Elastic-driven slender filaments subjected to compressive follower forces provide a synthetic way to mimic the oscillatory beating of biological flagella and cilia. Here, we use a continuum model to study the dynamical, nonlinear buckling instabilities that arise due to the action of nonconservative follower forces on a prestressed slender rod clamped at both ends and allowed to move in a fluid. Stable oscillatory responses are observed as a result of 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 fluid dissipation. Initial buckling instabilities are initiated by the effect of the follower forces and inertia; fluid drag subsequently allows for the active energy pumped into the system to be dissipated away and results in self-limiting amplitudes. By integrating the equations of equilibrium and compatibility conditions with linear constitutive laws, we compute the critical follower forces for the onset of oscillations, emergent frequencies of these solutions, and the postcritical nonlinear rod shapes for two forms of the drag force, namely linear Stokes drag and quadratic Morrison drag. For a rod with fixed inertia and drag parameters, the minimum (critical) force required to initiate stable oscillations depends on the initial slack and weakly on the nature of the drag force. Emergent frequencies and the amplitudes postonset are determined by the extent of prestress as well as the nature of the fluid drag. Far from onset, for large follower forces, the frequency of the oscillations can be predicted by evoking a power balance between the energy input by the active forces and the dissipation due to fluid drag.
Skip Nav Destination
Article navigation
December 2018
Research-Article
Nonlinear Oscillations Induced by Follower Forces in Prestressed Clamped Rods Subjected to Drag
Soheil Fatehiboroujeni,
Soheil Fatehiboroujeni
Department of Mechanical Engineering,
University of California,
Merced, CA 95343
e-mail: sfatehiboroujeni@ucmerced.edu
University of California,
Merced, CA 95343
e-mail: sfatehiboroujeni@ucmerced.edu
Search for other works by this author on:
Arvind Gopinath,
Arvind Gopinath
Department of Bioengineering,
Health Science Research Institute,
University of California,
Merced, CA 95343
e-mail: agopinath@ucmerced.edu
Health Science Research Institute,
University of California,
Merced, CA 95343
e-mail: agopinath@ucmerced.edu
Search for other works by this author on:
Sachin Goyal
Sachin Goyal
Department of Mechanical Engineering,
Health Science Research Institute,
University of California,
Merced, CA 95343
e-mail: sgoyal2@ucmerced.edu
Health Science Research Institute,
University of California,
Merced, CA 95343
e-mail: sgoyal2@ucmerced.edu
Search for other works by this author on:
Soheil Fatehiboroujeni
Department of Mechanical Engineering,
University of California,
Merced, CA 95343
e-mail: sfatehiboroujeni@ucmerced.edu
University of California,
Merced, CA 95343
e-mail: sfatehiboroujeni@ucmerced.edu
Arvind Gopinath
Department of Bioengineering,
Health Science Research Institute,
University of California,
Merced, CA 95343
e-mail: agopinath@ucmerced.edu
Health Science Research Institute,
University of California,
Merced, CA 95343
e-mail: agopinath@ucmerced.edu
Sachin Goyal
Department of Mechanical Engineering,
Health Science Research Institute,
University of California,
Merced, CA 95343
e-mail: sgoyal2@ucmerced.edu
Health Science Research Institute,
University of California,
Merced, CA 95343
e-mail: sgoyal2@ucmerced.edu
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received March 19, 2018; final manuscript received September 30, 2018; published online October 29, 2018. Assoc. Editor: Anindya Chatterjee.
J. Comput. Nonlinear Dynam. Dec 2018, 13(12): 121005 (8 pages)
Published Online: October 29, 2018
Article history
Received:
March 19, 2018
Revised:
September 30, 2018
Citation
Fatehiboroujeni, S., Gopinath, A., and Goyal, S. (October 29, 2018). "Nonlinear Oscillations Induced by Follower Forces in Prestressed Clamped Rods Subjected to Drag." ASME. J. Comput. Nonlinear Dynam. December 2018; 13(12): 121005. https://doi.org/10.1115/1.4041681
Download citation file:
Get Email Alerts
Numerical Simulation Method for the Rain-Wind Induced Vibration of the Three-Dimensional Flexible Stay Cable
J. Comput. Nonlinear Dynam
A Numerical Study for Nonlinear Time-Space Fractional Reaction-Diffusion Model of Fourth-Order
J. Comput. Nonlinear Dynam (March 2025)
An Investigation of Dynamic Behavior of Electric Vehicle Gear Trains
J. Comput. Nonlinear Dynam (March 2025)
Nonlinear Dynamic Analysis Framework for Slender Structures Using the Modal Rotation Method
J. Comput. Nonlinear Dynam (March 2025)
Related Articles
The Stability of Fluid Production From a Flexible Riser
J. Energy Resour. Technol (June,2002)
Snap Buckling in Overhand Knots
J. Appl. Mech (April,2023)
Quasi-Periodic Response Regimes of Linear Oscillator Coupled to Nonlinear Energy Sink Under Periodic Forcing
J. Appl. Mech (March,2007)
Hydrodynamic In-Line Force Coefficients of Oscillating Bluff Cylinders (Circular and Square) at Low Reynolds Numbers
J. Vib. Acoust (October,2011)
Related Proceedings Papers
Related Chapters
Formation of Absolute PBG of 2D Square Lattice by Changing the Shapes and Orientations of Rods
International Conference on Instrumentation, Measurement, Circuits and Systems (ICIMCS 2011)
Small Raindrops
Case Studies in Fluid Mechanics with Sensitivities to Governing Variables
Part 2, Section II—Materials and Specifications
Companion Guide to the ASME Boiler and Pressure Vessel Code, Volume 1, Third Edition