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Nonlinear modal interactions and low order modeling of a kicked flexible rod
Author(s) -
Cusumano Joseph P.
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700602
Subject(s) - quasiperiodic function , bifurcation , nonlinear system , chaotic , modal , piecewise , piecewise linear function , mode (computer interface) , physics , classical mechanics , bifurcation diagram , statistical physics , control theory (sociology) , mathematics , mathematical analysis , computer science , quantum mechanics , materials science , control (management) , artificial intelligence , polymer chemistry , operating system
A magnetically kicked flexible‐beam oscillator is studied experimentally. Spectral bifurcation diagrams of the attracting steady states are obtained, and the system is seen to exhibit periodic, quasiperiodic and chaotic responses. The proper orthogonal decomposition (POD) is applied to spatial strain gauge data, and a specific nonlinear two‐mode interaction is shown to be present in all responses. Based on these experimental observations, a two degree of freedom piecewise linear autonomous model is developed, which captures much of the behavior observed in the experiments. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)