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Some remarks on parametric excitation in circulatory systems
Author(s) -
Karev Artem,
DeBroeck Lara,
Hagedorn Peter
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800061
Subject(s) - excitation , parametric statistics , context (archaeology) , stability (learning theory) , instability , amplitude , work (physics) , dynamical systems theory , physics , parametric oscillator , statistical physics , mathematics , computer science , mechanics , quantum mechanics , statistics , geology , paleontology , machine learning
Dynamical systems with time‐periodic coefficients, i.e. with parametric excitation, have been studied in different fields for over a hundred years. It is well known that the presence of parametric excitation acts mostly destabilizing, leading to the emergence of instability regions depending on the amplitude and frequency of excitation. However, most of the work is done on systems with synchronous parametric excitation, while there are only few papers dealing with out‐of‐phase time‐periodicity. At the same time little to no research in this context is done on systems containing gyroscopic or circulatory terms. The present paper demonstrates different approaches for stability assessment of time‐periodic systems featuring nonconservative terms. In particular, out‐of‐phase parametric excitation as well as circulatory forces are considered in an example which is treated analytically and numerically. The derived stability boundaries show that the interaction of both features leads to the occurrence of rather unexpected resonance areas. The results extend the understanding of the influence of parametric excitation and encourage study of more general systems.