Reduced Model of a Bar Impacting an Obstacle Using Karhunen-Loeve Basis

Abstract

This work aims to discuss the Karhunen-Loève Decomposition and its capacity of capturing the non–linearities of a nonlinear dynamical system. A model of a bar impacting an obstacle is developed, where the impact forces come from a spring system. The system of equations of this nonlinear dynamical
system is discretized by means of the Finite Element Method, and then the model is reduced by means of two different bases: Normal Modes and Karhunen-Loève Basis. The construction of the Karhunen-Loève Basis is discussed in details for both Direct Method and Snapshots Method. The numerical results show that Karhunen-Loève Basis is the most efficient basis to project the dynamics studied.