Characterizing the Dynamics of 3-D Elastic Nonlinear Continua Using the Method of Proper Orthogonal Decompositions

A novel and systematic way is presented to characterize the modal structure of the free dynamics of three-dimensional elastic continua. In particular, the method of Proper Orthogonal Decomposition (POD) for multi-field dynamics is applied to analyze the dynamics of prisms and moderately thick beams. A nonlinear finite element model is used to compute accurate approximations to free motions which in turn are processed by POD. The extension of POD to analyze the dynamics of three-dimensional elastic continua, which are multi-field coupled dynamical system, is carried out by vector and matrix quantization of the finite element dynamics. An important outcome of this study is the fact that POD provides the means to systematically identify the shapes of nonlinear normal modes of vibration of three-dimensional structures from high resolution finite element simulations.

Identifying the Shapes of Coupled Vibrations and Deriving Reduced Order Models for Nonlinear Shafts: A Finite Element-Proper Orthogonal Decomposition Approach

The spatial structure of the dynamics of a rotating nonlinear shaft is identified by processing its finite element dynamics by the method of Proper Orthogonal Decompositions. The Proper Orthogonal modes furnish characteristic signatures for the rigid body and the whirling modes of a motion. The pattern of energy distribution over the components of a mode reveals the strength of coupling between rigid body rotations and coupled vibrations. These modes are used to derive a two-degree-of freedom reduced model for the whirling motion of the rotating shaft.

POD Analysis of In-Cylinder Flows

Both time-dependent and time-invariant Proper Orthogonal Decompositions are performed on LES and PIV data as an initial step in a study of tumble breakdown in in-cylinder flows. Evidence of tumble instability during compression is found in the time-dependent POD of both data sets. Time-invariant POD modes are presented which will be used later in low-dimensional models of these systems.