Nonlinear modeling of combined galloping and vortex-induced vibration of square sections under flow

There is no critical mass ratio for galloping of a square cylinder under flow

“…In this section, we recall the ROM proposed by Han et al (2021a). Considering a two-dimensional elastically supported square cylinder under flow, see figure 1(a), the cross-flow displacement Y satisfies a simple oscillator equation…”

“…Here, ω f is the vortex-shedding angular frequency defined as 2πS t U/D, where S t is the Strouhal number for flow over a stationary cylinder. In this equation, ε = 0.3, B 1 = 10 and B 2 = 0.1 are constant coefficients derived from experimental data, see Han et al (2021a), and Appendix A for more details on the derivation of these values. The left-hand side of (2.3) is a van der Pol equation with a reference frequency ω f and a growth rate ε.…”

“…Additionally, Sourav & Sen (2019) raised the question of the effect of structural damping on these behaviours at low mass ratio. This is an important issue, as damping is known to affect the interaction between VIV and galloping (Parkinson & Smith 1964;Han et al 2021a). Moreover, in the applications in the field of energy harvesting from vibrations, the low mass ratio case is of practical interest, and damping is then a key parameter (Jayatunga et al 2015;Han et al 2021b).…”

“…For this we shall use a ROM, in both its nonlinear and linear versions, and DNS. In § 2, we recall the ROM for VIV and galloping of Han et al (2021a), present the DNS we use and show their validation in the present range of parameters. In § 3, we use the ROM to explore the effect of mass ratio on the response and confirm our findings by DNS.…”

Advances in stability, bifurcations and nonlinear vibrations in mechanical systems

“…A first grouping of papers deals with problems of stability and bifurcations arising in fluid/structure problems with a special emphasis on aeroelastic systems. Problems related to flutter analysis in classical or supersonic conditions [1][2][3], vortex-induced vibrations [4,5] and galloping instabilities [6,7] are thoughtfully addressed, together with more theoretical problems related to the Ziegler column [8] and the existence of global attractors in subsonic flows [9].…”