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

This study employs the method of proper orthogonal decomposition (POD). als o known as the Karhunen-Loeve (K-L) method, to extract dominant coherent st ructures (modes that approximate the system behavior) from time-series data . These mode shapes can be used in a Galerkin reconstruction process to obt ain lower dimensional models For the structural systems under consideration . The mode shapes and the energies obtained by this process can also be use d to predict certain kinds of periodic or non-periodic non-linear motions. The K-L method has been applied successfully to fluid dynamical, thermal pr ocesses and signal processing. However, only a handful of works exist in th e area of vibration analysis and structural mechanics. An extensive K-L ana lysis is performed numerically for two vibroimpacting systems: a beam and a rotor. Lower dimensional models are created and used to study non-linear e nergy transmission from low to higher K-L modes. Extensive reconstructions are also performed to prove the efficacy of the K-L method to provide accur ate low-dimensional dynamical models. In addition, experimental investigati ons are presented for the case of the overhung impacting rotor and qualitat ive comparisons with the theoretical analysis are presented. (C) 2001 Acade mic Press.