Nonlinear Transient Localization and Beat Phenomena Due to Backlash in a Coupled Flexible System

Abstract

Transient nonlinear localization and beat phenomena are studied in a system of two rods coupled with a nonlinear backlash spring. The method of Karhunen-Loeve (K-L) decomposition is used to reduce the order of the dynamics, and to study nonlinear effects by considering energy transfers between leading K-L modes. The computed K-L modes are used to discretize the governing partial differential equations, thus creating accurate and computationally efficient low-dimensional nonlinear models of the system. Reconstruction of transient nonlinear responses using these low dimensional models reveals the accuracy of the order reduction. Poincare´ maps are utilized to study the nonlinear localization and beat phenomena caused by the clearance connecting the coupled rods.