Aeroelastic Behavior of Noise-Reducing Membranes for Aircraft Lifting Surfaces Part I: Theory

Abstract

Commercial transport aircrafts generate a significant amount of noise during approach and landing. A substantial portion of this noise is due to the interaction of vortices and structure at the discontinuity between the wing and the deployed trailing edge flap. One method to reduce this noise is to introduce a thin flexible fairing that can smoothly connect the edge of the flap to the wing. For design purposes, it is important to analyze the aeroelastic behavior of such fairings, which can be modeled as membranes or elastic panels. Past studies have considered panel flutter with an assortment of boundary conditions, but only recently have efforts begun to consider boundary conditions geometrically the trailing edge flap fairing -side edges and leading edge fixed, trailing edge free. This paper presents a theoretical study of the aeroelastic behavior of elastic plates with this boundary condition. Specifically the paper discusses a vortex lattice aerodynamic model coupled with a classical plate/membrane model. The model is used to predict the linear flutter boundary and flutter characteristics of the panel while the support structure size, streamwise length, and normal direction tension are varied. The stability boundary is determined to be relatively insensitive to the support structure size, but varies non-simply with both the streamwise chord and the tension in the normal direction. Additionally the results are compared to previous aeroelastic simulations which suggested a higher mode flutter which is not encountered in the current simulations. Experimental validation of the structural and aeroelastic models is presented in the companion paper.

Aeroelastic Optimization of Membrane Prestress on a Flapping Wing

“…The flutter calculations were first performed with zero structural damping on the system, which led to a large error as compared to the experimental analysis. However, it was found in Gibbs, et al 13 that a small amount of structural damping was required in their nonlinear plate-membrane system to correctly calculate the flutter of a clamped-clamped-clampedfree membrane. So some stiffness proportional structural damping was added to the system and the newly calculated flutter speeds are indicated by the blue dots.…”

“…Similar membrane stability studies have been done using linear 10,11 and non-linear studies. 12, 13 Richter and Patil 14 showed that different prestresses in a membrane wing change both the aerodynamic force generation, as well as the stability of a hovering configuration. Walker et al 15 coupled a novel two-dimensional aerodynamic model 16 with a two-dimensional Galerkin approximation to the membrane equation.…”