Reduced order modelling in nonlinear mechanical oscillators with energy pumping

Energy pumping in nonlinear mechanical oscillators has been discovered and studied in mechanical systems consisting of weakly coupled, linear and nonlinear components [1-3]. In this paper this phenomenon is further studied and numerically verified on an 11 degree of freedom system. It also presents a technique to create low dimensional models for energy pumping systems using the Karhunen-Loeve (K-L) decomposition method. It is shown that energy pumping can be identified from the dominant K-L modes. The low dimensional models are used to reconstruct the system responses. From the comparisons between the reconstructed and simulated response, we can see that the K-L mode-based low-dimensional model can represent the system responses; it can be used for monitoring, diagnosis and control purposes.