Analytical and Experimental Flutter Analysis of a Typical Wing Section Carrying a Flexibly Mounted Unbalanced Engine

2019 ◽  
Vol 19 (02) ◽  
pp. 1950013 ◽  
Author(s):  
A. S. Mirabbashi ◽  
A. Mazidi ◽  
M. M. Jalili
Keyword(s):  
Stability Domain ◽  
Governing Equations ◽  
Lagrange Equations ◽  
Wing Section ◽  
Unbalanced Force ◽  
Engine Thrust ◽  
Finite State Model ◽  
Flutter Analysis ◽  
Finite State ◽  
The Stability

In this paper, both experimental and analytical flutter analyses are conducted for a typical 5-degree of freedon (5DOF) wing section carrying a flexibly mounted unbalanced engine. The wing flexibility is simulated by two torsional and longitudinal springs at the wing elastic axis. One flap is attached to the wing section by a torsion spring. Also, the engine is connected to the wing by two elastic joints. Each joint is simulated by a spring and damper unit to bring the model close to reality. Both the torsional and longitudinal motions of the engine are considered in the aeroelastic governing equations derived from the Lagrange equations. Also, Peter’s finite state model is used to simulate the aerodynamic loads on the wing. Effects of various engine parameters such as position, connection stiffness, mass, thrust and unbalanced force on the flutter of the wing are investigated. The results show that the aeroelastic stability region is limited by increasing the engine mass, pylon length, engine thrust and unbalanced force. Furthermore, increasing the damping and stiffness coefficients of the engine connection enlarges the stability domain.

Stability Analysis of an Aeroelastic System with Actuator Saturation

2012 ◽  
Vol 463-464 ◽  
pp. 1527-1532
Author(s):  
Adrian Mihail Stoica ◽  
Marius Stoia-Djeska ◽  
Gabriela Stroe
Keyword(s):  
Actuator Saturation ◽  
Equations Of Motion ◽  
Stability Domain ◽  
Lagrange Equations ◽  
Aeroelastic System ◽  
Aerospace Vehicles ◽  
Control Laws ◽  
The Stability ◽  
The Mathematical Model ◽  
Weight Structures

Aeroelastic problems of light weight structures of modern aerospace vehicles are the result of interactions between aerodynamics, structural and inertial forces. The mathematical model of the aeroelastic problem is based on the Lagrange equations of motion for the structural dynamics and on a quasi-steady approach of the generalized unsteady incompressible aerodynamic forces. The oscillations of such aeroelastic system can be suppressed using linear active control techniques. In the case when the control is saturated the stability domain shrinks. The describing function method is used in this paper to determine the periodic solutions of an experimental aeroelastic system for two control laws.

Flutter suppression of an aircraft wing with a flexibly mounted mass using magneto-rheological damper

2019 ◽  
Vol 234 (3) ◽  
pp. 827-839
Author(s):  
Amir Hossein Ghasemikaram ◽  
Abbas Mazidi ◽  
Mohammad Reza Fazel ◽  
Seyed Ahmad Fazelzadeh
Keyword(s):  
Differential Equations ◽  
State Feedback ◽  
Structural Model ◽  
Aerodynamic Force ◽  
Governing Equations ◽  
Aircraft Wing ◽  
Flutter Suppression ◽  
Flutter Analysis ◽  
Finite State ◽  
Magneto Rheological

Flutter analysis and suppression of an aircraft wing with a flexibly mounted external store using a magneto-rheological damper are investigated. The wing performs as a cantilever beam and the structural model, which incorporates bending-torsion flexibility, is used. A modified Bouc–Wen model is utilized in order to model the elastic connection between the store and the wing. The modified Peter’s finite-state loading is also considered to simulate the aerodynamic force and moment. The governing equations are obtained via Hamilton’s principle and assumed modes method is subsequently applied to transform the resulting partial differential equations into a set of ordinary differential equations. Numerical simulations are validated against several previously published papers by using a clean Goland wing. In order to control the vertical and rotational vibrations of the store and the wing, a state feedback controller and a compensator with full-order observer are designed. The performance of these controllers is compared together in several situations. Eventually, the performances are treated when disturbance is applied to the system. The results show that magneto-rheological damper’s performance is suitable for controlling the limit cycle oscillations of the wing and external store, in flutter condition.

scholarly journals STABILITY ANALYSIS AND SIMULATION OF N-CLASS RETRIAL SYSTEM WITH CONSTANT RETRIAL RATES AND POISSON INPUTS

2014 ◽  
Vol 31 (02) ◽  
pp. 1440002 ◽  
Author(s):  
K. AVRACHENKOV ◽  
E. MOROZOV ◽  
R. NEKRASOVA ◽  
B. STEYAERT
Keyword(s):  
Queueing System ◽  
Stability Domain ◽  
Single Server ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
Single Orbit ◽  
Transmission Control Protocols ◽  
Regenerative Approach ◽  
The Stability ◽  
Multi Access

In this paper, we study a new retrial queueing system with N classes of customers, where a class-i blocked customer joins orbit i. Orbit i works like a single-server queueing system with (exponential) constant retrial time (with rate [Formula: see text]) regardless of the orbit size. Such a system is motivated by multiple telecommunication applications, for instance wireless multi-access systems, and transmission control protocols. First, we present a review of some corresponding recent results related to a single-orbit retrial system. Then, using a regenerative approach, we deduce a set of necessary stability conditions for such a system. We will show that these conditions have a very clear probabilistic interpretation. We also performed a number of simulations to show that the obtained conditions delimit the stability domain with a remarkable accuracy, being in fact the (necessary and sufficient) stability criteria, at the very least for the 2-orbit M/M/1/1-type and M/Pareto/1/1-type retrial systems that we focus on.

One-dimensional models of fourth and sixth orders for rods derived from three-dimensional elasticity

2016 ◽  
Vol 22 (2) ◽  
pp. 158-175 ◽  
Author(s):  
Erick Pruchnicki
Keyword(s):  
Order Term ◽  
Three Dimensional ◽  
Transverse Dimension ◽  
Lagrange Equations ◽  
Transverse Shearing ◽  
Natural Boundary Conditions ◽  
The Stability ◽  
Shearing Energy ◽  
Three Dimensional Elasticity ◽  
Double Symmetry

The displacement field in rods can be approximated by using a Taylor–Young expansion in transverse dimension of the rod. These involve that the highest-order term of shear is of second order in the transverse dimension of the rod. Then we show that transverse shearing energy is removed by the fourth-order truncation of the potential energy and so we revisit the model presented by Pruchnicki. Then we consider the sixth-order truncation of the potential which includes transverse shearing and transverse normal stress energies. For these two models we show that the potential energies satisfy the stability condition of Legendre–Hadamard which is necessary for the existence of a minimizer and then we give the Euler–Lagrange equations and the natural boundary conditions associated with these potential energies. For the sake of simplicity we consider that the cross-section of the rod has double symmetry axes.

A Finite State Model for the Control of Adrenal Cortical Steroid Secretion

1968 ◽  
pp. 185-200 ◽  
Author(s):  
Donald S. Gann ◽  
Lee E. Ostrander ◽  
James D. Schoeffler
Keyword(s):  
State Model ◽  
Steroid Secretion ◽  
Finite State Model ◽  
Finite State

scholarly journals The development of biofilm architecture

2016 ◽  
Vol 472 (2188) ◽  
pp. 20150798 ◽  
Author(s):  
A. C. Fowler ◽  
T. M. Kyrke-Smith ◽  
H. F. Winstanley
Keyword(s):  
Bacterial Biofilm ◽  
Governing Equations ◽  
Biofilm Growth ◽  
One Dimensional ◽  
Direct Numerical Solution ◽  
The Common ◽  
Common Observation ◽  
The Stability ◽  
The One ◽  
A Free Boundary Problem

We extend the one-dimensional polymer solution theory of bacterial biofilm growth described by Winstanley et al . (2011 Proc. R. Soc. A 467 , 1449–1467 ( doi:10.1098/rspa.2010.0327 )) to deal with the problem of the growth of a patch of biofilm in more than one lateral dimension. The extension is non-trivial, as it requires consideration of the rheology of the polymer phase. We use a novel asymptotic technique to reduce the model to a free-boundary problem governed by the equations of Stokes flow with non-standard boundary conditions. We then consider the stability of laterally uniform biofilm growth, and show that the model predicts spatial instability; this is confirmed by a direct numerical solution of the governing equations. The instability results in cusp formation at the biofilm surface and provides an explanation for the common observation of patterned biofilm architectures.

Domains and Types of Aeroelastic Instability of Slender Beam

2007 ◽  
Author(s):  
Jirˇi´ Na´prstek
Keyword(s):  
Stability Boundary ◽  
Stability Loss ◽  
Stability Domain ◽  
Theoretical Explanation ◽  
Point Of View ◽  
System Response ◽  
Physical Point ◽  
Model Response ◽  
Gyroscopic Forces ◽  
The Stability

Slender structures exposed to a cross air flow are prone to vibrations of several types resulting from aeroelastic interaction of a flowing medium and a moving structure. Aeroelastic forces are the origin of nonconservative and gyroscopic forces influencing the stability of a system response. Conditions of a dynamic stability loss and a detailed analysis of a stability domain has been done using a linear mathematical model. Response properties of a system located on a stability boundary together with tendencies in its neighborhood are presented and interpreted from physical point of view. Results can be used for an explanation of several effects observed experimentally but remaining without theoretical explanation until now.

Conceptual Flutter Analysis of Stepped Labyrinth Seals

2019 ◽  
Author(s):  
Roque Corral ◽  
Almudena Vega ◽  
Michele Greco
Keyword(s):  
Natural Frequency ◽  
Fundamental Mode ◽  
Second Step ◽  
Pressure Side ◽  
Dimensional Model ◽  
Labyrinth Seals ◽  
Acoustic Frequency ◽  
Flutter Analysis ◽  
Dimensional Parameters ◽  
The Stability

Abstract A simple non-dimensional model to describe the flutter onset of two-fin straight labyrinth seals [1] is extended to stepped seals. The effect of the axial displacement of the seal is analyzed first in isolation. It is shown that this fundamental mode is always stable. In a second step, the combination of axial and torsion displacements is used to determine the damping of modes with arbitrary torsion centers. It is concluded that the classical Abbot’s criterion stating that seals supported in the low-pressure side of the seal are stable provided that natural frequency of the mode is greater than the acoustic frequency breaks down under certain conditions. An analytical expression for the non-dimensional work-per-cycle is derived and new non-dimensional parameters controlling the seal stability identified. It is finally concluded the stability of stepped seals can be assimilated to that of a straight through seal if the appropriate distance of the torsion center to the seal is chosen.

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