Phasing mechanisms between the in-line and cross-flow vortex-induced vibrations of a long tensioned beam in shear flow

The mechanisms of phasing between the in-line and cross-flow vortex-induced vibrations of a cylindrical tensioned beam in non-uniform flow are studied by direct numerical simulation. Three types of responses are considered, mono-frequency, narrowband, and broadband multi-frequency vibrations; in all cases, in-line and cross-flow vibration components occurring with a frequency ratio of 2 are phase-locked within regions of wake-body synchronization. The in-line/cross-flow phase difference exhibits a persistent spanwise drift when vibration components present significant traveling-wave behavior; this drift depends linearly on the in-line/cross-flow wavenumber difference, controlled by the beam non-linear dispersion relation and also impacted by the effective added mass variability.