Aeroelastic Flutter of Continuous Systems: A Generalized Laplace Transform Method

Abstract

This paper presents a generalization of the Laplace transform method (LTM) for determining the flutter points of a linear ordinarydifferential aeroelastic system—a linear system involving a spatial derivative as well as a timeeigenvalue parameter. Current implementations of the LTM have two major problems: they are unable to solve systems of arbitrary size, order, and boundary conditions, and they require certain key operations to be performed by hand or with symbolic manipulation libraries. Our generalized method overcomes both these problems. We also devise a new method for solving and visualizing the algebraic system that arises from the LTM procedure. We validate our generalized LTM and novel solution method against both the Goland wing model and a large system of high differential order, as a demonstration of their effectiveness for solving such systems.