  We present results from 2-D numerical simulations based on Immersed Boundary
Method of a cylinder in uniform fluid flow attached to bistable springs
undergoing Vortex-Induced Vibrations (VIV). The elastic spring potential for
the bistable springs, consisting of 2 potential wells, is defined by the
spacing between the potential minima and the depth of the potential wells. We
perform simulations of VIV with linear spring, as well as bistable springs with
two different inter-well separations, over a wide range of reduced velocity. As
expected, large oscillation amplitudes correspond to lock-in of the lift force
with the natural frequency of the spring-mass system. The range of reduced
velocity over which lock-in occurs is significantly higher for VIV with
bistable springs compared to VIV with linear springs, although the maximum
possible amplitude appears to be independent of the spring type. For VIV with
bistable springs, the cylinder undergoes double-well oscillations in the
lock-in regime. Range of reduced velocity over which lock-in occurs increases
when the inter-well distance is reduced. The vortex shedding patterns and
amplitude trends look similar at the same equivalent reduced velocity for the
different springs. The results here are consistent with our prior theory, in
which we propose a new "Equilibrium-Constraint (EC)" based on average kinetic
energy budget of the structure. For a given spring potential, the intersection
of natural frequency curves with the EC curve yields the possible range of
reduced velocities over which lock-in should occur. Our numerical simulations
show a collapse of the amplitude-versus-structure frequency data for all the
simulations onto roughly the same curve, thus supporting the existence of the
EC, and providing an explanation for the trends in the VIV oscillations.
