Veering Phenomena in Systems With Gyroscopic Coupling

2004 ◽  
Vol 72 (5) ◽  
pp. 641-647 ◽  
Author(s):  
Stefano Vidoli ◽  
Fabrizio Vestroni
Keyword(s):  
System Parameter ◽  
Critical Value ◽  
Forced Response ◽  
Perturbation Approach ◽  
Continuous Systems ◽  
System A ◽  
Electromechanical Interaction ◽  
Gyroscopic Coupling ◽  
Internal Coupling

The sharp divergence of two root-loci for a critical value of the parameters is called veering. Veering phenomena are interesting since they involve relevant energetic exchanges between the eigenmodes and strongly affect the undamped forced response of the system. A straightforward perturbation approach has already been used in the literature to analyze the dependence of the eigensprectrum on a system parameter and formulate a veering criterion. This perturbation approach and other ideas are generalized to the study of veering in discrete and continuous systems with gyroscopic operators of internal coupling and the results applied to a real electromechanical interaction.

The Combined Closed Form-Perturbation Approach to the Analysis of Mistuned Bladed Disks

1993 ◽  
Vol 115 (4) ◽  
pp. 771-780 ◽  
Author(s):  
M. P. Mignolet ◽  
C.-C. Lin
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Approximate Solutions ◽  
Forced Response ◽  
Perturbation Approach ◽  
Perturbation Techniques ◽  
Step Method ◽  
Bladed Disk

A two-step method is presented for the determination of reliable approximations of the probability density function of the forced response of a randomly mistuned bladed disk. Under the assumption of linearity, an integral representation of the probability density function of the blade amplitude is first derived. Then, deterministic perturbation techniques are employed to produce simple approximations of this function. The adequacy of the method is demonstrated by comparing several approximate solutions with simulation results.

The Asymptotic Stability of Weakly Perturbed Two Dimensional Hamiltonian Systems

2001 ◽  
Author(s):  
Ludwig Arnold ◽  
Peter Imkeller ◽  
N. Sri Namachchivaya
Keyword(s):  
Lyapunov Exponent ◽  
Equations Of Motion ◽  
Perturbation Approach ◽  
Two Dimensional ◽  
White Noise Process ◽  
System A ◽  
Additive White Noise ◽  
Small Dissipation ◽  
Small Intensity ◽  
Single Well

Abstract The purpose of this work is to obtain an approximation for the top Lyapunov exponent, the exponential growth rate, of the response of a single-well Kramers Oscillator driven by either a multiplicative or an additive white noise process. To this end, we consider the equations of motion as dissipative and noisy perturbations of a two-dimensional Hamiltonian system. A perturbation approach is used to obtain explicit expressions for the exponent in the presence of small intensity noise and small dissipation. We show analytically that the top Lyapunov exponent is positive, and for small values of noise intensity ε and dissipation ε the exponent grows proportional to ε1/3.

Range of Variability in the Dynamics of Semi-Cylindrical Friction Dampers for Turbine Blades

2008 ◽  
Author(s):  
Stefano Zucca ◽  
Daniele Botto ◽  
Muzio M. Gola
Keyword(s):  
Degrees Of Freedom ◽  
Turbine Blades ◽  
Numerical Test ◽  
Forced Response ◽  
Numerical Code ◽  
Test Case ◽  
Force Coefficient ◽  
System A ◽  
Flat Side ◽  
Fatigue Failures

Under-platform dampers are used to reduce resonant stresses in turbine blades to avoid high cycle fatigue failures. In this paper a model of semi-cylindrical under-platform damper (i.e. with one flat side and one curved side) for turbine blades is described. The damper kinematics is characterized by three degrees of freedom (DOFs): in-plane translations and rotation. Static normal loads acting on the damper sides are computed using the three static balance equations of the damper. Non-uniqueness of normal pre-loads acting on the damper sides is highlighted. Implementation of the model in a numerical code for the forced response calculation of turbine blades with under-platform dampers shows that non-uniqueness of normal pre-loads leads to non-uniqueness of the forced response of the system. A numerical test case is presented to show the capabilities of the model and to analyze the effect of the main system parameters (damper mass, excitation force, coefficient of friction and damper rotation) on the damper behavior and on the system dynamics.

The Effects of Fines on Post Liquefaction Strength and Deformation Characteristics of Sand

2012 ◽  
Vol 594-597 ◽  
pp. 23-27 ◽  
Author(s):  
Yan Li Wang ◽  
Yong Wang
Keyword(s):  
Axial Strain ◽  
Strain Curve ◽  
Critical Value ◽  
Deformation Characteristics ◽  
Compression Tests ◽  
Recovery Stage ◽  
Fines Content ◽  
System A ◽  
Strength Recovery ◽  
Strength And Deformation

This study has been carried out to determine how the fines content affects the post liquefaction strength and deformation characteristics of sand. With the GDS dynamic triaxial system, a series of monotonic undrained compression tests of the sand after liquefaction with variation in fines content from 0 to 40% were conducted, and effects of fines content on the post liquefaction strength and deformation characteristics of sand were analyzed. Results show that with the addition of fines up to a fines content of 30%, the stress-strain curve moves downward and axial strain at low intensive stage is increased, beyond this critical value of fines content the trend is reversed. However, shear strength of post-liquefied sand first decreases with increasing fines content, and beyond the critical value of fines content it increases with increasing fines content at the strength recovery stage when are subjected to monotonic loading. At the same time, the strength recovery rate decreases firstly and then increases with the increasing fines content.

scholarly journals EXPLORING THE KIBBLE–ZUREK MECHANISM IN A SECONDARY BIFURCATION

2012 ◽  
Vol 22 (07) ◽  
pp. 1250165 ◽  
Author(s):  
M. A. MIRANDA ◽  
J. BURGUETE ◽  
W. GONZÁLEZ-VIÑAS ◽  
H. MANCINI
Keyword(s):  
Correlation Length ◽  
Domain Walls ◽  
Critical Value ◽  
Convective System ◽  
Strong Decay ◽  
Response Dynamics ◽  
Dynamical Phase Transition ◽  
Dynamical Phase ◽  
System A ◽  
Secondary Bifurcation

We present new experimental results on the quenching dynamics of an extended thermo-convective system (a network array of approximately 100 convective oscillators) going through a secondary subcritical bifurcation. We characterize a dynamical phase transition through the nature of the domain walls (1D-fronts) that connect the basic multicellular pattern with the new oscillating one. Two different mechanisms of the relaxing dynamics at the threshold are characterized depending on the crossing rate [Formula: see text] of the quenched transition. From the analysis of fronts, we show that these mechanisms follow different correlation length scales ξ ~ μ-σ. Below a critical value μc, a slow response dynamics yields a spatiotemporal coherent front with weak coupling between oscillators. Above μc, for rapid quenches, defects are trapped at the front with a strong coupling between oscillators, similarly to the Kibble–Zurek mechanism in quenched phase transitions. These defects, pinned to the fronts, yield a strong decay of the correlation length.

scholarly journals LOCALIZATION IN A STRONGLY DISORDERED SYSTEM: A PERTURBATION APPROACH

2013 ◽  
Vol 27 (13) ◽  
pp. 1350051
Author(s):  
MARCO FRASCA
Keyword(s):  
Scaling Law ◽  
Localization Length ◽  
Perturbation Approach ◽  
Dimensional System ◽  
Two Dimensional ◽  
Disordered System ◽  
System A ◽  
Large Perturbation ◽  
Two Dimensional System ◽  
Diagonal Disorder

We prove that a strongly disordered two-dimensional system localizes with a localization length given analytically. We get a scaling law with a critical exponent ν = 1 in agreement with the Chayes criterion ν ≥ 1. The case we are considering is for off-diagonal disorder. The method we use is a perturbation approach holding in the limit of an infinitely large perturbation as recently devised and the Anderson model is considered with a Gaussian distribution of disorder. The localization length diverges when energy goes to zero with a scaling law in agreement to numerical and theoretical expectations.

Maximum Bladed Disk Forced Response From Distortion of a Structural Mode

2002 ◽  
Author(s):  
J. A. Kenyon ◽  
J. H. Griffin ◽  
D. M. Feiner
Keyword(s):  
Forced Response ◽  
Maximum Response ◽  
Strong Response ◽  
Bladed Disk ◽  
System A ◽  
Random Mistuning ◽  
Harmonic Components ◽  
Structural Mode

A method is presented for obtaining maximum bladed disk forced response from distortion of a structural mode. It is shown that maximum response from mode distortion in a bladed disk occurs when the harmonic components of a distorted mode superimpose in a certain manner, causing localization of the mode and strong response in a particular blade. In addition, it is shown that the response of an intentionally mistuned system with maximum response does not change significantly when small random mistuning is added to the system. A method is described for calculating the structural mistuning necessary to obtain the distorted mode that gives maximum response. The theory is validated numerically.

scholarly journals Regularization of the Boundary-Saddle-Node Bifurcation

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Xia Liu
Keyword(s):  
Vector Field ◽  
Center Manifold ◽  
Continuous System ◽  
Critical Value ◽  
Continuous Systems ◽  
Local Behavior ◽  
Saddle Node Bifurcation ◽  
Node Point ◽  
Perturbation Problem ◽  
Saddle Node

In this paper we treat a particular class of planar Filippov systems which consist of two smooth systems that are separated by a discontinuity boundary. In such systems one vector field undergoes a saddle-node bifurcation while the other vector field is transversal to the boundary. The boundary-saddle-node (BSN) bifurcation occurs at a critical value when the saddle-node point is located on the discontinuity boundary. We derive a local topological normal form for the BSN bifurcation and study its local dynamics by applying the classical Filippov’s convex method and a novel regularization approach. In fact, by the regularization approach a given Filippov system is approximated by a piecewise-smooth continuous system. Moreover, the regularization process produces a singular perturbation problem where the original discontinuous set becomes a center manifold. Thus, the regularization enables us to make use of the established theories for continuous systems and slow-fast systems to study the local behavior around the BSN bifurcation.

Aeroelastic Flutter of Continuous Systems: A Generalized Laplace Transform Method

2016 ◽  
Vol 83 (8) ◽  
Author(s):  
Arion Pons ◽  
Stefanie Gutschmidt
Keyword(s):  
Laplace Transform ◽  
Continuous Systems ◽  
Laplace Transform Method ◽  
Aeroelastic System ◽  
Transform Method ◽  
Wing Model ◽  
System A ◽  
Aeroelastic Flutter ◽  
The Laplace Transform ◽  
Eigenvalue Parameter

This paper presents a generalization of the Laplace transform method (LTM) for determining the flutter points of a linear ordinary-differential aeroelastic system—a linear system involving a spatial derivative as well as a time-eigenvalue parameter. Current implementations of the LTM have two major problems: they are unable to solve systems of arbitrary size, order, and boundary conditions, and they require certain key operations to be performed by hand or with symbolic manipulation libraries. Our generalized method overcomes both these problems. We also devise a new method for solving and visualizing the algebraic system that arises from the LTM procedure. We validate our generalized LTM and novel solution method against both the Goland wing model and a large system of high differential order, as a demonstration of their effectiveness for solving such systems.

scholarly journals Vibrational Response Analysis of Mistuned Bladed Disk System of Grouped Blades

1998 ◽  
Author(s):  
Y. Kaneko ◽  
K. Mori ◽  
H. Ohyama ◽  
E. Watanabe
Keyword(s):  
Synthesis Method ◽  
Forced Response ◽  
Response Analysis ◽  
Analysis Method ◽  
Disk System ◽  
Vibrational Response ◽  
Bladed Disk ◽  
System A ◽  
Vibrational Characteristics ◽  
Grouped Blades

For the purpose of the efficient analysis of a mistuned bladed disk system, a new analysis method which applies the substructure synthesis method and the modal analysis method is proposed. Using the proposed method, the vibrational characteristics of the grouped blades structure are studied. From the results, it is found that the grouped blades structure is very sensitive to the mistuning. It is also found that the mixed grouped blades structure (a bladed disk system consisting of some different types of grouped blades relating to the number of blades contained) has an undesirable effect on the forced response. Moreover, by comparing the vibrational characteristics of the integral shroud blades (ISB) structure with those of the grouped blades structure, it is clarified that the reliability of the ISB structure is superior to other structures also from the viewpoint of the mistuning.

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