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

Abstract : 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 the vibration of interest is restricted to small neighborhoods of the static equilibrium positions, then the assumption of a linear system can be made. The corresponding analysis procedure is then greatly simplified, through the use of modern tools such as Finite Element Analysis and Modal Analysis. In contrast, when the amplitudes of oscillations are large, beyond the scale of linearization, or when a system behaves inherently nonlinearly with respect to its equilibrium configurations, then nonlinear equations of motion must be used in the model.

It is well known that nonlinear systems exhibit much richer and more complex behavior than their linear counterparts (i.e., bifurcations, internal resonances, sensitivity to initial conditions, etc.). Moreover, for a nonlinear system linear superposition is no longer valid, and the internal nonlinear coupling present between the linear normal modes of the system may necessitate the use of models with a relatively large number of degrees of freedom (DOF) in order to capture the system dynamics accurately. As a result, studies of nonlinear systems often sacrifice either time (through a large, expensive computer model) or accuracy (through the elimination of possibly significant mechanisms).

This research is aimed at the development and implementation of model reduction methods for certain classes of nonlinear structural systems, based on the invariant manifold approach initially developed by Shaw and Pierre [1?4], and further developed and implemented by Boivin [5, 6] and Pesheck [7]. The primary goal of this dissertation is to extend the nonlinear modal analysis methodology to large-scale structural systems (particularly
those modeled with the finite element method) with various types of nonlinearities (e.g., polynomial and piecewise linear), including systems subject to external excitation and those with internal resonances. Another objective of this work is to apply the invariant manifold approach to an industrial structure with a complex, intrinsic nonlinearity. The nonlinear dynamics of an important class of engineering rotating structures are investigated, namely rotorcraft blades.
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  • HAL Id : tel-00361013, version 1

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Dongying Jiang. Nonlinear modal analysis based on invariant manifolds - Application to rotating blade systems. Mechanics [physics.med-ph]. University of Michigan, 2004. English. ⟨tel-00361013⟩

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