On the modal response of mobile cables

Abstract

The paper presents methodologies for tracing modal responses of a translating cable. Governing system equations are obtained based on perturbation of the response around the stationary position of the translating catenary. Then, after separation of spatio-temporal system variables, a multiple scale method is endowed for treatment of equations in space. Frequencies and mode shapes of the system are detected by imposing solvability conditions on the system equations and/or via expansion of system variables in the form of Fourier series accompanied by imposing the existence of non-trivial solutions. Finally, obtained results are confronted with those which are obtained by finite difference method.

Reduced-Order Model for the Nonlinear Dynamics of Cables

“…The latter is more suitable to retain the influence of system curvature and tension on the modes and frequencies. The methodology has already been endowed by the authors in [9].…”

A Didactic Procedure to Solve the Equation of Steady-Static Response in Suspended Cables

“…Changes in the static state of suspended cables are due to temperature variations [17,18], ice loads [19,20], moving mass [21][22][23], vibrations [24][25][26][27], or intentional power overloads that raise cable temperatures [28]. Although most of the works start from an initial static curved state [16][17][18][19][20][21][22][23][24][25][26][27][28], Yang [29] considered the initial state without mechanical tension (stress) and with the cable in a horizontal position. Luongo and Zulli [30] described the first step in solving the static response equation in cables under vertical loads.…”