Numerical investigation of aeroelastic mode distribution for aircraft wing model in subsonic air flow

In this paper, the numerical results on two problems originated in aircraft wing modeling have been presented. The first problem is 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 problem is 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

Boundary feedback stabilization of a flexible wing model under unsteady aerodynamic loads

This paper addresses the boundary stabilization of a flexible wing model, both in bending and twisting displacements, under unsteady aerodynamic loads, and in presence of a store. The wing dynamics is captured by a distributed parameter system as a coupled Euler-Bernoulli and Timoshenko beam model. The problem is tackled in the framework of semigroup theory, and a Lyapunov-based stability analysis is carried out to assess that the system energy, as well as the bending and twisting displacements, decay exponentially to zero. The effectiveness of the proposed boundary control scheme is evaluated based on simulations.Comment: Published in Automatica as a brief pape

Reduction of boundary value problem to Possio integral equation in theoretical aeroelasticity

The present paper is the first in a series of works devoted to the solvability of the Possio singular integral equation. This equation relates the pressure distribution over a typical section of a slender wing in subsonic compressible air flow to the normal velocity of the points of a wing (downwash). In spite of the importance of the Possio equation, the question of the existence of its solution has not been settled yet. We provide a rigorous reduction of the initial boundary value problem involving a partial differential equation for the velocity potential and highly nonstandard boundary conditions to a singular integral equation, the Possio equation. The question of its solvability will be addressed in our forthcoming work. Copyright (C) 2008 A. V. Balakrishnan and M. A. Shubov

Micro - and macro - mechanical properties of aerospace composite structures and their dynamic behaviour

The research presented in this thesis focuses on the micro- and macro-mechanical properties of aerospace composite structures, and their buckling, free vibration, and flutter behaviour. The first part of the thesis concentrates on fundamental experimental research into prediction and enrichment of polymers composites with nanoparticles with particular emphasis on polyurethane and polyaniline. To this end, a conducting thermoplastic elastomer is developed and characterised using physiochemical methods for thermo-mechanical properties. Consequently, a sophisticated new polyurethane nanocomposite elastomer with improved mechanical and thermal properties is developed. The second part of the thesis is a development of an accurate dynamic stiffness matrix for a three-layered sandwich beam of asymmetric cross-section using the Timoshenko beam theory, Hamiltonian mechanics and symbolic computation. The resulting dynamic stiffness matrix is used to investigate the free vibration characteristics of a number of sandwich beams examples and their results are validated by experiment. Next, a detailed analysis is carried out to establish the rigidity properties (stiffnesses) of fibre reinforced composite structures with particular emphasis on solid rectangular and thin-walled box section. The effect of ply orientation on rigidity properties and the consequent coupling between various modes of deformation is studied. Buckling analysis is carried out to provide an estimate of the stiffnesses. Free vibration investigations on flat and box carbon fibre-reinforced composite beams are then carried out to gain important insights into the material- geometrical coupling effects, and modal interchange in bending-torsion coupled behaviour. Although the dynamic stiffness method is primarily used in the analyses, some complementary finite element analysis and experimental modal analysis using an Impulse Hammer Kit were performed to confirm the predictable accuracy of the dynamic stiffness method. A few carefully designed composite beams were fabricated for the experimental work. Flutter behaviour of swept and unswept wing is also investigated. The results are discussed with significant conclusions drawn. A scope for further work is outlined

C0-Semigroup Methods for Delay Equations

In der Dissertation werden Werkzeuge zur Analyse von Wohlgestelltheit und Asymptotik von Integro-Differential- und Verzögerungsgleichungen entwickelt. Im ersten Teil der Arbeit (Kapitel 1 und 2) werden Methoden zur Bestimmung der Modulhalbgruppe (kleinste dominierende C0-Halbgruppe) einer C0-Halbgruppe zur Verfügung gestellt, die unter anderem auf Volterra-Halbgruppen (die aus Integro-Differentialgleichungen hervorgehen) und Evolutionshalbgruppen (Rückkopplungsgleichungen mit Zeitverzögerung, Transport in Netzwerken) angewendet werden. Im Mittelpunkt des zweiten Teils (Kapitel 3 und 4) steht ein Integro-Differentialgleichungstyp, der Schwingungsphänomene von Tragswerksflächen im Unterschallbereich beschreibt. Das besondere dieser Gleichung ist das Auftreten der Zeitableitung der gesuchten Funktion im Integralterm. Es werden eine Reihe von Wohlgestelltheitskriterien hergeleitet, welche Wohlgestelltheit der Gleichung liefern, ohne das es möglich ist, durch partielle Integration die Zeitableitung im Integralterm zu beseitigen und dadurch die Gleichung auf einen bekannten Integro-Differentialgleichungstyp zurückzuführen. Die entwickelten Methoden eignen sich auch für die Herleitung neuer Wohlgestelltheitskriterien für andere Verzögerungsgleichungen. Entsprechende Resultate werden in Kapitel 4 hergeleitet.In the dissertation tools for the analysis of well-posedness and asymptotic behaviour of integro-differential equations and delay equations are developed. In the first part (chapter 1 and 2) methods for the determination of the modulus semigroup (smallest dominating C0-semigroup) of a C0-semigroup are provided and applied to various examples such as Volterra semigroups and evolution semigroups and transport evolution equations in networks. The main interest of the second part (chapter 3 and 4) is a type of an integro-differential equation which occurs in the modelling of the flutter of airfoils at subsonic speed. The remarkable property of the equation is the time derivative of the sought function in the integral term. A number of well-posedness criteria are proved for which integration by parts is not possible. The developed methods are also suitable for the derivation of new well-posedness results for other delay semigroups. Corresponding criteria are presented in chapter 4