Helicopter Ground Resonance Phenomenon With Blade Stiffness Dissimilarities: Experimental and Theoretical Developments

2012 ◽  
Author(s):  
Leonardo Sanches ◽  
Guilhem Michon ◽  
Alain Berlioz ◽  
Daniel Alazard
Keyword(s):  
Equations Of Motion ◽  
Resonance Phenomenon ◽  
Aging Effects ◽  
Ground Resonance ◽  
Different Types ◽  
Stability Chart ◽  
Instability Regions ◽  
The Stability ◽  
Theoretical Results ◽  
Theoretical Developments

Recent works study the ground resonance in helicopters under the aging effects. Indeed, the blades lead-lag stiffness may vary randomly with time and be different from each other (i.e.: anisotropic rotor). The influence of stiffness dissimilarities between blades on the stability of the ground resonance phenomenon is determined through numerical investigations on the periodical equations of motion, treated by using Floquet’s theory. Stability chart highlights the appearance of new instability zones as function of the perturbation introduced on the lead-lag stiffness of one blade. In order to validate the theoretical results, a new experimental setup is designed and developed. The ground resonance instabilities are investigated for different types of rotor configurations (i.e.: isotropic and anisotropic rotors) and the boundaries of stability are determined. A good correlation between both theoretical and experimental results is obtained and the new instability zones, found in asymmetric rotors, are verified experimentally. The temporal responses of the measured signals highlight the exponential divergence at the instability regions.

Helicopter Ground Resonance Phenomenon With Blade Stiffness Dissimilarities: Experimental and Theoretical Developments

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Leonardo Sanches ◽  
Guilhem Michon ◽  
Alain Berlioz ◽  
Daniel Alazard
Keyword(s):  
Equations Of Motion ◽  
Experimental Results ◽  
Resonance Phenomenon ◽  
Experimental Setup ◽  
Numerical Investigations ◽  
Ground Resonance ◽  
Stability Chart ◽  
The Stability ◽  
Theoretical Results ◽  
Theoretical Developments

Recent works have studied ground resonance in helicopters under the aging or damage effects. Indeed, blade lead-lag stiffness may vary randomly with time and differ from blade to blade. The influence of stiffness dissimilarities between blades on the stability of the ground resonance phenomenon was determined through numerical investigations into the periodic equations of motion, treated using Floquet's theory. A stability chart highlights the appearance of new instability zones as a function of the perturbation introduced on the lead-lag stiffness of one blade. In order to validate the theoretical results, a new experimental setup was designed and developed. The ground resonance instabilities were investigated using different rotors and the boundaries of stability were determined. A good correlation between both theoretical and experimental results was obtained and the new instability zones, found in asymmetric rotors, were verified experimentally. The temporal responses of the measured signals highlighted the exponential divergence in the instability zones.

The Equations of Motion of n-Bladed Propellers with Arbitrarily Positioned Hinges and Their Application to an Experimental One-Bladed Wind Turbine

1985 ◽  
Vol 199 (4) ◽  
pp. 237-244
Author(s):  
M Person
Keyword(s):  
Wind Turbine ◽  
Equations Of Motion ◽  
Stability Analyses ◽  
Start Up ◽  
Different Types ◽  
The Stability

The equations of motion of n-bladed propellers with arbitrarily positioned hinges are derived out of the equations of a one-bladed propeller, by superposition. Different types of propellers are compared for time variances at the equations. An unbalanced start-up and the stability analyses (Floquet) of an experimental one-bladed propeller illustrate the need to consider the interaction of the motions of nacelle or hub and blade.

Self-Excited Vibrations and Damping in Circulatory Systems

2014 ◽  
Vol 81 (10) ◽  
Author(s):  
Peter Hagedorn ◽  
Manuel Eckstein ◽  
Eduard Heffel ◽  
Andreas Wagner
Keyword(s):  
Transmission Lines ◽  
Mechanical Engineering ◽  
Equations Of Motion ◽  
The Self ◽  
Engineering Systems ◽  
Common Assumption ◽  
Damping Matrix ◽  
Stiffness Matrices ◽  
Ground Resonance ◽  
The Stability

Self-excited vibrations in mechanical engineering systems are in general unwanted and sometimes dangerous. There are many systems exhibiting self-excited vibrations which up to this day cannot be completely avoided, such as brake squeal, the galloping vibrations of overhead transmission lines, the ground resonance in helicopters and others. These systems have in common that in the linearized equations of motion the self-excitation terms are given by nonconservative, circulatory forces. It has been well known for some time, that such systems are very sensitive to damping. Recently, several new theorems concerning the effect of damping on the stability and on the self-excited vibrations were proved by some of the authors. The present paper discusses these new mathematical results for practical mechanical engineering systems. It turns out that the structure of the damping matrix is of utmost importance, and the common assumption, namely, representing the damping matrix as a linear combination of the mass and the stiffness matrices, may give completely misleading results for the problem of instability and the onset of self-excited vibrations. The authors give some indications on improving the description of the damping matrix in the linearized problems, in order to enhance the modeling of the self-excited vibrations. The improved models should lead to a better understanding of these unwanted phenomena and possibly also to designs oriented toward their avoidance.

Bifurcations and Synchronization of Delay-Coupled Neuronal Networks with Autaptic Connections

2018 ◽  
Vol 28 (06) ◽  
pp. 1850071 ◽  
Author(s):  
Xiaochen Mao
Keyword(s):  
System Performance ◽  
Time Delays ◽  
Electrical Synapse ◽  
Stability Criteria ◽  
Neural Activities ◽  
Coupled Networks ◽  
Different Types ◽  
The Stability ◽  
Multistability Coexistence ◽  
Theoretical Results

This paper focuses on the dynamic behaviors of delay-coupled networks consisting of an arbitrary number of nonidentical neurons with unidirectional connections and an electrical synapse from one neuron onto itself. The stability criteria and different types of bifurcations are discussed by decomposing and analyzing the associated characteristic equation. Then, the study turns to the validation of theoretical results through numerical simulations and various interesting neural activities are observed, such as nontrivial equilibria, different patterns of oscillations, multistability coexistence, multiple switches between the quiescent and different periodic states, and transitions between the coexisting equilibria and the coexistence of equilibria and periodic oscillations. It is shown that time delays play important roles in the system performance and can be used to control neural activities.

scholarly journals Bifurcation Analysis of a Delayed Infection Model with General Incidence Function

2019 ◽  
Vol 2019 ◽  
pp. 1-16
Author(s):  
Suxia Zhang ◽  
Hongsen Dong ◽  
Jinhu Xu
Keyword(s):  
Hopf Bifurcation ◽  
Local Stability ◽  
Infection Model ◽  
Positive Equilibrium ◽  
Hopf Bifurcations ◽  
Incidence Function ◽  
Stability And Instability ◽  
Different Types ◽  
The Stability ◽  
Theoretical Results

In this paper, an infection model with delay and general incidence function is formulated and analyzed. Theoretical results reveal that positive equilibrium may lose its stability, and Hopf bifurcation occurs when choosing delay as the bifurcation parameter. The direction of Hopf bifurcation and the stability of the periodic solutions are also discussed. Furthermore, to illustrate the numerous changes in the local stability and instability of the positive equilibrium, we conduct numerical simulations by using four different types of functional incidence, i.e., bilinear incidence, saturation incidence, Beddington–DeAngelis response, and Hattaf–Yousfi response. Rich dynamics of the model, such as Hopf bifurcations and chaotic solutions, are presented numerically.

An Investigation of Riser Fairing Instability

2015 ◽  
Author(s):  
Trygve Kristiansen ◽  
Henning Braaten ◽  
Halvor Lie ◽  
Rolf Baarholm ◽  
Kjetil Skaugset
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Diameter Ratio ◽  
Instability Region ◽  
The Other ◽  
Two Degrees Of Freedom ◽  
Linearized Equations ◽  
Different Types ◽  
Instability Regions ◽  
Damping Model

An analysis of galloping of two different types of riser fairings is presented. The first is named “long fairing” (LF) and the other “Short Crab Claw” (Short CC). The first one has a traditionally winged formed shape with a cord-to-diameter ratio of 2.43. The other one is more truncated in shape, and has cord-to-diameter ratio of only 1.4. Results from two related experimental set-ups are included in the work; one 2D experiment with towing tests of fairings that are free to translate and rotate to investigate instability regions, and one 2D experiment with fixed fairings to obtain drag, moment and lift curves. The present analysis is based on two-degrees of freedom, linearized equations of motion, and predicts a range of velocities where instability occurs. Below and above this region, the fairing is stable. Damping complicates the analysis. An empirical damping model is included and discussed. The two fairing types inhibit appreciably different instability characteristics. In particular, the Short CC fairing has a narrower instability region than the long fairing, and is therefore less prone to instabilities.

scholarly journals Dynamic Stability in a Cracked Turbo Blade-Disk

1999 ◽  
Author(s):  
J. H. Kuang ◽  
B. W. Huang
Keyword(s):  
Multiple Scales ◽  
Rotation Speed ◽  
Equations Of Motion ◽  
Crack Depth ◽  
Disk System ◽  
Rotating Blade ◽  
Blade System ◽  
Instability Regions ◽  
The Stability ◽  
Multiple Scales Perturbation Method

Analysis of the stability in a cracked blade-disk system is proposed. The effect of modal localization on the stability in a rotating blade-disk was studied. A crack near the root of a blade is regarded as a local disorder in this periodically coupled blade system. Hamilton’s principle and Galerkin’s method were used to formulate the equations of motion for the cracked blade-disk. The instability regions of this cracked blade-disk system were specified by employing the multiple scales perturbation method. Numerical results indicate that the rotation speed, shroud stiffness and crack depth in the blades affect the stability regions of this mistuned system significantly.

Nonlinear Vibration of Buckled Beams

1972 ◽  
Vol 94 (2) ◽  
pp. 637-645 ◽  
Author(s):  
Gwo-Bao Min ◽  
J. G. Eisley
Keyword(s):  
Equations Of Motion ◽  
Single Mode ◽  
Analog Computer ◽  
State Response ◽  
Buckled Beams ◽  
Mode Solution ◽  
Instability Regions ◽  
The Stability ◽  
Parametric Response ◽  
Assumed Mode

The steady state response and stability of free and forced vibration of simply supported, axially restrained, buckled beams is investigated. The equations of motion dealing with the buckled state include the effect of an initial displacement either by initial load or by initial temperature. By an assumed mode solution, the response and stability of two types of vibration are determined—snap-through (symmetrical) and one-sided (unsymmetric) vibration. The theoretical results of the response and stability are verified by analog computer simulation. It is concluded that the stability of the unsymmetric vibration is not a problem and that the different orders of parametric response of the rest modes (the modes originally not excited) in symmetric vibration correspond to the instability regions determined for the approximate single mode response.

ASSESSMENT OF PINE CROPS GROWTH IN BAIMAK FORESTRY

2020 ◽  
Vol 37 (3) ◽  
pp. 83-90
Author(s):  
T.Z. Mutallapov ◽  
Keyword(s):  
Scots Pine ◽  
Forest Ecosystem ◽  
Distribution Curve ◽  
Comparative Assessment ◽  
Tree Distribution ◽  
Entire Structure ◽  
Structure Changes ◽  
Large Trees ◽  
Different Types ◽  
The Stability

The article presents the results of evaluating the growth of Scots pine in the Baymak forest area. The analysis of forestry and taxation indicators of Scots pine crops on the studied sample areas is carried out, and a comparative assessment of the growth of forest crops growing in different types of forest is given. Increased competition in plantings leads to the natural decline of stunted trees, which is the result of differentiation in the stand. As a result, its structure changes, the number of large trees increases, and, accordingly, the stability of the forest ecosystem increases. In this regard, the appearance of the tree distribution curve by thickness levels also changes. It becomes more "flat", and its competitive load is more evenly distributed over the entire structure of the stand, and competition is weakened.

Investigation of the stability of periodic motions in a nonlinear automatic control system based on the fast fourier transform

2003 ◽  
Vol 3 ◽  
pp. 297-307
Author(s):  
V.V. Denisov
Keyword(s):  
Fourier Transform ◽  
Control System ◽  
Automatic Control ◽  
Fast Fourier Transform ◽  
Automatic Control System ◽  
Resonance Phenomenon ◽  
Periodic Motions ◽  
Multiply Connected ◽  
Non Linear ◽  
The Stability

An approach to the study of the stability of non-linear multiply connected systems of automatic control by means of a fast Fourier transform and the resonance phenomenon is considered.

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