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An Energy-Preserving Description of Nonlinear Beam Vibrations in Modal Coordinates

The quality and nature of finite dimensional approximating systems for the dynamics of nonlinear beams are investigated. Approximations are constructed which are energy-preserving and, surprisingly, this property is independent of the dimension of the approximating system, which is useful in control system design. Important potential applications include new-generation lightweight, flexible aircraft, such as the tailless Lockheed Martin X56a, which possess nontrivial nonlinear dynamics and therefore require advanced control systems to maintain flight. Understanding and simply representing this nonlinear behaviour, for example using the methods developed in this paper, is therefore essential to the successful design of such controllers.