Wake-Oscillator Simulation of Vortex-Induced Vibrations: Reduced Velocity and Lock-In Behavior

This study uses a reduced-order wake oscillator to analyze vortex-induced vibrations (VIV) of an elastically mounted circular cylinder. The framework couples the structural equation of motion with a Van der Pol-type wake oscillator to show unsteady vortex shedding. Systematic parameter sweeps were performed across reduced velocity and coupling/damping parameters; amplitude and frequency responses were analyzed using Welch spectral estimates. The system response was computed using normalized root mean-square (RMS) amplitudes and dominant frequencies. The simulations reproduce the lock-in phenomenon (frequency synchronization between structural response and vortex shedding) around reduced velocity U* =  4-6 which is consistent with the experimental literature analyzed. This project shows that even with limited resources, students can reproduce an important fluid-structure interaction phenomenon using only a mathematical model and software. These results show that the wake oscillator, even though it is very simple, provides a valuable insight into the crucial dynamics of VIV. This model also gives an accessible way for students and educators to analyze and investigate fluid-structure interactions without needing expensive laboratory resources; this makes it well suited for research and classroom use.