Energy-Based Modal Basis Selection Procedure for Reduced-Order Nonlinear Simulation

Abstract

A study is undertaken to investigate energy-based modal basis selection procedure aimed at enhancing accuracy and computational efficiency of reduced-order nonlinear simulation. System identification is first performed by means of both proper orthogonal decomposition and smooth orthogonal decomposition so that the energy participation factor of each proper orthogonal mode can be obtained and used to select the most contributing ones. Next, the modal assurance criterion or modal expansion theorem is used to determine a set of linear normal modes best representing the selected set of proper orthogonal modes. Linear normal modes, which contrary to proper orthogonal modes are load independent, are used as a robust basis to reduce the system size. Linear and nonlinear simulations of a simplysupported plate structure subjected to free vibrations and stationary ergodic random Gaussian uniform pressure excitations serve as the application examples. The quality of the reduced-order nonlinear simulation is examined through the comparison with computationally taxing full order nonlinear simulation in physical degrees-of-freedom. It is found that the proposed technique enables accurate and efficient modal identification and, thus, reduced-order nonlinear simulations.