Nonlinear vibrations of suspended cables—Part III: Random excitation and interaction with fluid flow

Abstract

This review article deals with the random excitation of nonlinear strings and suspended cables in air and fluid flow. For strings and 1D cables, the system dynamics is governed by different forms of Duffing oscillator. A brief review is devoted to the stochastic excitation of a Duffing oscillator. Under random excitation, this oscillator may or may not possess multiple solutions depending on the excitation bandwidth and level. One may be interested in estimating response statistics, first passage problem, and power spectral density. Particular attention is given to the complex response phenomena associated with increasing the spectral density level of excitation. The numerical results of the problem of nonlinear modal interaction in suspended cables will be discussed in the neighborhood of multiple internal resonance conditions. For a unimodal response, the linear theory fails to predict nonzero mean response and underestimates the mean square response under white noise excitation. Complex response phenomena such as “on-off” intermittency, energy transfer, and stochastic bifurcation are reviewed. The dynamic behavior of suspended cables in still air is different from that in flowing fluid or severe wind current due to the action of vortices, fluid normal forces, added fluid inertia force, and fluid drag force. Aeolian and galloping vibration of suspended cables in air and their dynamics in fluid flow are discussed, together with the influence of dynamic tension. In the absence of external excitation, the action of fluid forces induces vibration to the cable. The dynamics of cables subjected to steady and random fluid flow is reviewed for mooring systems. Depending on the flow speed, the cable may experience divergence or flutter similar to the case of aeroelastic structures. While the deterministic theory of strings and cables has reached an advanced stage, the reader will realize that these systems need further investigations under random excitations. There are 297 references cited in this review article.

A boundary modulation formulation for cable’s non-planar coupled dynamics under out-of-plane support motion

“…The longitudinal kinetic condensation technique has been utilized in Eqs. (1) and (2), and thus, the longitudinal displacement u(x, t) is condensed. This is mainly due to fact that the longitudinal dynamic time scale is much small (thus fast) than the transversal ones (vertical and out-of-plane).…”

“…Due to its elasticity, initial sag, nonlinear axial stretching, and complex boundary connections, cable's dynamic behaviors are very rich and extensive investigations into cable's dynamics have been undertaken by many researchers in the past few decades [1][2][3][4][5][6][7].…”

Nonlinear interactions and chaotic dynamics of suspended cables with three-to-one internal resonances

“…Much of these literatures are summarized in recent review articles (Rega, 2004a,b;Ibrahim, 2004). In general, the nonlinear dynamics of elastic suspended cables have been explored for a variety of phenomena through single-degree-of-freedom (SDOF) model.…”

Dynamic instability of inclined cables under combined wind flow and support motion

“…On the other hand, wind-exposed fixed-support inclined cables were studied in a stochastic [34] and a deterministic [35][36][37] context. In particular, wind-tunnel tests were reported in [36] for inclined cables with attached fixed or moving rain-induced rivulets, which possibly lead to galloping, induced by the asymmetry in the cross section.…”