scholarly journals Effects of Structural Coupling on Mistuned Cascade Flutter and Response

1984 ◽  
Vol 106 (1) ◽  
pp. 17-24 ◽  
Author(s):  
R. E. Kielb ◽  
K. R. V. Kaza
Keyword(s):  
Coupled System ◽  
Aeroelastic Stability ◽  
Resonant Frequencies ◽  
Structural Coupling ◽  
Aerodynamic Loads ◽  
Natural Modes ◽  
Section Model ◽  
Cascade Flutter ◽  
The Stability ◽  
Two Degree Of Freedom

The effects of structural coupling on mistuned cascade flutter and response are analytically investigated using an extended typical section model. Previous work using two degree of freedom per blade typical section models has included only aerodynamic coupling. The present work extends this model to include both structural and aerodynamic coupling between the blades. The model assumes that the structurally coupled system natural modes have been determined and can be represented in the form of N bending and N torsional uncoupled modes for each blade, where N is the number of blades and, hence, is only valid for blade dominated motion. The aerodynamic loads are calculated by using two-dimensional unsteady cascade theories in the subsonic and supersonic flow regimes. The results show that the addition of structural coupling can affect both the aeroelastic stability and frequency. The stability is significantly affected only when the system is mistuned. The resonant frequencies can be significantly changed by structural coupling in both tuned and mistuned systems, however, the peak response is significantly affected only in the latter.

On the Natural Modes and Their Stability in Nonlinear Two-Degree-of-Freedom Systems

1959 ◽  
Vol 26 (3) ◽  
pp. 377-385
Author(s):  
R. M. Rosenberg ◽  
C. P. Atkinson
Keyword(s):  
Free Vibrations ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Natural Modes ◽  
Theoretical Predictions ◽  
Stability Chart ◽  
The Stability ◽  
Two Parameters ◽  
Two Degree Of Freedom

Abstract The natural modes of free vibrations of a symmetrical two-degree-of-freedom system are analyzed theoretically and experimentally. This system has two natural modes, one in-phase and the other out-of-phase. In contradistinction to the comparable single-degree-of-freedom system where the free vibrations are always orbitally stable, the natural modes of the symmetrical two-degree-of-freedom system are frequently unstable. The stability properties depend on two parameters and are easily deduced from a stability chart. For sufficiently small amplitudes both modes are, in general, stable. When the coupling spring is linear, both modes are always stable at all amplitudes. For other conditions, either mode may become unstable at certain amplitudes. In particular, if there is a single value of frequency and amplitude at which the system can vibrate in either mode, the out-of-phase mode experiences a change of stability. The experimental investigation has generally confirmed the theoretical predictions.

scholarly journals Advanced Ducted Engines: Impact of Unsteady Aerodynamics on Fan Vibration Properties

1992 ◽  
Author(s):  
Arno H. Klose
Keyword(s):  
Mode Coupling ◽  
Unsteady Aerodynamics ◽  
Light Weight ◽  
Aeroelastic Stability ◽  
Resonant Frequencies ◽  
Aerodynamic Loads ◽  
Reinforced Plastics ◽  
Unsteady Aerodynamic ◽  
Vibration Properties ◽  
Carbon Fibre Reinforced Plastics

Fans of Advanced Ducted Engines (ADE) will be built from light-weight materials such as carbon-fibre-reinforced plastics (CFRP). Due to their low density, the aeroelastic behaviour of these fan blades is significantly different from that of conventional titanium fan blading. Calculations performed during the design of ADE fan bladings show that self-induced aerodynamic loads can significantly alter the resonant frequencies; furthermore, aerodynamic coupling of the different in-vacuo eigenmodes can occur. This is not the case for conventional titanium fan blading, where the vibration properties are largely unaffected by unsteady aerodynamic forces. It is concluded that for light-weight fan blading, it is necessary to take into account aerodynamic stiffening and aerodynamic mode coupling when computing eigenfrequencies and aeroelastic stability.

scholarly journals A Theoretical Model for the Transmission Dynamics of the Buruli Ulcer with Saturated Treatment

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Ebenezer Bonyah ◽  
Isaac Dontwi ◽  
Farai Nyabadza
Keyword(s):  
Human Population ◽  
Reproduction Number ◽  
Buruli Ulcer ◽  
Coupled System ◽  
Model Parameters ◽  
The Public ◽  
Treatment Function ◽  
Medical Facilities ◽  
The Stability ◽  
Saturated Treatment

The management of the Buruli ulcer (BU) in Africa is often accompanied by limited resources, delays in treatment, and macilent capacity in medical facilities. These challenges limit the number of infected individuals that access medical facilities. While most of the mathematical models with treatment assume a treatment function proportional to the number of infected individuals, in settings with such limitations, this assumption may not be valid. To capture these challenges, a mathematical model of the Buruli ulcer with a saturated treatment function is developed and studied. The model is a coupled system of two submodels for the human population and the environment. We examine the stability of the submodels and carry out numerical simulations. The model analysis is carried out in terms of the reproduction number of the submodel of environmental dynamics. The dynamics of the human population submodel, are found to occur at the steady states of the submodel of environmental dynamics. Sensitivity analysis is carried out on the model parameters and it is observed that the BU epidemic is driven by the dynamics of the environment. The model suggests that more effort should be focused on environmental management. The paper is concluded by discussing the public implications of the results.

On the Stability of the Linearly Related Modes of Certain Nonlinear Two-Degree-of-Freedom Systems

1961 ◽  
Vol 28 (1) ◽  
pp. 71-77 ◽  
Author(s):  
C. P. Atkinson
Keyword(s):  
Nonlinear Differential Equations ◽  
Mass Ratio ◽  
Positive Mass ◽  
Fourth Degree ◽  
Real Roots ◽  
General Stability ◽  
The Stability ◽  
The Masses ◽  
Spring Constants ◽  
Two Degree Of Freedom

This paper presents a method for analyzing a pair of coupled nonlinear differential equations of the Duffing type in order to determine whether linearly related modal oscillations of the system are possible. The system has two masses, a coupling spring and two anchor springs. For the systems studied, the anchor springs are symmetric but the masses are not. The method requires the solution of a polynomial of fourth degree which reduces to a quadratic because of the symmetric springs. The roots are a function of the spring constants. When a particular set of spring constants is chosen, roots can be found which are then used to set the necessary mass ratio for linear modal oscillations. Limits on the ranges of spring-constant ratios for real roots and positive-mass ratios are given. A general stability analysis is presented with expressions for the stability in terms of the spring constants and masses. Two specific examples are given.

An Application of the Poincare´ Map to the Stability of Nonlinear Normal Modes

1980 ◽  
Vol 47 (3) ◽  
pp. 645-651 ◽  
Author(s):  
L. A. Month ◽  
R. H. Rand
Keyword(s):  
Floquet Theory ◽  
Poincaré Map ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Theory Approach ◽  
Poincare Map ◽  
Linearized Stability ◽  
Nonlinear Normal ◽  
The Stability ◽  
Two Degree Of Freedom

The stability of periodic motions (nonlinear normal modes) in a nonlinear two-degree-of-freedom Hamiltonian system is studied by deriving an approximation for the Poincare´ map via the Birkhoff-Gustavson canonical transofrmation. This method is presented as an alternative to the usual linearized stability analysis based on Floquet theory. An example is given for which the Floquet theory approach fails to predict stability but for which the Poincare´ map approach succeeds.

Fractal Boundary Explorations for a Nonlinear Two Degree-of-Freedom System

2012 ◽  
Author(s):  
Benjamin A. M. Owens ◽  
Brian P. Mann
Keyword(s):  
Initial Conditions ◽  
Coupled System ◽  
Basins Of Attraction ◽  
Degree Of Freedom ◽  
Fractal Boundary ◽  
Final State ◽  
Potential Wells ◽  
Mechanical Coupling ◽  
Mass Spring ◽  
Two Degree Of Freedom

This paper explores a two degree-of-freedom nonlinearly coupled system with two distinct potential wells. The system consists of a pair of linear mass-spring-dampers with a non-linear, mechanical coupling between them. This nonlinearity creates fractal boundaries for basins of attraction and forced well-escape response. The inherent uncertainty of these fractal boundaries is quantified for errors in the initial conditions and parameter space. This uncertainty relationship provides a measure of the final state and transient sensitivity of the system.

scholarly journals Aeroelastic Behavior of Low Aspect Ratio Metal and Composite Blades

1986 ◽  
Author(s):  
James F. White ◽  
Oddvar O. Bendiksen
Keyword(s):  
Aspect Ratio ◽  
Opposite Effect ◽  
Design Parameters ◽  
Aeroelastic Stability ◽  
Low Aspect Ratio ◽  
Supersonic Flutter ◽  
Type Mode ◽  
The Stability ◽  
Composite Blades ◽  
Plate Type

The aeroelastic stability of titanium and composite blades of low aspect ratio is examined over a range of design parameters, using a Rayleigh-Ritz formulation. The blade modes include a plate-type mode to account for chordwise bending. Chordwise flexibility is found to have a significant effect on the unstalled supersonic flutter of low aspect ratio blades, and also on the stability of tip sections of shrouded fan blades. For blades with a thickness of less than approximately four percent of chord, the chordwise, second bending, and first torsion branches are all unstable at moderately high supersonic Mach numbers. For composite blades, the important structural coupling between bending and torsion cannot be modeled properly unless chordwise bending is accounted for. Typically, aft fiber sweep produces beneficial bending-torsion coupling that is stabilizing, whereas forward fiber sweep has the opposite effect. By using crossed-ply laminate configurations, critical aeroelastic modes can be stabilized.

Investigation of Mistuned Oscillating Cascade Using Fully-Coupled Method

2021 ◽  
Author(s):  
H. M. Phan ◽  
L. He
Keyword(s):  
Striking Difference ◽  
Influence Coefficient ◽  
Aeroelastic Stability ◽  
Mode Localization ◽  
Coupled Method ◽  
Reduced Frequency ◽  
Systematic Understanding ◽  
Cascade Flutter ◽  
The Individual ◽  
Fully Coupled

Abstract The uncoupled phase-shifted single-passage simulation is commonly used for turbomachinery aeroelastic problems. However, it has difficulties in dealing with unconventional phenomena such as strong fluid-structure interaction effects as well as blade mistuning effects. Regarding mistuning effects, structural mistuning has been studied extensively while aerodynamic mistuning has received far less attention. There seems to be a lack of clear and systematic understanding of physical behaviour and mechanisms of mistuned bladerows, particularly in the context of the aerodynamic mistuning versus structural one. In the present work, direct fully-coupled method is adopted to investigate the dynamics mechanism of a mistuned oscillating cascade. Both structurally and aerodynamically mistuned cascades show that the blades would couple and oscillate at a unique frequency and a constant inter-blade phase angle regardless of the individual blade’s eigen-frequency. The vibration amplitudes of blades of a mistuned row are different when excited. For structural mistuning, the mode localization effect is seen to be responsible for a monotonic increase of cascade aeroelastic stability with mistuning. On the other hand, the aerodynamically mistuned cascade shows a stabilizing effect at small amount of mistuning but exhibits a destabilizing effect at large mistuning. Such non-monotonic tendency could be explained using the aero-damping decomposition by the influence coefficient approach. At low reduced frequency, there is a striking difference between the tuned and aero-mistuned cascade. Although the tuned cascade is stable, the aero-mistuned cascade may experience flutter. A close inspection of the aero-mistuned cascade flutter reveals that there are two oscillating waves forming a beating signal.

Resistive Ballooning Modes in Three-Dimensional Configurations

1982 ◽  
Vol 37 (8) ◽  
pp. 848-858 ◽  
Author(s):  
D. Correa-Restrepo
Keyword(s):  
Growth Rates ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Coupled System ◽  
Small Constant ◽  
Ballooning Mode ◽  
The Stability ◽  
The Magnetic Field ◽  
Symmetric Systems ◽  
The Ideal

Resistive ballooning modes in general three-dimensional configurations are studied on the basis of the equations of motion of resistive MHD. Assuming small, constant resistivity and perturbations localized transversally to the magnetic field, a stability criterion is derived in the form of a coupled system of two second-order differential equations. This criterion contains several limiting cases, in particular the ideal ballooning mode criterion and criteria for the stability of symmetric systems. Assuming small growth rates, analytical results are derived by multiple-length-scale expansion techniques. Instabilities are found, their growth rates scaling as fractional powers of the resistivity

Galloping response of sector-shape iced eight bundle conductors

2020 ◽  
Vol 47 (10) ◽  
pp. 1201-1213
Author(s):  
Meng-qi Cai ◽  
Lin-shu Zhou ◽  
Qian Xu ◽  
Xiao-hui Yang ◽  
Xiao-hui Liu
Keyword(s):  
Transmission Lines ◽  
Theoretical Basis ◽  
Wind Tunnel Test ◽  
Dynamic Responses ◽  
Test Results ◽  
The Finite Element Method ◽  
Aerodynamic Coefficients ◽  
Aerodynamic Loads ◽  
Natural Modes ◽  
Wind Velocities

Wind tunnel test results of the aerodynamic coefficients of sector-shape iced eight bundle conductors varying with wind attack angles are presented. Then, by means of the user-defined cable elements, the aerodynamic loads are applied on the cable elements of each sub-conductor through the finite element method (FEM). In addition, the galloping responses of sector-shape iced eight bundle conductors are discussed. Finally, galloping responses, including dynamic responses (natural modes and frequencies), galloping orbits, and amplitudes of typical sector-shape iced eight bundle conductor transmission lines in the cases of different span lengths, wind velocities, and angles of wind attack are studied, respectively. These results provide useful references for a theoretical basis for the study of galloping and the technique of anti-galloping in cold regions.

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