Extreme Instability Phenomena in Autonomous Weakly Damped Systems: Hopf Bifurcations, Double Pure Imaginary Eigenvalues, Load Discontinuity

2011 ◽  
pp. 91-130
Author(s):  
Anthony N. Kounadis
Keyword(s):  
Hopf Bifurcations ◽  
Damped Systems ◽  
Pure Imaginary Eigenvalues

scholarly journals Stabilizing and destabilizing perturbations of PT -symmetric indefinitely damped systems

2013 ◽  
Vol 371 (1989) ◽  
pp. 20120051 ◽  
Author(s):  
O. N. Kirillov
Keyword(s):  
Tangent Cone ◽  
Symmetric Matrix ◽  
Stability Boundary ◽  
Stability Domain ◽  
Exceptional Point ◽  
Damped System ◽  
Whitney Umbrella ◽  
The Stability ◽  
Damped Systems ◽  
Pure Imaginary Eigenvalues

Eigenvalues of a potential dynamical system with damping forces that are described by an indefinite real symmetric matrix can behave as those of a Hamiltonian system when gain and loss are in a perfect balance. This happens when the indefinitely damped system obeys parity–time ( ) symmetry. How do pure imaginary eigenvalues of a stable -symmetric indefinitely damped system behave when variation in the damping and potential forces destroys the symmetry? We establish that it is essentially the tangent cone to the stability domain at the exceptional point corresponding to the Whitney umbrella singularity on the stability boundary that manages transfer of instability between modes.

Nonbaseband residual flexibility method of component mode synthesis for proportionally damped systems

AIAA Journal ◽  
1999 ◽  
Vol 37 ◽  
pp. 1285-1291
Author(s):  
Jeffrey A. Morgan ◽  
Christophe Pierre ◽  
Gregory M. Hulbert
Keyword(s):  
Component Mode Synthesis ◽  
Damped Systems

A MODIFIED GENERALIZED LORENZ-TYPE SYSTEM AND ITS CANONICAL FORM

2009 ◽  
Vol 19 (06) ◽  
pp. 1931-1949 ◽  
Author(s):  
QIGUI YANG ◽  
KANGMING ZHANG ◽  
GUANRONG CHEN
Keyword(s):  
Special Form ◽  
Topological Structure ◽  
Complex Dynamics ◽  
Type System ◽  
Chaotic Attractors ◽  
Hopf Bifurcations ◽  
Compound Structure ◽  
Two Parameters ◽  
First Time ◽  
New System

In this paper, a modified generalized Lorenz-type system is introduced, which is state-equivalent to a simple and special form, and is parameterized by two parameters useful for chaos turning and system classification. More importantly, based on the parameterized form, two classes of new chaotic attractors are found for the first time in the literature, which are similar but nonequivalent in topological structure. To further understand the complex dynamics of the new system, some basic properties such as Lyapunov exponents, Hopf bifurcations and compound structure of the attractors are analyzed and demonstrated with careful numerical simulations.

A System Identification Method for Excitation-Frequency Dependent Rotordynamic Coefficients

2012 ◽  
Author(s):  
Timothy W. Dimond ◽  
Amir A. Younan ◽  
Paul Allaire
Keyword(s):  
System Identification ◽  
Measurement Uncertainty ◽  
Excitation Frequency ◽  
Frequency Dependent ◽  
Rotordynamic Coefficients ◽  
Adjoint Systems ◽  
Dynamic Coefficients ◽  
Backward Whirl ◽  
Identification Technique ◽  
Damped Systems

Experimental identification of rotordynamic systems presents unique challenges. Gyroscopics, generally damped systems, and non-self-adjoint systems due to fluid structure interaction forces mean that symmetry cannot be used to reduce the number of parameters to be identified. Rotordynamic system experimental measurements are often noisy, which complicates comparisons with theory. When linearized, the resulting dynamic coefficients are also often a function of excitation frequency, as distinct from operating speed. In this paper, a frequency domain system identification technique is presented that addresses these issues for rigid-rotor test rigs. The method employs power spectral density functions and forward and backward whirl orbits to obtain the excitation frequency dependent effective stiffness and damping. The method is highly suited for use with experiments that employ active magnetic exciters that can perturb the rotor in the forward and backward whirl directions. Simulation examples are provided for excitation-frequency reduced tilting pad bearing dynamic coefficients. In the simulations, 20 and 50 percent Gaussian output noise was considered. Based on ensemble averages of the coefficient estimates, the 95 percent confidence intervals due to noise effects were within 1.2% of the identified value. The method is suitable for identification of linear dynamic coefficients for rotordynamic system components referenced to shaft motion. The method can be used to reduce the effect of noise on measurement uncertainty. The statistical framework can also be used to make decisions about experimental run times and acceptable levels of measurement uncertainty. The data obtained from such an experimental design can be used to verify component models and give rotordynamicists greater confidence in the design of turbomachinery.

A fifth-order multiple-scale solution for Hopf bifurcations

2004 ◽  
Vol 82 (31-32) ◽  
pp. 2723-2731 ◽  
Author(s):  
D. Dessi ◽  
F. Mastroddi ◽  
L. Morino
Keyword(s):  
Multiple Scale ◽  
Hopf Bifurcations ◽  
Fifth Order
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