On the dynamics of finite-strain rods undergoing large motions a geometrically exact approach
Computer Methods in Applied Mechanics and Engineering
Numerical Recipes in C: The Art of Scientific Computing
Numerical Recipes in C: The Art of Scientific Computing
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Herein, a novel reduction procedure is applied to a simplified rotor blade model, yielding a single degree of freedom reduced-order model with exceptional accuracy. This approach is advantageous, as the nonlinear interactions present in rotorcraft systems often necessitate large-scale models when traditional finite-element or linear modal expansion methods are applied. These large models are cumbersome and may incur considerable computational cost for accurate simulations. The proposed procedure may ease this computational burden by producing a reduced set of governing equations which correctly account for the nonlinear behavior of the original system. This reduction is achieved through a Galerkin-based solution for the invariant manifold which governs the nonlinear normal mode of interest for the rotor blade. This solution method is primarily numerical, and is much more accurate than the previous asymptotic approaches. Results are shown for an example of a nine meter blade, for which peak to peak blade amplitudes of one meter can be accurately captured using a single nonlinear normal mode. The reduced-order, single degree of freedom model dynamics are shown to be nearly indistinguishable from those of a reference system which possesses 18 degrees of freedom. Though the blade model used here is quite simple in terms of geometry, the reduction method is easily applicable to much more general blade models, as well as to other nonlinear structural systems.