Limit Cycle Stability Reversal via Singular Perturbation and Wing-Flap Flutter

2002 ◽  
Author(s):  
Daniele Dessi ◽  
Franco Mastroddi
Keyword(s):  
Singular Perturbation ◽  
Limit Cycles ◽  
Degrees Of Freedom ◽  
Perturbation Technique ◽  
Equations Of Motion ◽  
Control Surface ◽  
System Response ◽  
Singular Perturbation Technique ◽  
Nonlinear Springs ◽  
Time Marching

A three degrees of freedom aeroelastic typical section with control surface is theoretically modeled including nonlinear springs and augmented states for linear unsteady aerodynamic description. The system response is determined by time marching of the governing equations by using a standard Runge-Kutta algorithm in conjunction with a ‘shooting method’ to find out stable and unstable limit cycles along with stability reversal in the neighborhood of the Hopf bifurcation. Furthermore, the equations of motion are analyzed by a singular perturbation technique, specifically, by using a normal form method. Approximate analytical expressions for amplitudes and frequencies of limit cycles are obtained and the terms which are responsible of the nonlinear system behavior are identified.

scholarly journals Laminar condensation on a moving drop. Part 1. Singular perturbation technique

1984 ◽  
Vol 139 ◽  
pp. 105-130 ◽  
Author(s):  
J. N. Chung ◽  
P. S. Ayyaswamy ◽  
S. S. Sadhal
Keyword(s):  
Singular Perturbation ◽  
Perturbation Technique ◽  
Continuous Phase ◽  
Transport Processes ◽  
Forced Flow ◽  
Saturated Steam ◽  
Singular Perturbation Technique ◽  
Spherical Drop ◽  
Coupled Equations ◽  
Induced Velocity

In this paper, laminar condensation on a spherical drop in a forced flow is investigated. The drop experiences a strong, radial, condensation-induced velocity while undergoing slow translation. In view of the high condensation velocity, the flow field, although the drop experiences slow translation, is not in the Stokes-flow regime. The drop environment is assumed to consist of a mixture of saturated steam (condensable) and air (non-condensable). The study has been carried out in two different ways. In Part 1 the continuous phase is treated as quasi-steady and the governing equations for this phase are solved through a singular perturbation technique. The transient heat-up of the drop interior is solved by the series-truncation numerical method. The solution for the total problem is obtained by matching the results for the continuous and dispersed phases. In Part 2 both the phases are treated as fully transient and the entire set of coupled equations are solved by numerical means. Validity of the quasi-steady assumption of Part 1 is discussed. Effects due to the presence of the non-condensable component and of the drop surface temperature on transport processes are discussed in both parts. A significant contribution of the present study is the inclusion of the roles played by both the viscous and the inertial effects in the problem treatment.

On reflexion and trapping of upper-hybrid waves

1983 ◽  
Vol 29 (2) ◽  
pp. 195-215 ◽  
Author(s):  
Einar Mjølhus
Keyword(s):  
Magnetic Field ◽  
Singular Perturbation ◽  
Radio Wave ◽  
Perturbation Technique ◽  
Magnetized Plasma ◽  
Small Scale ◽  
Hybrid Wave ◽  
Singular Perturbation Technique ◽  
Hybrid Waves ◽  
Electron Density Irregularities

The theme of the paper is the relation between the so-called Z mode and the upper-hybrid wave in a magnetized plasma. First, certain problems as to reflexion and transmission of upper-hybrid waves at quasi cut-off (that is, cut-off predicted within electrostatic approximation) are stated and solved by singular perturbation technique. Then the theory is extended to a problem concerning generation and trapping of upper-hybrid waves in magnetic field aligned electron density irregularities. First a single density depression is considered, and then the formalism is further extended to a system of many parallel density depressions. The study was motivated by problems in the theory of artificial small-scale ionospheric irregularities occurring in radio wave experiments.

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