Nonlinear modal analysis based on invariant manifolds: Application to rotating blade systems

摘要: In the design-analysis cycle of complex structural systems such as rotorcraft, aircraft, and ground vehicles, it is necessary to understand their vibratory response thoroughly. If vibration interest restricted small neighborhoods static equilibrium positions, then assumption a linear system can be made. The corresponding analysis procedure greatly simplified, through use modern tools Finite Element Analysis Modal Analysis. contrast, when amplitudes oscillations are large, beyond scale linearization, or behaves inherently nonlinearly with respect its configurations, nonlinear equations motion must used in model. It well known that exhibit much richer more behavior than counterparts (i.e., bifurcations, internal resonances, sensitivity initial conditions, etc.). Moreover, for superposition no longer valid, coupling present between normal modes may necessitate models relatively large number degrees freedom (DOF) order capture dynamics accurately. As result, studies often sacrifice either time (through expensive computer model) accuracy elimination possibly significant mechanisms). This research aimed at development implementation model reduction methods certain classes systems, based on invariant manifold approach initially developed by Shaw Pierre [1?4], further implemented Boivin [5, 6] Pesheck [7]. primary goal this dissertation extend modal methodology large-scale (particularly those modeled finite element method) various types nonlinearities (e.g., polynomial piecewise linear), including subject external excitation resonances. Another objective work apply an industrial structure complex, intrinsic nonlinearity. important class engineering rotating structures investigated, namely rotorcraft blades.