A Multibody Formulation for Helicopter Structural Dynamic Analysis

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Abstract
This paper presents a multibody formulation for helicopter nonlinear dynamic analysis. Cartesian coordinates are used to represent the configuration of each body. This approach involves more unknown coordinates than arc strictly necessary to define the configuration of the system; hence, constraint equations linking the redundant coordinates are an integral part of the formulation. In classical rotorcraft methodologies, elsstic bodies are revresented in a local, rotating frame of reference which amounts to separating rigid body and elastic motions. The approach followed in this work departs radically from this classical approach: the total motion of all elastic bodies is directly referred to a single inertial frame. This approach readily allows the development of computer models to deal with arbitrarily complex multibody configurations. In this work, finite rotations are represented using the components of the conformal rotation vector, and the constraint equations are enforced via an augmented Lagrangian formulation. Simple numerical examples are presented to validate the formulation, and the classical ground resonance problem is treated here as a multibody problem. Good correlation is found between analytical solutions and multibody formulations.

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