Limit cycle oscillation suppression of 2-DOF airfoil using nonlinear energy sink

We study the nonlinear fluid-structure interaction of an elastically supported rigid circular cylinder in a laminar flow. Periodic shedding of counter-rotating vortices from either side of the cylinder results in vortex-induced vibration of the cylinder. We demonstrate the passive suppression of the limit cycle oscillation (LCO) of the cylinder with the use of an essentially nonlinear element, the nonlinear energy sink (NES). The computational study is performed at a Reynolds number (Re) of 100; Re is defined based on the cylinder diameter and inlet velocity. The variational multiscale residual-based stabilized finite-element method is used to compute approximate solutions of the incompressible Navier-Stokes equations. The NES is comprised of a small mass, an essentially nonlinear spring, and a linear damper. With appropriate values for the NES parameters, the coupled system of flow-cylinder-NES exhibits resonant interactions, resulting in targeted energy transfer (TET) from the flow via the cylinder to the NES, where the energy is dissipated by the linear damper. The NES interacts with the fluid via the cylinder by altering the phase relation between the lift force and the cylinder displacement; this brings about significant reduction in the LCO amplitude of the cylinder for several set of values of the NES parameters.

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Limit cycle oscillation suppression controller design and stability analysis of the periodically time-varying flapping flight dynamics in hover

Nonlinear Dynamics ◽

10.1007/s11071-021-07145-0 ◽

2022 ◽

Author(s):

Liang Wang ◽

Wuyao Jiang ◽

Zongxia Jiao ◽

Longfei Zhao

Keyword(s):

Stability Analysis ◽

Limit Cycle ◽

Controller Design ◽

Flight Dynamics ◽

Flapping Flight ◽

Limit Cycle Oscillation ◽

Time Varying ◽

Oscillation Suppression ◽

Cycle Oscillation

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Dynamic responses and mitigation of limit cycle oscillations in Van der Pol–Duffing oscillator with nonlinear energy sink

Journal of Sound and Vibration ◽

10.1016/j.jsv.2013.05.001 ◽

2013 ◽

Vol 332 (21) ◽

pp. 5489-5507 ◽

Cited By ~ 25

Author(s):

E. Domany ◽

O.V. Gendelman

Keyword(s):

Limit Cycle ◽

Duffing Oscillator ◽

Nonlinear Energy Sink ◽

Dynamic Responses ◽

Limit Cycle Oscillations ◽

Van Der Pol ◽

Energy Sink ◽

Nonlinear Energy

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Sliding mode control-based limit cycle oscillation suppression for UAVs using synthetic jet actuators

2015 International Workshop on Recent Advances in Sliding Modes (RASM) ◽

10.1109/rasm.2015.7154584 ◽

2015 ◽

Cited By ~ 1

Author(s):

Natalie Ramos-Pedroza ◽

William MacKunis ◽

Mahmut Reyhanoglu

Keyword(s):

Sliding Mode Control ◽

Limit Cycle ◽

Sliding Mode ◽

Synthetic Jet ◽

Limit Cycle Oscillation ◽

Synthetic Jet Actuators ◽

Mode Control ◽

Jet Actuators ◽

Oscillation Suppression ◽

Cycle Oscillation

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Suppression of Limit Cycle Oscillations in a Van der Pol Oscillator by Means of a Passive Nonlinear Energy Sink

Volume 1: 20th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C ◽

10.1115/detc2005-84691 ◽

2005 ◽

Author(s):

Young S. Lee ◽

Alexander F. Vakakis ◽

Lawrence A. Bergman ◽

D. Michael McFarland

Keyword(s):

Vibration Control ◽

Limit Cycle ◽

Nonlinear Energy Sink ◽

Van Der Pol Oscillator ◽

Numerical Continuation ◽

Parameter Study ◽

Limit Cycle Oscillations ◽

Van Der Pol ◽

Energy Sink ◽

Nonlinear Energy

We present a study of passive but efficient vibration control, wherein a so-called nonlinear energy sink (NES) completely eliminates the limit cycle oscillations (LCOs) of a van der Pol oscillator. We first perform a parameter study in order to get overall understanding of responses with respect to parameters. Then, we establish a slow flow dynamics model to perform analytical study of the suppression mechanism which corresponds to classical nonlinear energy pumping, i.e., passive, broadband, and targeted energy transfer through 1:1 resonance capture. Utilizing the method of numerical continuation of equilibrium, we also study the bifurcation of the steady state solutions. It turns out that the system may have either subcritical or supercritical LCOs, and that for some parameter domain the LCOs are completely eliminated. This suggests applicability of the NES to vibration control in self-excited systems.

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