Model reduction of large structural dynamic models using proper orthogonal decomposition

This work considers use of Proper Orthogonal Decomposition (POD) to obtain reduced order dynamic models of nonlinear structural systems. The study applies POD to simulated time series data to extract dominant "modes" that describe the system behavior. The "POD modes" are used to formulate reduced order differential equation models (ROM's) of the structure in which the dependent variables are the POD modal coordinates. The objective of this process is to improve the accuracy of the reduced order model while keeping the whole process computationally inexpensive. In quest of this objective, simulations were conducted for a variety of cases for several nonlinear systems.;Three approaches that appear to be new are proposed in this work: (1) development of a "correction matrix" allowing a reduced model to be extended to changed system parameters. The results are shown for a chain of oscillator problem having twenty degrees of freedom; (2) use of band limited random excitation to generate responses from which the POD modes are obtained. Two example systems are considered: (a) a clamped beam whose tip is placed between attracting magnets; POD analysis of this system was done by Kerschen and Feeny [1] using harmonic excitation to excite chaotic motions, which were analyzed to develop the POD modes for reduced order modeling, and (b) a chain of oscillators having an isolated nonlinear Duffing element. (3) a new Ritz vector that is used to augment the POD modes. Results are shown for a fixed-free chain of oscillator system with isolated nonlinearity.