scholarly journals On fluttering modes for aircraft wing model in subsonic air flow

2014 ◽  
Vol 470 (2172) ◽  
pp. 20140582 ◽  
Author(s):  
Marianna A. Shubov
Keyword(s):  
Air Flow ◽  
Spectral Characteristics ◽  
Reduced Model ◽  
Mode Shapes ◽  
Model Parameters ◽  
Aircraft Wing ◽  
Generalized Resolvent ◽  
Wing Model ◽  
The Laplace Transform ◽  
Two Parameter

The paper deals with unstable aeroelastic modes for aircraft wing model in subsonic, incompressible, inviscid air flow. In recent author’s papers asymptotic, spectral and stability analysis of the model has been carried out. The model is governed by a system of two coupled integrodifferential equations and a two-parameter family of boundary conditions modelling action of self-straining actuators. The Laplace transform of the solution is given in terms of the ‘generalized resolvent operator’, which is a meromorphic operator-valued function of the spectral parameter λ, whose poles are called the aeroelastic modes. The residues at these poles are constructed from the corresponding mode shapes. The spectral characteristics of the model are asymptotically close to the ones of a simpler system, which is called the reduced model. For the reduced model, the following result is shown: for each value of subsonic speed, there exists a radius such that all aeroelastic modes located outside the circle of this radius centred at zero are stable. Unstable modes, whose number is always finite, can occur only inside this ‘circle of instability’. Explicit estimate of the ‘instability radius’ in terms of model parameters is given.

A Study on Vibration-Based Damage Detection and Location in an Aircraft Wing Scaled Model

2006 ◽  
Vol 3-4 ◽  
pp. 309-314 ◽  
Author(s):  
Irina Trendafilova
Keyword(s):  
Damage Detection ◽  
Natural Frequencies ◽  
Element Model ◽  
Vibration Response ◽  
Mode Shapes ◽  
Aircraft Wing ◽  
Scaled Model ◽  
Damage Location ◽  
Wing Model ◽  
Simplified Finite Element Model

This study investigates the possibilities for damage detection and location using the vibration response of an aircraft wing. A simplified finite element model of an aircraft wing is used to model its vibration response. The model is subjected to modal analysis- its natural frequencies are estimated and the mode shapes are determined. Two types of damage are considered - localised and distributed. The wing model is divided into a number of volumes. The goal of the study is to investigate the possibility to use the vibration response of an aircraft wing and especially its modal characteristics for the purposes of damage detection. So we’ll be trying to find suitable features, which can be used to detect damage and restrict it to one of the introduced volumes. The sensitivity of the modal frequencies of the model to damage in different locations is studied. Some general trends in the behaviour of these frequencies with change of the damage location are investigated. The utilization of the modal frequencies for detecting damage in a certain part of the wing is discussed

Riesz basis property of mode shapes for aircraft wing model (subsonic case)

2005 ◽  
Vol 462 (2066) ◽  
pp. 607-646 ◽  
Author(s):  
Marianna A Shubov
Keyword(s):  
Los Angeles ◽  
Laplace Transform ◽  
Riesz Basis ◽  
Basis Property ◽  
Research Center ◽  
Mode Shapes ◽  
Aircraft Wing ◽  
Riesz Basis Property ◽  
Wing Model ◽  
Systems Research

The present paper is devoted to the Riesz basis property of the mode shapes for an aircraft wing model in an inviscid subsonic airflow. The model has been developed in the Flight Systems Research Center of the University of California at Los Angeles in collaboration with NASA Dryden Flight Research Center. The model has been successfully tested in a series of flight experiments at Edwards Airforce Base, CA, and has been extensively studied numerically. The model is governed by a system of two coupled integro-differential equations and a two parameter family of boundary conditions modelling the action of the self-straining actuators. The system of equations of motion is equivalent to a single operator evolution–convolution equation in the energy space. The Laplace transform of the solution of this equation can be represented in terms of the so-called generalized resolvent operator, which is a finite—meromorphic operator—valued function of the spectral parameter. Its poles are precisely the aeroelastic modes. In the author's previous works, it has been shown that the set of aeroelastic modes asymptotically splits into two disjoint subsets called the β -branch and the δ -branch, and precise spectral asymptotics with respect to the eigenvalue number have been derived for both branches. The asymptotical approximations for the mode shapes have also been obtained. In the present work, the author proves that the set of the mode shapes forms an unconditional basis (the Riesz basis) in the Hilbert state space of the system. The results of this paper will be important for the reconstruction of the solution of the original initial boundary-value problem from its Laplace transform and for the analysis of the flutter phenomenon in the forthcoming work.

scholarly journals Numerical Investigation of Aeroelastic Mode Distribution for Aircraft Wing Model in Subsonic Air Flow

2010 ◽  
Vol 2010 ◽  
pp. 1-23 ◽  
Author(s):  
Marianna A. Shubov ◽  
Stephen Wineberg ◽  
Robert Holt
Keyword(s):  
Boundary Value Problem ◽  
Numerical Investigation ◽  
Air Flow ◽  
Affirmative Answer ◽  
Positive Answer ◽  
Aircraft Wing ◽  
Aircraft Wings ◽  
Flutter Speed ◽  
Wing Model ◽  
Analytical Formulas

In this paper, the numerical results on two problems originated in aircraft wing modeling have been presented.The first problemis concerned with the approximation to the set of the aeroelastic modes, which are the eigenvalues of a certain boundary-value problem. The affirmative answer is given to the following question: can the leading asymptotical terms in the analytical formulas be used as reasonably accurate description of the aeroelastic modes? The positive answer means that these leading terms can be used by engineers for practical calculations.The second problemis concerned with the flutter phenomena in aircraft wings in a subsonic, incompressible, inviscid air flow. It has been shown numerically that there exists a pair of the aeroelastic modes whose behavior depends on a speed of an air flow. Namely, when the speed increases, the distance between the modes tends to zero, and at some speed that can be treated as the flutter speed these two modes merge into one double mode.

scholarly journals Surface force spectroscopic point load measurements and viscoelastic modelling of the micromechanical properties of air flow sensitive hairs of a spider ( Cupiennius salei )

2008 ◽  
Vol 6 (37) ◽  
pp. 681-694 ◽  
Author(s):  
Michael E. McConney ◽  
Clemens F. Schaber ◽  
Michael D. Julian ◽  
William C. Eberhardt ◽  
Joseph A.C. Humphrey ◽  
...  
Keyword(s):  
Air Flow ◽  
Surface Force ◽  
Rate Of Change ◽  
Model Parameters ◽  
Solid Model ◽  
Power Functions ◽  
Cupiennius Salei ◽  
Micromechanical Properties ◽  
Angular Velocities ◽  
Two Parameter

The micromechanical properties of spider air flow hair sensilla (trichobothria) were characterized with nanometre resolution using surface force spectroscopy (SFS) under conditions of different constant deflection angular velocities (rad s −1 ) for hairs 900–950 μm long prior to shortening for measurement purposes. In the range of angular velocities examined (4×10 −4 −2.6×10 −1 rad s −1 ), the torque T (Nm) resisting hair motion and its time rate of change (Nm s −1 ) were found to vary with deflection velocity according to power functions. In this range of angular velocities, the motion of the hair is most accurately captured by a three-parameter solid model, which numerically describes the properties of the hair suspension. A fit of the three-parameter model (3p) to the experimental data yielded the two torsional restoring parameters, S 3p =2.91×10 −11  Nm rad −1 and =2.77×10 −11 Nm rad −1 and the damping parameter R 3p =1.46×10 −12 Nm s rad −1 . For angular velocities larger than 0.05 rad s −1 , which are common under natural conditions, a more accurate angular momentum equation was found to be given by a two-parameter Kelvin solid model. For this case, the multiple regression fit yielded S 2p =4.89×10 −11  Nm rad −1 and R 2p =2.83×10 −14  Nm s rad −1 for the model parameters. While the two-parameter model has been used extensively in earlier work primarily at high hair angular velocities, to correctly capture the motion of the hair at both low and high angular velocities it is necessary to employ the three-parameter model. It is suggested that the viscoelastic mechanical properties of the hair suspension work to promote the phasic response behaviour of the sensilla.

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