## Sensitivity analysis of wing aeroelastic responses

##### Abstract

In this study, flutter characteristic of a typical section in subsonic compressible flow is examined using a state-space unsteady aerodynamic representation. The sensitivity of the flutter speed of the typical section with respect to its mass and stiffness parameters, namely, mass ratio, static unbalance, radius of gyration, bending frequency and torsional frequency is calculated analytically. A strip-theory formulation is newly developed to represent the unsteady aerodynamic forces on a wing. This is coupled with an equivalent plate structural model based on a Rayleigh-Ritz formulation and the aeroelastic equations are solved as an eigenvalue problem to determine the critical speed of the wing. The sensitivity of divergence and flutter speeds to shape parameters, namely, aspect ratio, area, taper ratio and sweep angle are computed analytically. The aeroelastic equations are also integrated with respect to time using the Wilson-B method at different values of freest ream speed, to observe the aeroelastic phenomena in real time. of divergence and flutter speeds to shape parameters, namely, aspect ratio, area, taper ratio and sweep angle are computed analytically. The aeroelastic equations are also integrated with respect to time using the Wilson-B method at different values of freest ream speed, to observe the aeroelastic phenomena in real time.

Flutter analysis of the wing is also carried out using a lifting-surface subsonic
kernel function aerodynamic theory (FAST) and an equivalent plate structural
model The flutter speed is obtained using a *V-g* type of solution. The novel
method of automatic differentiation using ADIFOR is implemented to generate
exact derivatives of the flutter speed with respect to shape and modal parameters
of the wing.

Finite element modeling of the wing is done using NASTRAN so that wing structures made of spars and ribs and top and bottom wing skins could be analyzed. The free vibration modes of the wing obtained from NASTRAN are input into FAST to compute the flutter speed. The derivatives of flutter speed with respect to shape parameters are computed using a combination of central difference scheme and ADIFOR and the sensitivity to modal parameters is calculated using ADIFOR.

An equivalent plate model which incorporates first-order shear deformation theory is then examined so it can be used to model thick wings, where shear deformations are important. The sensitivity of natural frequencies to changes in shape parameters is obtained using ADIFOR. A simple optimization effort is made towards obtaining a minimum weight design of the wing, subject to flutter constraints, lift requirement constraints for level flight and side constraints on the planform parameters of the wing using the IMSL subroutine NCONG, which uses successive quadratic programming.

##### Collections

- Doctoral Dissertations [12627]