Eigenvalue Analysis of a Long Cable Modeled as Assembled Links

Abstract

A formulation to evaluate the natural frequencies of a long, elastic cable that hangs down from the top suspension and swings due to its own-weight in a vertical plane is presented. A model of the serial assembly of rigid links interconnected by virtual revolute springs at their joints is employed. The Lagrange’s equations of motion are derived based on the generalized coordinates taken as the link angles. The eigenvalue problem is constituted by means of linearizing the equations. The validity of the present formulation is demonstrated by the numerical examples of a steel cable with flexural rigidity.