Floquet stability analysis of a circular cylinder on a viscoelastic support

A numerical stability analysis of the wake of a circular cylinder undergoing vortex-induced vibration (VIV) subject to viscoelastic support is presented. For this structural setup, the arrangement of the springs and damper is similar to that for the standard linear solid (SLS) model used to model a viscoelastic material. The SLS system is governed by two parameters: (a) the ratio of the linear spring constants, R, and (b) the damping ratio, ζ. All simulations are done for R=1, but covering ζ=0,0.001,1, and 10. Stability is investigated for the reduced velocity range over which there is a strong resonant response: Ur=[4.5,8], and for a mass ratio of m*=2.546. The dominant instability modes present are analogous to modes A, B, and QP (quasi-periodic) observed for a stationary circular cylinder wake, except at Ur=4.5, which shows modes B, QP, and a subharmonic mode, SH. The critical Reynolds number for two- to three-dimensional transition is observed to decrease with an increase of Ur. In this resonant range, for both the standard spring–damper system and the SLS-based VIV model, the critical Reynolds number below which two-dimensional simulations remain valid is Recr≈212, with transition first occurring at Ur=8 for a critical spanwise wavelength λcr≈4.0D. The results can be employed for setting Reynolds-number/reduced-velocity limits on two-dimensional numerical investigations of VIV under viscoelastic support.