A discrete model of a rope with bending stiffness or viscous damping

Abstract

A discrete model of a rope is developed and used to simulate the plane motion of the rope fixed at one end. Actually, two systems are presented, whose members are rigid but non-ideal joints involve elasticity or dissipation. The dissipation is reflected simply by viscous damping model, whereas the bending stiffness conception is based on the classical curvature-bending moment relationship for beams and simple geometrical formulas. Equations of motion are derived and their complexity is discussed from the computational point of view. Since modified extended backward differentiation formulas (MEBDF) of Cash are implemented to solve the resulting initial value problems, the technique scheme is outlined. Numerical experiments are performed and influences of the elasticity and damping on behaviour of the model are analyzed. Basic energy principles are used to verify the obtained results.