Numerical Investigation of Damped Vibrations in Slender Flexible Structures

Flexible structures interacting with the viscous incompressible fluid are encountered in the study of fish swimming, underwater cables, transmission cables, flapping wings, sensors or resonators, etc. Estimation of drag or damping coefficient is important for the efficient design of devices where vibration induced motions are involved. While studying vibration induced vortex, flexible beam can be modeled as having a wobbly motion and its damping in the viscous fluid can be studied. In this work, an immersed boundary method-based IB2d code is used for the estimation of drag or damping coefficients for vertical flexible structure. The slender flexible vertical beam of fixed length is subject to the sinusoidal-wobbly mode shapes. Under various mode shapes, the temporal evolution of the non-dimensional damping force is obtained. The results exhibited an expected exponential decay in the drag force acting over the beam. It is concluded that the damping coefficient obtained is seen to reduce with an increase in amplitude with certain exceptions.