Vortex-induced vibration of a circular cylinder on a nonlinear viscoelastic support

Abstract

The effect of structural nonlinearity on vortex-induced vibration of a rigid circular cylinder has been studied computationally for a fixed mass ratio of m∗=2.546 at Re=150. The arrangement of the springs and damper is similar to setup for the Standard Linear Solid (SLS) model used to model a viscoelastic material. One linear spring is in series with the damper and another nonlinear spring is parallel with the damper. The nonlinear structural system is governed by the following three parameters: (a) the ratio of the linear spring constants (R), (b) damping ratio (ζ), and (c) nonlinearity strength (λ). The focus of the present study is to examine the response of the cylinder to VIV by changing ζ and λ. The peak amplitude decreases in comparison with a linear spring, as spring softening (λ<0) is increased; in contrast, the peak amplitude increases for a hardening spring (λ>0). The equivalent reduced velocity (Ureq), a measure of nonlinearity, is affected by damping, showing the non-monotonic variation with ζ. There exists a critical value ζ≈1 below which the equivalent reduced velocity decreases and beyond which Ureq increases. We also observed at high values of λ (e.g. λ=4), the peak lift force coefficient is almost constant over a wide range of reduced velocity, with the absence of the lower branch for a very low (ζ=0.001) and high (ζ=10) values of damping. This near constant amplitude range suggests a hardening spring may be useful for extending the operational range for energy extraction applications. Finally, increased system nonlinearity leads to considerably richer spectral content in the displacement and force signals, reflected in the wake development.