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Elastically driven filaments subjected to animating compressive followerforces provide a synthetic way to mimic the oscillatory beating of activebiological filaments such as eukaryotic cilia. The dynamics of such activefilaments can, under favorable conditions, exhibit stable time-periodicresponses that result due to the interplay of elastic buckling instabilities,geometric constraints, boundary conditions, and dissipation due to fluid drag.In this paper, we use a continuum elastic rod model to estimate the criticalfollower force required for the onset of the stable time-periodic flappingoscillations in pre-stressed rods subjected to fluid drag. The pre-stress isgenerated by imposing either clamped-clamped or clamped-pinned boundaryconstraints and the results are compared with those of clamped-free case, whichis without pre-stress. We find that the critical value increases with theinitial slack--that quantifies the pre-stress, and strongly depends on the typeof the constraints at the boundaries. The frequency of oscillations far fromthe onset, however, depends primarily on the magnitude of the follower force,not on the boundary constraints. Interestingly, oscillations for theclamped-pinned case are observed only when the follower forces are directedtowards the clamped end. This finding can be exploited to design a mechanicalswitch to initiate or quench the oscillations by reversing the direction of thefollower force or altering the boundary conditions.

Effect of Boundary Constraints on the Nonlinear Flapping of Filaments Animated by Follower Forces