Energy-Weighted Modes Selection in Reduced-Order Nonlinear Simulations

Abstract

A study is undertaken to improve the linear normal mode selection procedure using the energy information of the proper orthogonal modes generated in the full physical simulation of a nonlinear system. In a typical reduced-order simulation using proper orthogonal decomposition, system identification is performed to simulation data in physical DoFs by means of proper orthogonal decomposition. However, frequency information is also acquired so that the energy participation factor of each proper orthogonal mode can be obtained. In this paper, first, the frequency estimation of resulting proper orthogonal modes is performed by using the modal kinetic energy without using complicated smooth orthogonal decomposition. Second, the similarity matrix between the proper orthogonal modes and the linear normal modes are weighted with energy participation of proper orthogonal modes so that the selected linear normal modes are not only similar to corresponding proper orthogonal modes, but also based on the most energy contributing ones. Linear and nonlinear simulations of a simply-supported plate structure subjected to free vibrations, and random pressure excitations are examined as the application examples. Initial examples show that the proposed technique enables accurate and efficient frequency estimation of proper orthogonal modes and has the potential of improving the mode selection procedure for reduced-order nonlinear simulations.