We present results from two-dimensional numerical simulations based on Immersed Boundary Method (IBM) 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 two potential wells, is completely 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. The present study provides fundamental insights into VIV characteristics of bistable springs, which may be useful for designing broadband energy harvesters.

我们提出了基于浸入边界方法（IBM）的二维数值模拟结果，该方法是将圆柱体在均匀流体流中附接到经受涡激振动（VIV）的双稳态弹簧上。由两个势阱组成的双稳态弹簧的弹性弹簧势完全由势最小值和势阱深度之间的间距确定。我们使用线性弹簧以及具有两种不同孔间间距的双稳态弹簧在很大的降低速度范围内进行VIV的仿真。不出所料，较大的振荡幅度对应于弹簧质量系统固有频率的提升力锁定。与使用线性弹簧的VIV相比，使用双稳态弹簧的VIV发生锁定的降低速度范围明显更高，尽管最大可能振幅似乎与弹簧类型无关。对于具有双稳态弹簧的VIV，气缸在锁定状态下会发生双井振荡。当井间距离减小时，发生锁定的降低速度的范围会增加。对于不同的弹簧，在相同的等效减小的速度下，涡旋脱落模式和振幅趋势看起来相似。这里的结果与我们先前的理论是一致的，在该理论中，我们根据结构的平均动能预算提出了一种新的“平衡约束（EC）”。对于给定的弹簧电势，固有频率曲线与EC曲线的交点会产生可能发生的速度降低范围，在此范围内可能发生锁定。我们的数值模拟结果表明，所有模拟的振幅对结构频率数据都崩溃在大致相同的曲线上，从而支持了EC的存在，并为VIV振荡的趋势提供了解释。本研究为双稳态弹簧的VIV特性提供了基本的见识，这可能对设计宽带能量收集器很有用。