Proper orthogonal decomposition (POD) of a class of vibroimpact oscillations

This study employs the method of proper orthogonal decomposition (POD), also known as the Karhunen-Loeve (K-L) method, to extract dominant coherent structures (modes that approximate the system behavior) from time-series data. These mode shapes can be used in a Galerkin reconstruction process to obtain lower dimensional models for the structural systems under consideration. The mode shapes and the energies obtained by this process can also be used to predict certain kinds of periodic or non-periodic non-linear motions. The K-L method has been applied successfully to fluid dynamical, thermal processes and signal processing. However, only a handful of works exist in the area of vibration analysis and structural mechanics. An extensive K-L analysis is performed numerically for two vibroimpacting systems: a beam and a rotor. Lower dimensional models are created and used to study non-linear energy transmission from low to higher K-L modes. Extensive reconstructions are also performed to prove the efficacy of the K-L method to provide accurate low-dimensional dynamical models. In addition, experimental investigations are presented for the case of the overhung impacting rotor and qualitative comparisons with the theoretical analysis are presented.