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Physical Fundamentals of Oscillations

Frequency Analysis of Periodic Motion Stability

  • Leonid Chechurin
  • Sergej Chechurin

Table of contents

  1. Front Matter
    Pages i-xv
  2. Amplitude–Phase–Frequency Characteristics of Linear Steady-State Systems

    1. Front Matter
      Pages 1-1
    2. Leonid Chechurin, Sergej Chechurin
      Pages 3-19
    3. Leonid Chechurin, Sergej Chechurin
      Pages 21-26
    4. Leonid Chechurin, Sergej Chechurin
      Pages 27-30
  3. Parametric Oscillations of Linear Periodically Nonstationary Systems

    1. Front Matter
      Pages 31-31
    2. Leonid Chechurin, Sergej Chechurin
      Pages 33-43
    3. Leonid Chechurin, Sergej Chechurin
      Pages 45-58
    4. Leonid Chechurin, Sergej Chechurin
      Pages 59-62
  4. Parametric Resonance in Nonlinear System Oscillations

    1. Front Matter
      Pages 63-63
    2. Leonid Chechurin, Sergej Chechurin
      Pages 65-81
    3. Leonid Chechurin, Sergej Chechurin
      Pages 83-97
    4. Leonid Chechurin, Sergej Chechurin
      Pages 99-116
  5. Parametric Oscillation Control

    1. Front Matter
      Pages 117-117
    2. Leonid Chechurin, Sergej Chechurin
      Pages 119-125
    3. Leonid Chechurin, Sergej Chechurin
      Pages 127-143
  6. Applications

    1. Front Matter
      Pages 145-145
    2. Leonid Chechurin, Sergej Chechurin
      Pages 147-154
    3. Leonid Chechurin, Sergej Chechurin
      Pages 155-159
    4. Leonid Chechurin, Sergej Chechurin
      Pages 161-182
    5. Leonid Chechurin, Sergej Chechurin
      Pages 183-209
  7. Multifrequency Oscillations, Stability and Robustness

    1. Front Matter
      Pages 211-211
    2. Leonid Chechurin, Sergej Chechurin
      Pages 229-238
    3. Leonid Chechurin, Sergej Chechurin
      Pages 239-261
  8. Back Matter
    Pages 263-264

About this book

Introduction

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.

Keywords

Oscillation Theory Control Theory Stability Analysis Frequency Based Methods Periodic Motion Stability

Authors and affiliations

  • Leonid Chechurin
    • 1
  • Sergej Chechurin
    • 2
  1. 1.Lappeenranta University of TechnologyLappeenrantaFinland
  2. 2.St. Petersburg State Polytechnic UniversitySt.PetersburgRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-75154-2
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2017
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-75153-5
  • Online ISBN 978-3-319-75154-2
  • Buy this book on publisher's site
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