Fatehiboroujeni Soheil, Gopinath Arvind, Goyal Sachin
Department of Mechanical Engineering, University of California, Merced, California 95343, USA.
Department of Bioengineering, University of California, Merced, California 95343, USA.
Phys Rev E. 2021 Jan;103(1-1):013005. doi: 10.1103/PhysRevE.103.013005.
Initially straight slender elastic filaments or rods with constrained ends buckle and form stable two-dimensional shapes when prestressed by bringing the ends together. Beyond a critical value of this prestress, rods can also deform off plane and form twisted three-dimensional equilibrium shapes. Here, we analyze the three-dimensional instabilities and dynamics of such deformed filaments subject to nonconservative active follower forces and fluid drag. We find that softly constrained filaments that are clamped at one end and pinned at the other exhibit stable two-dimensional planar flapping oscillations when active forces are directed toward the clamped end. Reversing the directionality of the forces quenches the instability. For strongly constrained filaments with both ends clamped, computations reveal an instability arising from the twist-bend-activity coupling. Planar oscillations are destabilized by off-planar perturbations resulting in twisted three-dimensional swirling patterns interspersed with periodic flipping or reversal of the swirling direction. These striking swirl-flip transitions are characterized by two distinct timescales: the time period for a swirl (rotation) and the time between flipping events. We interpret these reversals as relaxation oscillation events driven by accumulation of torsional energy. Each cycle is initiated by a fast jump in torsional deformation with a subsequent slow decrease in net torsion until the next cycle. Our work reveals the rich tapestry of spatiotemporal patterns when weakly inertial strongly damped rods are deformed by nonconservative active forces. Taken together, our results suggest avenues by which prestress, elasticity, and activity may be used to design synthetic macroscale pumps or mixers.
最初，两端受限的笔直细长弹性细丝或杆在通过将两端靠拢而施加预应力时会发生屈曲，并形成稳定的二维形状。当这种预应力超过临界值时，杆也会偏离平面变形，形成扭曲的三维平衡形状。在此，我们分析了此类变形细丝在非保守主动跟随力和流体阻力作用下的三维不稳定性和动力学。我们发现，一端夹紧另一端 pinned（此处原文有误，推测可能是pinned，意为“固定”）的软约束细丝在主动力指向夹紧端时会表现出稳定的二维平面拍打振荡。力的方向反转会抑制这种不稳定性。对于两端都夹紧的强约束细丝，计算结果显示出一种由扭转 - 弯曲 - 活性耦合引起的不稳定性。平面振荡会因平面外扰动而失稳，导致扭曲的三维涡旋模式，其间穿插着涡旋方向的周期性翻转或反转。这些引人注目的涡旋 - 翻转转变具有两个不同的时间尺度：涡旋（旋转）的时间周期和翻转事件之间的时间间隔。我们将这些反转解释为由扭转能量积累驱动的弛豫振荡事件。每个周期由扭转变形的快速跳跃开始，随后净扭转缓慢减小，直至下一个周期。我们的工作揭示了弱惯性强阻尼杆在非保守主动力作用下变形时丰富的时空模式。综上所述，我们的结果提出了利用预应力、弹性和活性来设计合成宏观泵或混合器的途径。
