C1 Book

Physical Fundamentals of Oscillations. Frequency Analysis of Periodic Motion Stability

LUT Authors / Editors

Publication Details
Authors: Chechurin Leonid, Chechurin Sergei
Publishing place: Berlin
Publication year: 2017
Language: English
ISBN: 978-3-319-75153-5
eISBN: 978-3-319-75154-2
JUFO-Level of this publication: 2
Open Access: Not an Open Access publication


The book introduces possibly the most compact, simple and physically
understandable tool that can describe, explain, predict and design the
widest set of phenomena in time-variant and nonlinear oscillations. The
phenomena described include parametric resonances, combined resonances,
instability of forced oscillations, synchronization, distributed
parameter oscillation and flatter, parametric oscillation control,
robustness of oscillations and many others. Although the realm of
nonlinear oscillations is enormous, the book relies on the concept of
minimum knowledge for maximum understanding. This unique tool is the
method of stationarization, or one frequency approximation of parametric
resonance problem analysis in linear time-variant dynamic systems. The
book shows how this can explain periodic motion stability in stationary
nonlinear dynamic systems, and reveals the link between the harmonic
stationarization coefficients and describing functions. As such, the
book speaks the language of control: transfer functions, frequency
response, Nyquist plot, stability margins, etc. An understanding of the
physics of stability loss is the basis for the design of new oscillation
control methods for, several of which are presented in the book. These
and all the other findings are illustrated by numerical examples, which
can be easily reproduced by readers equipped with a basic simulation
package like MATLAB with Simulink. The book offers a simple tool for all
those travelling through the world of oscillations, helping them
discover its hidden beauty. Researchers can use the method to uncover
unknown aspects, and as a reference to compare it with other, for
example, abstract mathematical means. Further, it provides engineers
with a minimalistic but powerful instrument based on physically
measurable variables to analyze and design oscillatory systems.

Last updated on 2019-11-10 at 07:31