Journal of Aerospace Engineering

This paper presents a new abstract function space formulation of the subsonic small disturbance potential field equations of aeroelasticity and an operator theoretic treatment of the Possio integral equation in the generality of the Laplace transform variable λ. A key result is the new form of the kernel—which is shown to be analytic in the whole plane, excepting the negative real axis—using an existence and uniqueness theorem is proved valid for small |λ|. The main new feature is the use of spatial $L_p-L_q$ Fourier transforms for $1<p<2$ and Mikhlin multiplier theory.

A recently developed three-dimensional viscous aeroelastic solver is applied to the solution of nonlinear panel flutter. The solution scheme implicitly couples a well validated Navier-Stokes code with a finite-difference procedure for the Von Karman plate equations by employing a subiteration strategy. Both low supersonic, $M_{\infty }=1.2\text{,}$ and subsonic, $M_{\infty }=0.95\text{,}$ cases are computed. For the supersonic case, the presence of either a laminar or turbulent boundary layer delays the onset of flutter, with higher flutter dynamic pressures resulting for thicker boundary layers. This effect is much less pronounced when the boundary layers are turbulent. In the subsonic case multiple solutions are obtained. The downwardly divergent solution displays a very complex interaction between the laminar boundary layer and the flexible panel that results in significant acoustic radiation from the vibrating panel.

While piezoelectric (PZT) actuators exhibit only mild nonlinear response at low voltage levels, it is well known that the response can be profoundly nonlinear at high field strengths. Moreover, the use of mechanical linkages and structural design to amplify the stroke of PZT-based actuation likewise induces sources of mechanical hysteresis (friction, backlash, etc.) that can couple with this material nonlinearity to yield a structural scale nonlinearity that is nonnegligible. These two sources of hysteresis, due to mechanism response and nonlinear material response, are not easily decoupled. In this paper, we investigate such a nonlinear response in a PZT actuated trailing edge flap attached to a scaled helicopter rotor blade. While the example studied in this paper is quite specific, the methodology derived is generally applicable. We extend the results of previous papers for the derivation of closed loop control for active material actuated devices. The goal is to derive a control methodology that accounts for the overall, total hysteresis due to material nonlinearities and mechanism response. In this technique, a compensator derived from an offline identification of a Krasnoselskii-Pokrovskii hysteresis operator is cascaded with the plant. We show that the methodology is well posed for the class of problems under consideration; we describe relevant closed loop stability and robustness conditions that can be associated with the prediction error in the identified hysteresis operator. We study the performance of our methodology in numerical examples and discuss relevant experimental results.

The problem of pollution within Earth’s orbital environment has gained considerable recognition over the past decades. Determining adequate passive protection schemes is an unending process that attempts to meet different objectives for widely varying types of missions. Significant amounts of resources have been expended toward development of numerical and analytical models that model the response of a variety of target systems under high-speed orbital debris impacts. The objective of the study whose results are presented herein was to improve upon an existing oblique hypervelocity impact model that characterizes the various secondary debris clouds created in such an impact. This was accomplished by reducing the model’s dependence on empirical user-defined parameters and by correcting an error in one of its equations. Predictions of the improved model are compared with numerical simulations generated during previous impact studies under comparable conditions. It is found that the improved model does a reasonable job of predicting the characteristics of the secondary debris clouds created in an oblique hypervelocity impact.