Nonlinear transient localization and beat phenomena due to backlash in a coupled flexible system

Transient nonlinear localization and beat phenomena are studied in a system of two rods coupled with a nonlinear backlash spring. The method of Karhun en-Loeve (K-L) decomposition is used to reduce the order of the dynamics, a nd to study nonlinear effects by considering energy transfers between leadi ng K-L modes. The computed K-L modes are used to discretize the governing p artial differential equations, thus creating accurate and computationally e fficient low-dimensional nonlinear models of the system. Reconstruction of transient nonlinear responses using these low dimensional models reveals th e accuracy of the order reduction. Poincare maps are utilized to study the nonlinear localization and beat phenomena caused by the clearance connectin g the coupled rods.