P. Warnitchai et al., A NONLINEAR DYNAMIC-MODEL FOR CABLES AND ITS APPLICATION TO A CABLE-STRUCTURE SYSTEM, Journal of sound and vibration, 187(4), 1995, pp. 695-712
A set of governing equations for dynamic transverse motions of a cable
with small sag is firstly obtained where effects of finite motions of
the cable and small support motions are included. Cable motions are s
eparated into two parts; quasi-static motions and modal motions. The q
uasi-static motions are the displacements of the cable which moves as
an elastic tendon due to the support movements. The modal motions are
expressed as a combination of the linear undamped modes of a cable wit
h fixed ends. By Lagrange's equations of motion, the governing equatio
ns of the non-linear cable motions are obtained, where quadratic as we
ll as cubic non-linear couplings appear. The cable model developed is
next applied to a cable-structure system. A global/local mode approach
is employed; the total motions are expressed in terms of global and l
ocal motions. The local motions are the modal motions of the cable, wh
ile the global motions are 3-D motions of the structure which include
quasi-static motions of the cables only. The global are expressed as a
combination of the eigenmodes computed by 3-D FEM in which cables are
treated as tendons. By using Lagrange's formulation, algebraic govern
ing equations are finally obtained in which global-local interaction a
ppears as linear and quadratic couplings. The model for the system is
modified to include the actuator motions at the cable supports; the ac
tuator motions are in the cable axis direction. The study shows many p
ossibilities for the control of global and/or local modes. (C) 1995 Ac
ademic Press Limited.