Karhunen–Loève decomposition of coupled axial/bending vibrations of beams subject to impacts

Proper orthogonal decomposition for model reduction of a vibroimpact system

“…If a linear system with proportional damping matrix is the one analyzed, then the basis generated by the normal modes are the optimum basis (Trindade et al (2005)). When dealing with a nonlinear problem one faces a difficulty, because there is no such thing as normal modes.…”

“…The system considered in this paper is simple, but the same procedure can be performed for more complicated situations as it was done in Trindade et al (2005). One motivation to study a vibroimpact system is its applications on drilling systems.…”

“…There are several approaches concerning reduced-order modeling; the present work is concerned with model reduction through the modal basis and through the proper orthogonal decomposition (POD). The LIN-basis (basis composed by the normal modes of the system) is the best basis for a linear dynamical system (Trindade et al (2005)), but the basis generated by POD has the capacity to describe the phenomenon of interest (linear or nonlinear dynamics, for example) in a reduced dimension that is able to capture most of the phenomenon (Holmes et al (1996)). It can be used as a tool for signal analysis, imaging processing, and other applications.…”

“…The objectives of this paper are: 1) to present and compare, in a didactic and detailed form, these reduction techniques for a simple vibroimpact system, 2) to quantify which strategy is better to be used in the future for the stochastic analysis, and 3) to investigate whether the use of 99% (or 99.9%) of the information in the reduced-order model (suggested by Sirovich Trindade et al (2005)) is sufficient to represent the details of the impact.…”

Low order dynamical system for fluid-rigid body interaction problem using POD method

“…In structure mechanics, POD is a recent investigation domain similar to modal analysis [9] in case of structure vibration. There are only few studies available in Fluid Structure Interaction.…”