Experimental and Theoretical Analysis of Flow-Induced Vibration of Cantilevered Flexible Plate

We experimentally and theoretically study the vibrational dynamics of a thin cantilevered flexible plate mounted to the lee side of a circular cylinder subjected to a free stream airflow. Plates of four different lengths having constant span and thickness are tested in a wind tunnel by varying wind velocity. Based on the dynamics of the plate’s motion, we find three regimes, namely pre-critical, transition, and post-critical regimes. In the post-critical regime, the plate reaches self-sustained limit cycle oscillation. A reduced-order wake oscillator model is developed to explain the experiment. The plate is modeled as an Euler–Bernoulli cantilever beam and the fluctuating lift force is modeled using van der Pol oscillator. This coupled wake oscillator model is able to describe the qualitative behavior of the experiment in a lock-in regime. We find that the coupled dynamics of the plate and flow exhibit similar characteristics as that of the vortex-induced vibration (VIV) of a cylinder.