Sliding window proper orthogonal decomposition: Application to linear and nonlinear modal identification

International audienceThe Proper Orthogonal Decomposition (POD) method is a tool well adapted to analyse vector signals whereas Continuous Gabor Transform (CGT) is suitable for scalar signal with multi-frequency components. In this paper, a method named Sliding Window Proper Orthogonal Decomposition (SWPOD) combining POD and CGT to analyse Multi-Degrees-Of-Freedom (MDOF) vibration system responses is presented. SWPOD gives access to the evolution of the coherent spacial structures and their frequency components versus time. The method is of principal interest in the case of swept-sine excitation of linear or nonlinear systems to access the resonance frequencies, mode shapes and modal damping ratios. A procedure is proposed to extract the linear and non-linear normal modes of weakly damped MDOF mechanical systems and illustrated using numerical examples