scholarly journals Stability analysis of whirl flutter in rotor-nacelle systems with freeplay nonlinearity

2021 ◽  
Vol 104 (1) ◽  
pp. 65-89
Author(s):  
Christopher Mair ◽  
Branislav Titurus ◽  
Djamel Rezgui
Keyword(s):  
Stability Analysis ◽  
Stability Boundary ◽  
Linear Analysis ◽  
Dynamical Behaviour ◽  
Model Complexity ◽  
Analysis Methods ◽  
Freeplay Nonlinearity ◽  
Whirl Flutter ◽  
The Stability ◽  
Parameter Ranges

AbstractTiltrotor aircraft are growing in prevalence due to the usefulness of their unique flight envelope. However, aeroelastic stability—particularly whirl flutter stability—is a major design influence that demands accurate prediction. Several nonlinearities that may be present in tiltrotor systems, such as freeplay, are often neglected for simplicity, either in the modelling or the stability analysis. However, the effects of such nonlinearities can be significant, sometimes even invalidating the stability predictions from linear analysis methods. Freeplay is a nonlinearity that may arise in tiltrotor nacelle rotation actuators due to the tension–compression loading cycles they undergo. This paper investigates the effect of a freeplay structural nonlinearity in the nacelle pitch degree of freedom. Two rotor-nacelle models of contrasting complexity are studied: one represents classical whirl flutter (propellers) and the other captures the main effects of tiltrotor aeroelasticity (proprotors). The manifestation of the freeplay in the systems’ dynamical behaviour is mapped out using Continuation and Bifurcation Methods, and consequently the change in the stability boundary is quantified. Furthermore, the effects on freeplay behaviour of (a) model complexity and (b) deadband edge sharpness are studied. Ultimately, the freeplay nonlinearity is shown to have a complex effect on the dynamics of both systems, even creating the possibility of whirl flutter in parameter ranges that linear analysis methods predict to be stable. While the size of this additional whirl flutter region is finite and bounded for the basic model, it is unbounded for the higher complexity model.

Instability of Heated Panels in Supersonic Air Flow

2008 ◽  
Vol 33-37 ◽  
pp. 1101-1108
Author(s):  
Zhi Chun Yang ◽  
Wei Xia
Keyword(s):  
Stability Analysis ◽  
Stability Boundary ◽  
Boundary Curve ◽  
Static Stability ◽  
Static Deformation ◽  
Limit Cycle Oscillation ◽  
Aerodynamic Load ◽  
Aeroelastic System ◽  
Aerodynamic Pressure ◽  
The Stability

An investigation on the stability of heated panels in supersonic airflow is performed. The nonlinear aeroelastic model for a two-dimensional panel is established using Galerkin method and the thermal effect on the panel stiffness is also considered. The quasi-steady piston theory is employed to calculate the aerodynamic load on the panel. The static and dynamic stabilities for flat panels are studied using Lyapunov indirect method and the stability boundary curve is obtained. The static deformation of a post-buckled panel is then calculated and the local stability of the post-buckling equilibrium is analyzed. The limit cycle oscillation of the post-buckled panel is simulated in time domain. The results show that a two-mode model is suitable for panel static stability analysis and static deformation calculation; but more than four modes are required for dynamic stability analysis. The effects of temperature elevation and dimensionless parameters related to panel length/thickness ratio, material density and Mach number on the stability of heated panel are studied. It is found that panel flutter may occur at relatively low aerodynamic pressure when several stable equilibria exist for the aeroelastic system of heated panel.

A Survey of Fractional-Order Neural Networks

2017 ◽  
Author(s):  
Shuo Zhang ◽  
YangQuan Chen ◽  
Yongguang Yu
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Fractional Order ◽  
Computational Science ◽  
General Introduction ◽  
Analysis Methods ◽  
Recent Trends ◽  
The Stability

In this paper, the literature of fractional-order neural networks is categorized and discussed, which includes a general introduction and overview of fractional-order neural networks. Various application areas of fractional-order neural networks have been found or used, and will be surveyed and summarized such as neuroscience, computational science, control and optimization. Recent trends in dynamics of fractional-order neural networks are presented and discussed. The results, especially the stability analysis of fractional-order neural networks, are reviewed and different analysis methods are compared. Furthermore, the challenges and conclusions of fractional-order neural networks are given.

Moment Stability of Stochastic Regenerative Cutting Process

2010 ◽  
Vol 97-101 ◽  
pp. 3038-3041
Author(s):  
Xiao Qin Zhou ◽  
Wen Cai Wang ◽  
Hong Wei Zhao
Keyword(s):  
Stability Analysis ◽  
Stability Boundary ◽  
Cutting Process ◽  
Damping Coefficients ◽  
Cutting Stability ◽  
Stationary Stochastic Processes ◽  
The Stability ◽  
Stiffness And Damping ◽  
Moment Stability ◽  
Stochastic Uncertainties

The stochastic uncertainties of regenerative cutting process (RCP) are taken into consideration, and both cutting stiffness and damping coefficients are modeled as two stationary stochastic processes. The eigenvalue equations are established for the stability analysis of stochastic RCP, corresponding to the differential equations of the first and second order moments. Thus the stability analysis of stochastic RCP is transformed into that of the first two order moments. The influence of stochastic uncertainties on the cutting stability of RCP is discussed. The numerical experiments have verified that with the increase of stochastic uncertainties, the cutting stability boundary was shifted downwards significantly, and the number of lobes was also multiplied.

Analysis of the Chatter Instability in a Nonlinear Model for Drilling

2006 ◽  
Vol 1 (4) ◽  
pp. 294-306 ◽  
Author(s):  
Sue Ann Campbell ◽  
Emily Stone
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Nonlinear Models ◽  
Stability Boundary ◽  
Vibration Modes ◽  
Loss Of Stability ◽  
Chatter Vibration ◽  
Cutting Depth ◽  
Stability And Bifurcation Analysis ◽  
The Stability

In this paper we present stability analysis of a non-linear model for chatter vibration in a drilling operation. The results build our previous work [Stone, E., and Askari, A., 2002, “Nonlinear Models of Chatter in Drilling Processes,” Dyn. Syst., 17(1), pp. 65–85 and Stone, E., and Campbell, S. A., 2004, “Stability and Bifurcation Analysis of a Nonlinear DDE Model for Drilling,” J. Nonlinear Sci., 14(1), pp. 27–57], where the model was developed and the nonlinear stability of the vibration modes as cutting width is varied was presented. Here we analyze the effect of varying cutting depth. We show that qualitatively different stability lobes are produced in this case. We analyze the criticality of the Hopf bifurcation associated with loss of stability and show that changes in criticality can occur along the stability boundary, resulting in extra periodic solutions.

scholarly journals Stability analysis of long hydrodynamic journal bearings based on the journal center trajectory

Friction ◽  
2020 ◽  
Author(s):  
Yu Huang ◽  
Haiyin Cao ◽  
Zhuxin Tian
Keyword(s):  
Stability Analysis ◽  
Equilibrium Point ◽  
Journal Bearing ◽  
Stability Boundary ◽  
Initial Point ◽  
Journal Bearings ◽  
Bearing Surface ◽  
Rotating Speed ◽  
Stability Threshold ◽  
The Stability

AbstractIn this study, we observe that there are two threshold speeds (stability threshold speed and second threshold speed) for the long journal bearing, which is different for the short bearing. When the rotating speed is below the stability threshold speed, the stability boundary nearly coincides with the clearance circle, and the journal center gradually returns to the equilibrium point after being released at an initial point. If the rotating speed is between the stability threshold speed and the second threshold speed, after being released at an initial point, the journal center converges to a contour containing the equilibrium point. In this situation, for a higher rotating speed, the corresponding contour is also larger. When the rotating speed exceeds the second threshold speed, the journal gradually moves towards the bearing surface after being released at an initial point.

Frequency Domain Linear Stability Analysis of Simplified Supercritical Water-Cooled Reactor

2009 ◽  
Author(s):  
Pengfei Liu ◽  
Yanhua Yang ◽  
Aijun Xue ◽  
Xu Cheng
Keyword(s):  
Stability Analysis ◽  
Characteristic Equation ◽  
Supercritical Water ◽  
Stability Boundary ◽  
System Model ◽  
Heating Zone ◽  
Critical Number ◽  
Boundary Points ◽  
System Pressure ◽  
The Stability

This paper presents the stability analysis of a supercritical water-cooled system. A model of simplified supercritical water-cooled system is introduced and then its thermal-hydraulic equations, initial conditions and boundary conditions are given. Based on perturbation linearization and Laplace transformation, the transfer function between inlet mass flow rate oscillation and pressure drop oscillation of the simplified system model is established, and the characteristic equation of the simplified system model is derived. Applying control theory to solve the characteristic equation, the stability boundary points are found by judging whether the real parts of all roots solved by characteristic equation are greater than zero. A stability map which consists of these stability boundary points is generated by using both dimensionless sub-pseudo-critical number and trans-pseudo-critical number. An unstable region nearby the pseudo-critical point is determined. The effects of some important parameters on the stability map are investigated also by using decay ratio. The sensitivity analysis shows that the system is stabilized with a higher hydraulic system resistance, fluid inlet velocity or system pressure. It also shows that a longer heating zone, a harder pump characteristics or a larger gravitational acceleration (orientation angle) leads to a larger stability margin of the system. The stability map is also found to be not sensitive to a higher friction resistance or system pressure.

scholarly journals V/C Digital Controlled DC-DC Converter

2020 ◽  
Vol 9 (3) ◽  
pp. 167-175
Keyword(s):  
Stability Analysis ◽  
Transient Analysis ◽  
Stability Boundary ◽  
Buck Converter ◽  
Sampled Data ◽  
Signal Model ◽  
Stability Range ◽  
Z Domain ◽  
Average Current ◽  
The Stability

In this paper, the switching of dc-dc converter using voltage/current digital control is proposed. It is the combination of existed digital average voltage and digital average current controls. The stability analysis of V/C digital controlled dc-dc converter is derived by using sampled data model. The transient analysis of V/C digital controlled dc-dc converter is also derived by using z-domain small signal model. The proposed V/C digital controlled dc-dc converter has over current protection, fast load transient response, no sub-harmonic oscillations at any value of duty cycle, and wider stability range. The proposed system is analysed with a simple buck converter. The output voltage and inductor current weighting factors influence the stability boundary and transient performances of V/C digital controlled dc-dc converter. The stability analysis and transient analysis is investigated and verified by circuit simulations

Convective instability of reaction fronts: Linear stability analysis

1998 ◽  
Vol 9 (5) ◽  
pp. 507-525 ◽  
Author(s):  
V. A. VOLPERT ◽  
A. I. VOLPERT
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Convective Instability ◽  
Eigenvalue Problems ◽  
Transport Coefficients ◽  
Stability Boundary ◽  
New Approaches ◽  
Reaction Fronts ◽  
The Stability

The paper is devoted to convective instability of reaction fronts. New approaches are developed to study some eigenvalue problems arising in chemical hydrodynamics. For gaseous combustion in the case of equality of transport coefficients, a linear stability analysis of an upward propagating front is carried out. A minimax representation of the stability boundary is obtained.

Hysteresis Effect in the Nonlinear Stability of Towed Wheels

2017 ◽  
Author(s):  
Sándor Beregi ◽  
Dénes Takács ◽  
David A. W. Barton
Keyword(s):  
Linear Stability ◽  
Stability Boundary ◽  
Hysteresis Effect ◽  
Structure Characteristic ◽  
Rectilinear Motion ◽  
Straight Line ◽  
Stable Periodic ◽  
Distributed Time Delay ◽  
The Stability ◽  
Parameter Ranges

In this paper the dynamics of towed elastic wheels are studied with the help of the brush tyre model. To calculate the lateral deformation of the contact patch centre-line distributed time-delay is taken into account for the rolling parts, whereas parabolic limits are used to determine the deformation in case of side-slip. After linear stability analysis of the rectilinear motion the limit cycles of the non-smooth time-delayed system are calculated with the method of numerical collocation. With the help of bifurcation diagrams it is demonstrated how the periodic orbits develop from the linear stability boundary in a structure characteristic of piecewise-smooth systems. Moreover, it is shown that the contact memory effect and the dry friction yield bistable parameter ranges besides the linearly unstable domains. Namely, for one particular towing velocity a stable equilibrium corresponding to straight-line motion and a stable periodic orbit coexist resulting a hysteresis effect in the stability of the straight-line motion.

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