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research-article

NONLINEAR OSCILLATIONS INDUCED BY FOLLOWER FORCES IN PRE-STRESSED CLAMPED RODS SUBJECTED TO DRAG

[+] Author and Article Information
Soheil Fatehiboroujeni

Department of Mechanical Engineering, University of California, Merced, California 95343
sfatehiboroujeni@ucmerced.edu

Arvind Gopinath

Department of Bioengineering, Health Science Research Institute, University of California, Merced, California 95343
agopinath@ucmerced.edu

Sachin Goyal

Department of Mechanical Engineering, Health Science Research Institute, University of California, Merced, California 95343
sgoyal2@ucmerced.edu

1Corresponding author.

ASME doi:10.1115/1.4041681 History: Received March 19, 2018; Revised September 30, 2018

Abstract

Flagella and cilia are examples of actively oscillating, whiplike biological filaments that are crucial to processes as diverse as locomotion, mucus clearance, embryogenesis and cell motility. Elastic driven rod-like filaments subjected to compressive follower forces provide a synthetic way to mimic such oscillatory beating. In the continuum limit, this time-periodic stable response results from the interplay between the structural elastic instability of the inextensible slender rod, geometric constraints that control the onset of instability, energy pumped into the system by the active follower forces, and motion-driven viscous dissipation in ambient media. In this paper, we use a continuum model to study the dynamical, nonlinear buckling instabilities that arise due to the action of non-conservative follower forces on a pre-stressed slender rod clamped at both ends. We systematically calculate the critical follower forces for onset of oscillations, the emergent frequencies and the spatiotemporal patterns of the nonlinear rod shapes that result for two types of fluid drag forces, namely, Stokes drag and Morrison drag. The minimum (critical) force required to initiate stable oscillations depends strongly on the initial slack and weakly on the nature of the drag force. The emergent frequencies at onset however depend strongly on both the extent of pre-stress as well as the nature of the fluid drag. Far from onset, and for large follower forces, the frequency of the oscillations is determined by a power balance between the energy input by the active forces and the dissipation due to fluid drag.

Copyright (c) 2018 by ASME
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