Aeroelastic Analysis of a Wing like Structure using Differential Transform Method

Abstract

Aeroelasticity has gained greater importance in the structural and aerodynamic design of newlinemodern high-speed aircrafts. During aircraft maneuvers, the aerodynamic lifting surfaces are newlinesubject to aerodynamic, inertial, and elastic forces, making them vulnerable to a potential newlineproblem known as flutter, an aerodynamic instability. Flutter leads to large amplitude newlineoscillations as the system absorbs energy from the fluid resulting in negative damping. newlineOccurrence of flutter on lifting surfaces like wings is to be suppressed to avoid the failure of newlinethe structure. The need for faster and higher performance in aircraft also requires increased newlineflexibility in the structures, resulting in a reduction in weight. Increase of the flutter speed newlinewithout weight penalties is a challenge in the field of aeroelasticity. Routine flutter analysis involves a linear representation of the structure and the aerodynamic newlineloading. The flutter speed or the critical speed is determined from the eigen values of the flutter newlinedeterminant. Conventional methods like the p, k, p-k methods are used to solve for the flutter newlinefrequency which involves rigorous iterative procedure. The accuracy of the critical speed also newlinedepends on the precise modeling of the aerodynamic loads. The quasi steady and the unsteady newlineaerodynamic models are generally used for the representation of the lift and aerodynamic newlinemoments. In the present study, differential transform method (DTM) based on the Taylor s series newlineexpansion is implemented to find the flutter speed and frequency of a linear aeroelastic system. newlinePrior to applying the methodology to an aeroelastic system, Timoshenko beam which exhibits newlinecoupled dynamics between the flexure and torsion mode is investigated for its free vibration newlinecharacteristics using DTM. The Timoshenko beam theory (TB) takes into account the newlinetransverse shear and rotary inertia, which are neglected in Euler-Bernoulli beam theory. newlineThe eigenvalues determined using DTM displayed a second spectrum of frequencies which is dominated by the rotational ...