Asymptotic analysis of a dynamical system for vortex-induced vibration and galloping

The present work presents an asymptotic analysis of a wake-oscillator model for the transverse oscillation of a rectangular cylinder in a cross airflow due to the interference of galloping instability and vortex shedding. Periodic synchronized solutions of the dynamical system are sought with the method of Krylov-Bogolyubov. The semi-analytical solutions are compared with the numerical solutions for several values of the mass-damping parameter of the system, showing a general agreement. Nevertheless, the study highlights the important role of the strong nonlinearity of the wake equation and the quasi-periodicity of the solution in some flow-velocity ranges. These features are not accounted for in the asymptotic analysis and are responsible for the shortcomings of the semi-analytical solutions.