Nonlinear Model Reduction based on Smooth Orthogonal Decomposition

D. Chelidze (USA) and G. Chelidze (Georgia)


Smooth orthogonal decomposition, nonlinear model reduc tion.


Large scale nonlinear model reduction based on smooth orthogonal decomposition (SOD) is presented. SOD is a multivariate time series analysis tool that provides optimal, low-dimensional representation of time series that are as smooth in time as possible. SOD is used to identify linear subspaces containing linear and nonlinear normal modes and span by smooth orthogonal modes (SOMs). Large fi nite element model (FEM) of a vibrating cantilever beam in a two-well potential is used to illustrate the model re duction. The SOMs of the simulated unforced, undamped FEM are used for model reduction. The performance of damped, forced FEM is then compared with three and five SOM based reduced-order models for various forcing pa rameters and close agreement is observed even for three SOM based reduced order model.

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