Response Analysis of a Circular Cylinder Undergoing Vortex Induced Vibrations Along Two Degrees of Freedom in the Presence of Noise

Abstract

In this study, we perform uncertainty quantification of a nonlinear dynamical system consisting of a circular cylinder undergoing free vibrations with two degrees-of-freedom in the presence of a fluctuating flow-field. Most of the studies in Vortex Induced Vibrations till now are conducted in a deterministic environment. Real life situations involving VIV are subjected to high amount of uncertainties, with the main culprit being the randomness in the incoming flow. Studies involving modelling of the flow with a prescribed set of parameters, represents only an idealistic situation and hence is not sufficient for a complete understanding of the associated dynamics. In this context, we make an attempt to characterise the flow by doing a stochastic modelling on the same. In the current study, we have mathematically modelled the noise through a uniform distribution. These fluctuations are superimposed on a mean flow at every time step. We use a Duffing Van der Pol combined system to model the structure and flow oscillators. It is observed that stochastic modelling brings noticeable changes in the structural responses both quantitatively and qualitatively. The influence of the fluctuations on both the transverse and inline oscillations have been studied. One of the most important changes in the response of the structure is in its amplitude. Noise amplifies the maximum amplitude attained both for transverse and inline oscillations. Further, additional qualitative types of responses are visible in the presence of noise which were absent in the deterministic environment. One such behaviour the ‘intermittent’ response which occurs during the transition from higher to lower amplitudes in the lock-in region. Intermittency is observed both for transverse and inline oscillations. It has been seen that the system undergoes stochastic Phenomenological bifurcations, which have been characterised by the probability density functions of both the transverse and inline responses.