Free-Response Simulation via the Proper Orthogonal Decomposition

Abstract

The proper orthogonal decomposition is applied to the response of linear and nonlinear beam models to construct a reduced-order model for predicting the response to various initial conditions without requiring the equations of motion for the structure. The proper orthogonal decomposition is interpreted as a modal sum, and the structural response to an initial condition is expressed as a weighted summation of proper orthogonal modes and corresponding proper orthogonal coordinate histories. A method for calculating the weights of each mode in the response to an altered initial condition is presented. This method is applied to predict the responses of a linear undamped beam model and a damped beam model with a nonlinear spring to various initial displacement and velocity profiles. The results obtained are compared with those from respective finite element models for each beam.