracy [11,19,25]. But in order to concentrate on the study of the comparison of the different models, a simplified Galerkin procedure is presented by using a sine series of the symmetric in-plane Shock and Vibration 5 modes as assumed shape functions [26]. So the displacements V, , and can be expressed as…”

Nonlinear Dynamic Phenomena in Mechanics

“…• Suspended cables in air under wind loads [39], stochastic excitations [82], or moving masses [75]. • Features of cable nonlinear dynamics in fluids ( [20], [63]), with consideration of all important nonlinearities [54].…”

Planar dynamics of large-deformation rods under moving loads

“…More recent works on moving loads or masses travelling along beams are [7][8][9], while more specific studies include moving loads or masses along curved beams or arches [10][11][12], inclined beams [13], multi-span beams [14,15] and tapered beams [16]. Meanwhile, loads or masses travelling along cables (modelled as strings, i.e., without bending stiffness), are studied in [17][18][19]. See also the review in [20].…”

“…These approximate equations are often arguably more complicated (and less transparent) than the geometrically exact equations. Moreover, these equations then still need to be solved numerically, typically by employing a Galerkin expansion 30 (using on the order of 10 terms) [8,19]. These Galerkin expansions are well known to suffer from lack of uniform convergence (Gibbs phenomenon) in problems with jump discontinuities, as occur in the internal force in moving-load problems [22,23].…”