Limit Cycle Oscillation Amplitude Tailorng Based on Describing Functions and $$\mu $$ Analysis

2017 ◽  
pp. 101-119
Author(s):  
Andrea Iannelli ◽  
Andrés Marcos ◽  
Mark Lowenberg
Keyword(s):  
Limit Cycle ◽  
Oscillation Amplitude ◽  
Limit Cycle Oscillation ◽  
Describing Functions ◽  
Cycle Oscillation

A Harmonic Balance Approach for Modeling Three-Dimensional Nonlinear Unsteady Aerodynamics and Aeroelasticity

2002 ◽  
Author(s):  
Jeffrey P. Thomas ◽  
Earl H. Dowell ◽  
Kenneth C. Hall
Keyword(s):  
Limit Cycle ◽  
Harmonic Balance ◽  
Structural Model ◽  
Oscillation Amplitude ◽  
Three Dimensional ◽  
Unsteady Aerodynamics ◽  
Finite Amplitude ◽  
Limit Cycle Oscillation ◽  
Unsteady Aerodynamic ◽  
Cycle Oscillation

Presented is a frequency domain harmonic balance (HB) technique for modeling nonlinear unsteady aerodynamics of three-dimensional transonic inviscid flows about wing configurations. The method can be used to model efficiently nonlinear unsteady aerodynamic forces due to finite amplitude motions of a prescribed unsteady oscillation frequency. When combined with a suitable structural model, aeroelastic (fluid-structure), analyses may be performed at a greatly reduced cost relative to time marching methods to determine the limit cycle oscillations (LCO) that may arise. As a demonstration of the method, nonlinear unsteady aerodynamic response and limit cycle oscillation trends are presented for the AGARD 445.6 wing configuration. Computational results based on the inviscid flow model indicate that the AGARD 445.6 wing configuration exhibits only mildly nonlinear unsteady aerodynamic effects for relatively large amplitude motions. Furthermore, and most likely a consequence of the observed mild nonlinear aerodynamic behavior, the aeroelastic limit cycle oscillation amplitude is predicted to increase rapidly for reduced velocities beyond the flutter boundary. This is consistent with results from other time-domain calculations. Although not a configuration that exhibits strong LCO characteristics, the AGARD 445.6 wing nonetheless serves as an excellent example for demonstrating the HB/LCO solution procedure.

Basin of Attraction and Limit Cycle Oscillation Amplitude of an Ankle-Hip Model of Balance on a Balance Board

2019 ◽  
Vol 141 (11) ◽  
Author(s):  
Erik Chumacero-Polanco ◽  
James Yang
Keyword(s):  
Limit Cycle ◽  
Basin Of Attraction ◽  
Oscillation Amplitude ◽  
Feedback Gain ◽  
Limit Cycle Oscillation ◽  
Physical Parameters ◽  
Risk Of Falls ◽  
Cycle Oscillation ◽  
Three Degree Of Freedom ◽  
Balance Board

The study of upright posture (UP) stability is of relevance to estimating risk of falls, especially among people with neuromuscular deficits. Several studies have addressed this problem from a system dynamic approach based on parameter bifurcation analyses, which provide the region of stability (RoS) and the delimiting bifurcation curves (usually Hopf and pitchfork) in some parameter-spaces. In contrast, our goal is to determine the effect of parameter changes on the size of the basin of attraction (BoA) of the UP equilibrium and the amplitude of the limit cycle oscillations (LCOs) emerging from the Hopf bifurcations (HBs). The BoA is an indicator of the ability of the UP to maintain balance without falling, while LCOs may explain the sway motion commonly observed during balancing. In this study, a three degree-of-freedom model for a human balancing on a balance board (BB) was developed. Analysis of the model revealed the BoAs and the amplitude of the LCOs. Results show that physical parameters (time-delays and feedback control gains) have a large impact on the size of the BoA and the amplitude of the LCOs. Particularly, the size of the BoA increases when balancing on a rigid surface and decreases when either proprioceptive or combined visual and vestibular (V&V) feedback gain is too high. With respect to the LCOs, it is shown that they emerge from both the subcritical and supercritical HBs and increase their amplitudes as some parameters vary.

Aeroelastic Stability Assessment of an Industrial Compressor Blade Including Mistuning Effects

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Yaoguang Zhai ◽  
Ronnie Bladh ◽  
Göran Dyverfeldt
Keyword(s):  
Limit Cycle ◽  
Oscillation Amplitude ◽  
Forced Response ◽  
Design Flow ◽  
Limit Cycle Oscillation ◽  
Flow Conditions ◽  
Aeroelastic Stability ◽  
Flexural Mode ◽  
Choked Flow ◽  
Cycle Oscillation

This paper presents a comprehensive investigation into the aeroelastic stability behavior of a transonic front blade in an industrial compressor when operating outside its normal range of service parameters. The evolution of the airfoil’s aeroelastic stability in the first flexural mode is studied as the front blade operation progresses towards choked flow conditions. First, linearized 3D flutter computations representing today’s industry standard are performed. The linearized calculations indicate a significant, shock-driven flutter risk at these off-design flow conditions. To further explore the aeroelastic behavior of the rotor and to find a viable solution toward flutter risk elimination, two parallel investigations are undertaken: (i) flow perturbation nonlinearity effects and potential presence of limit-cycle oscillation, and (ii) effects of blade mistuning and flutter mitigation potential of intentional mistuning, including its impact on forced response behavior. The nonlinear harmonic analyses show that the minimum aerodynamic damping increases rapidly and essentially linearly with blade oscillation amplitude beyond the linear regime. Thus, a state of safe limit-cycle oscillation is predicted for the fully tuned blade. Additionally, it is found that intentional, realizable blade frequency offsets in an alternating pattern efficiently stabilize the blade. Finally, it is verified that alternating mistuning has a beneficial effect versus the inevitable random mistuning also in the forced response.

Aeroelastic Stability Assessment of an Industrial Compressor Blade Including Mistuning Effects

2011 ◽  
Author(s):  
Yaoguang Zhai ◽  
Ronnie Bladh ◽  
Go¨ran Dyverfeldt
Keyword(s):  
Limit Cycle ◽  
Oscillation Amplitude ◽  
Forced Response ◽  
Design Flow ◽  
Limit Cycle Oscillation ◽  
Flow Conditions ◽  
Aeroelastic Stability ◽  
Flexural Mode ◽  
Choked Flow ◽  
Cycle Oscillation

This paper presents a comprehensive investigation into the aeroelastic stability behavior of a transonic front blade in an industrial compressor when operating outside its normal range of service parameters. The evolution of the airfoil’s aeroelastic stability in the first flexural mode is studied as the front blade operation progresses towards choked flow conditions. First, linearized 3D flutter computations representing today’s industry standard are performed. The linearized calculations indicate a significant, shock-driven flutter risk at these off-design flow conditions. To further explore the aeroelastic behavior of the rotor and to find a viable solution toward flutter risk elimination, two parallel investigations are undertaken: (i) flow perturbation nonlinearity effects and potential presence of limit-cycle oscillation; and (ii) effects of blade mistuning and flutter mitigation potential of intentional mistuning, including its impact on forced response behavior. The nonlinear harmonic analyses show that the minimum aerodynamic damping increases rapidly and essentially linearly with blade oscillation amplitude beyond the linear regime. Thus, a state of safe limit-cycle oscillation is predicted for the fully tuned blade. Additionally, it is found that intentional, realizable blade frequency offsets in an alternating pattern efficiently stabilize the blade. Finally, it is verified that alternating mistuning has a beneficial effect versus the inevitable random mistuning also in the forced response.

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