Transition to chaos in a two-sided collapsible channel flow

2021 ◽  
Vol 926 ◽  
Author(s):  
Qiuxiang Huang ◽  
Fang-Bao Tian ◽  
John Young ◽  
Joseph C.S. Lai
Keyword(s):  
Symmetry Breaking ◽  
Channel Flow ◽  
Period Doubling ◽  
External Pressure ◽  
Immersed Boundary ◽  
Limit Cycle Oscillation ◽  
External Pressures ◽  
Wide Range ◽  
Cycle Oscillation ◽  
The Stability

The nonlinear dynamics of a two-sided collapsible channel flow is investigated by using an immersed boundary-lattice Boltzmann method. The stability of the hydrodynamic flow and collapsible channel walls is examined over a wide range of Reynolds numbers $Re$ , structure-to-fluid mass ratios $M$ and external pressures $P_e$ . Based on extensive simulations, we first characterise the chaotic behaviours of the collapsible channel flow and explore possible routes to chaos. We then explore the physical mechanisms responsible for the onset of self-excited oscillations. Nonlinear and rich dynamic behaviours of the collapsible system are discovered. Specifically, the system experiences a supercritical Hopf bifurcation leading to a period-1 limit cycle oscillation. The existence of chaotic behaviours of the collapsible channel walls is confirmed by a positive dominant Lyapunov exponent and a chaotic attractor in the velocity-displacement phase portrait of the mid-point of the collapsible channel wall. Chaos in the system can be reached via period-doubling and quasi-periodic bifurcations. It is also found that symmetry breaking is not a prerequisite for the onset of self-excited oscillations. However, symmetry breaking induced by mass ratio and external pressure may lead to a chaotic state. Unbalanced transmural pressure, wall inertia and shear layer instabilities in the vorticity waves contribute to the onset of self-excited oscillations of the collapsible system. The period-doubling, quasi-periodic and chaotic oscillations are closely associated with vortex pairing and merging of adjacent vortices, and interactions between the vortices on the upper and lower walls downstream of the throat.

Dynamics and Stability of Partial Immersion Milling Operations

1999 ◽  
Author(s):  
M. X. Zhao ◽  
B. Balachandran ◽  
M. A. Davies ◽  
J. R. Pratt
Keyword(s):  
Hopf Bifurcation ◽  
Time Variation ◽  
Periodic Motion ◽  
Contact Time ◽  
Period Doubling ◽  
Experimental Investigations ◽  
Partial Immersion ◽  
Milling Operations ◽  
Wide Range ◽  
The Stability

Abstract In this paper, numerical and experimental investigations conducted into the dynamics and stability of partial immersion milling operations are presented. A mechanics based model is used for simulations of a wide range of milling operations and instabilities that arise due to regeneration and/or impact effects are studied. Poincaré sections are used to assess the stability of motions. The studies reveal that apart from Hopf bifurcation of a periodic motion, a period-doubling bifurcation of a periodic motion may also lead to chatter in partial immersion milling operations. Issues such as tooth contact time variation and structure of stability charts are also discussed.

Aeroelastic analysis of pre-stressed variable stiffness composite panels

2019 ◽  
Vol 26 (9-10) ◽  
pp. 724-734 ◽  
Author(s):  
Mehnaz Rasool ◽  
Maloy K Singha
Keyword(s):  
Dynamic Pressure ◽  
Variable Stiffness ◽  
Limit Cycle Oscillation ◽  
Composite Panels ◽  
Constant Stiffness ◽  
Aerodynamic Pressure ◽  
Aeroelastic Analysis ◽  
Divergence Type ◽  
Cycle Oscillation ◽  
The Stability

The effect of in-plane stresses on the stability behaviors of constant stiffness and variable stiffness composite panels, exposed to aerodynamic pressure, is studied using the finite element method. The dynamic pressure from the high velocity airflow is evaluated from the first-order piston theory, and the eigenvalue analysis is performed to investigate the flutter or divergence type of instabilities in such composite panels under combined mechanical and aerodynamic loads. Attempt is made to understand the effect of the lamination parameter on the stability characteristics of edge-supported and cantilever composite trapezoidal panels. Finally, the limit cycle oscillation of variable stiffness plates subjected to aerodynamic pressure is investigated.

Stability and Hopf Bifurcation in a Predator–Prey Model with the Cost of Anti-Predator Behaviors

2019 ◽  
Vol 29 (13) ◽  
pp. 1950185 ◽  
Author(s):  
Ting Qiao ◽  
Yongli Cai ◽  
Shengmao Fu ◽  
Weiming wang
Keyword(s):  
Hopf Bifurcation ◽  
Limit Cycle Oscillation ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Fear Effect ◽  
Existence And Stability ◽  
Cycle Oscillation ◽  
Predator Model ◽  
The Stability ◽  
The Cost

In this paper, we investigate the influence of anti-predator behavior in prey due to the fear of predators with a Beddington–DeAngelis prey–predator model analytically and numerically. We give the existence and stability of equilibria of the model, and provide the existence of Hopf bifurcation. In addition, we investigate the influence of the fear effect on the population dynamics of the model and find that the fear effect can not only reduce the population density of both predator and prey, but also prevent the occurrence of limit cycle oscillation and increase the stability of the system.

Nonlinear Control Methods for High Energy Limit Cycle Oscillations

1999 ◽  
Author(s):  
Thomas Strganac ◽  
John Junkins ◽  
J. Ko ◽  
Andrew J. Kurdila
Keyword(s):  
Nonlinear Control ◽  
Limit Cycle ◽  
Active Control ◽  
High Performance ◽  
High Energy ◽  
Limit Cycle Oscillation ◽  
Limit Cycle Oscillations ◽  
Cycle Oscillation ◽  
The Stability ◽  
Flight Regimes

Abstract Limit cycle oscillations, as they manifest in high performance fighter aircraft, remain an area of scrutiny by the aerospace industry and military. Tools for the simulation and prediction of the onset for limit cycle oscillations have matured significantly over the years. Suprisingly, less progress has been made in the derivation of active control methodologies for these inherently nonlinear dynamic phenomena. Even in the cases where it is known that limit cycle oscillation may be observed in particular flight regimes, and active control methodologies are employed to attenuate response, there are very few analytical results that study the stability of the closed loop system. In part, this may be attributed to the difficulty in characterizing the nature of the contributing nonlinear structural and nonlinear aerodynamic interactions that account for the motion. This paper reviews recent progress made by the authors in the derivation, development and implementation of nonlinear control methodologies for a class of low speed flutter problems. Both analytical and experimental results are summarized. Directions for future study, and in particular technical barriers that must be overcome, are summarized in the paper.

scholarly journals Limit cycle oscillation control and suppression

1999 ◽  
Vol 103 (1023) ◽  
pp. 257-263 ◽  
Author(s):  
G. Dimitriadis ◽  
J. E. Cooper
Keyword(s):  
Limit Cycle ◽  
Limit Cycles ◽  
Harmonic Balance Method ◽  
Limit Cycle Oscillation ◽  
Aeroelastic System ◽  
Oscillation Control ◽  
Control Scheme ◽  
Non Linear ◽  
Cycle Oscillation ◽  
The Stability

Abstract The prediction and characterisation of the limit cycle oscillation (LCO) behaviour of non-linear aeroelastic systems has become of great interest recently. However, much of this work has concentrated on determining the existence of LCOs. This paper concentrates on LCO stability. By considering the energy present in different limit cycles, and also using the harmonic balance method, it is shown how the stability of limit cycles can be determined. The analysis is then extended to show that limit cycles can be controlled, or even suppressed, by the use of suitable excitation signals. A basic control scheme is developed to achieve this, and is demonstrated on a simple simulated non-linear aeroelastic system.

Reexamination of Stability of a Two-Dimensional Finite Panel Exposed to an Incompressible Flow

1981 ◽  
Vol 48 (3) ◽  
pp. 472-478 ◽  
Author(s):  
Y. Matsuzaki
Keyword(s):  
Incompressible Flow ◽  
Harmonic Balance Method ◽  
Control Surface ◽  
Limit Cycle Oscillation ◽  
Two Dimensional ◽  
Elastic Channel ◽  
Fluid Forces ◽  
Cycle Oscillation ◽  
The Stability ◽  
The Galerkin Method

Stability of a flat or buckled panel exposed to an incompressible flow has been reanalyzed as the analyses on this problem by other investigators have errors in the fluid forces used. The deflection of the panel in an oscillatory motion is assumed in such a way that there occurs no change in the fluid volume in a control surface enclosing the panel. The nonlinear equation of motion of the panel on a continuous elastic spring is solved by using the Galerkin method and the generalized fluid forces which are derived in the author’s previous paper. The stability of the flat and buckled configuration in static equilibrium is examined against small disturbances. Existence of the limit cycle oscillation is studied by applying the harmonic balance method. Numerical results are compared with those of the analysis on a two-dimensional finite elastic channel conveying an almost incompressible flow.

Nonlinear Response of an Inextensible, Free–Free Beam Subjected to a Nonconservative Follower Force

2019 ◽  
Vol 15 (2) ◽  
Author(s):  
Kevin A. McHugh ◽  
Earl H. Dowell
Keyword(s):  
Stability Boundary ◽  
Expansion Method ◽  
Follower Force ◽  
Limit Cycle Oscillation ◽  
Modal Expansion ◽  
Modal Expansion Method ◽  
Time Histories ◽  
Cycle Oscillation ◽  
The Stability ◽  
Free Beam

Abstract A free–free beam with a compressive follower force applied to one end exhibits interesting flutter and limit cycle oscillation (LCO) responses. Here, the derivation from Lagrange's equations is given for the nonlinear inextensible beam with such a force applied. The inextensibility constraint is met with a Lagrange multiplier added to the Lagrangian, and the beam allowed three rigid body modes in planar motion in addition to its elastic deformation. The Rayleigh–Ritz modal expansion method and the Runge–Kutta method are used to calculate time histories of the forced beam response. This new model is validated against classical results for the stability boundary and new LCO bifurcation diagrams are computed.

Nonlinear Aeroelastic Characteristics of a Fighter-Type Wing With Control Surface

2002 ◽  
Author(s):  
Jae-Sung Bae ◽  
In Lee
Keyword(s):  
Limit Cycle ◽  
Chaotic Motion ◽  
Free Play ◽  
Control Surface ◽  
Limit Cycle Oscillation ◽  
Nonlinear Flutter ◽  
Wide Range ◽  
Flutter Boundary ◽  
Linear And Nonlinear ◽  
Cycle Oscillation

The nonlinear aeroelastic characteristics of a fighter-type wing with control surface have been investigated. The fictitious mass modal approach is used to reduce the problem size and the computation time in the linear and nonlinear flutter analyses. A Doublet-Hybrid method are used for the computation of subsonic unsteady aerodynamic forces. Structural nonlinearity of the control surface hinge is represented by a free-play spring. The linear and nonlinear flutter analyses indicate that the flapping mode of control surface and the hinge stiffness have significant effects on the flutter characteristics. The nonlinear flutter analysis shows that limit cycle oscillation and chaotic motion are observed in the wide range of air speed below the linear flutter boundary and the jump of limit cycle oscillation amplitude is observed. The nonlinear flutter characteristics and the nonlinear flutter boundary of limit cycle oscillation and chaotic motion have been investigated.

scholarly journals The effect of pressure on structural, stability, electronic, and optical properties of hydrogenated silicene: A first-principle study

2021 ◽  
Author(s):  
V Kumar ◽  
R. Santosh
Keyword(s):  
Optical Properties ◽  
Binding Energy ◽  
External Pressure ◽  
Optical Parameters ◽  
First Principle ◽  
Electronic And Optical Properties ◽  
External Pressures ◽  
The Stability ◽  
First Time ◽  
Good Agreement

Abstract The structural, electronic, and optical properties of hydrogenated silicene have been studied under different pressures using first-principle calculations. The binding energy and band structure have been calculated for two stable structures: Chair (C-) and Boat (B-) in the range of 0–21 GPa external pressure. The behavior of stability and energy bandgap have been analyzed under different external pressures. The stability has been verified using binding energy and phonon data. The C- and B- structures have zero bandgaps at 21 GPa and become unstable. The optical properties of B-configuration have been studied in the energy range of 0–20 eV. Five optical parameters such as conductivity threshold (σth), dielectric constant ε(0), refractive index n(0), birefringence Δn(0) and plasmon energy (ħωp) have been calculated for the first time under different pressures. The calculated values are in good agreement with the reported values at 0 GPa.

scholarly journals DC-DC Zeta Power Converter: Ramp Compensation Control Design and Stability Analysis

2021 ◽  
Vol 11 (13) ◽  
pp. 5946
Author(s):  
David Angulo-García ◽  
Fabiola Angulo ◽  
Juan-Guillermo Muñoz
Keyword(s):  
Power Systems ◽  
Duty Cycle ◽  
Extreme Values ◽  
Period Doubling ◽  
Power Converter ◽  
Large Set ◽  
Compensation Control ◽  
Stable Period ◽  
Wide Range ◽  
The Stability

The design of robust and reliable power converters is fundamental in the incorporation of novel power systems. In this paper, we perform a detailed theoretical analysis of a synchronous ZETA converter controlled via peak-current with ramp compensation. The controller is designed to guarantee a stable Period 1 orbit with low steady state error at different values of input and reference voltages. The stability of the desired Period 1 orbit of the converter is studied in terms of the Floquet multipliers of the solution. We show that the control strategy is stable over a wide range of parameters, and it only loses stability: (i) when extreme values of the duty cycle are required; and (ii) when input and reference voltages are comparable but small. We also show by means of bifurcation diagrams and Lyapunov exponents that the Period 1 orbit loses stability through a period doubling mechanism and transits to chaos when the duty cycle saturates. We finally present numerical experiments to show that the ramp compensation control is robust to a large set of perturbations.

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