Nonstationary Resonant Dynamics of Oscillatory Chains and Nanostructures

  • Leonid I. Manevitch
  • Agnessa Kovaleva
  • Valeri Smirnov
  • Yuli Starosvetsky

Part of the Foundations of Engineering Mechanics book series (FOUNDATIONS)

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Conservative Systems

    1. Front Matter
      Pages 1-1
    2. Leonid I. Manevitch, Agnessa Kovaleva, Valeri Smirnov, Yuli Starosvetsky
      Pages 3-26
    3. Leonid I. Manevitch, Agnessa Kovaleva, Valeri Smirnov, Yuli Starosvetsky
      Pages 27-66
    4. Leonid I. Manevitch, Agnessa Kovaleva, Valeri Smirnov, Yuli Starosvetsky
      Pages 67-83
    5. Leonid I. Manevitch, Agnessa Kovaleva, Valeri Smirnov, Yuli Starosvetsky
      Pages 85-140
    6. Leonid I. Manevitch, Agnessa Kovaleva, Valeri Smirnov, Yuli Starosvetsky
      Pages 141-152
  3. Extensions to Non-conservative Systems

    1. Front Matter
      Pages 153-153
    2. Leonid I. Manevitch, Agnessa Kovaleva, Valeri Smirnov, Yuli Starosvetsky
      Pages 155-186
    3. Leonid I. Manevitch, Agnessa Kovaleva, Valeri Smirnov, Yuli Starosvetsky
      Pages 187-194
    4. Leonid I. Manevitch, Agnessa Kovaleva, Valeri Smirnov, Yuli Starosvetsky
      Pages 195-223
  4. Applications

    1. Front Matter
      Pages 225-225
    2. Leonid I. Manevitch, Agnessa Kovaleva, Valeri Smirnov, Yuli Starosvetsky
      Pages 227-243
    3. Leonid I. Manevitch, Agnessa Kovaleva, Valeri Smirnov, Yuli Starosvetsky
      Pages 245-292
    4. Leonid I. Manevitch, Agnessa Kovaleva, Valeri Smirnov, Yuli Starosvetsky
      Pages 293-325
    5. Leonid I. Manevitch, Agnessa Kovaleva, Valeri Smirnov, Yuli Starosvetsky
      Pages 327-335
    6. Leonid I. Manevitch, Agnessa Kovaleva, Valeri Smirnov, Yuli Starosvetsky
      Pages 337-354
    7. Leonid I. Manevitch, Agnessa Kovaleva, Valeri Smirnov, Yuli Starosvetsky
      Pages 355-390
    8. Leonid I. Manevitch, Agnessa Kovaleva, Valeri Smirnov, Yuli Starosvetsky
      Pages 391-433
  5. Back Matter
    Pages 435-436

About this book

Introduction

This book suggests a new common approach to the study of resonance energy transport based on the recently developed concept of Limiting Phase Trajectories (LPTs), presenting  applications of the approach to significant nonlinear problems from different fields of physics and mechanics. In order to highlight the novelty and perspectives of the developed approach, it places the LPT concept in the context of dynamical phenomena related to the energy transfer problems and applies the theory to numerous problems of practical importance. This approach leads to the conclusion that strongly nonstationary resonance processes in nonlinear oscillator arrays and nanostructures are characterized either by maximum possible energy exchange between the clusters of oscillators (coherence domains) or by maximum energy transfer from an external source of energy to the chain. The trajectories corresponding to these processes are referred to as LPTs. The development and the use of the LPTs concept are motivated by the fact that non-stationary processes in a broad variety of finite-dimensional physical models are beyond the well-known paradigm of nonlinear normal modes (NNMs), which is fully justified either for stationary processes or for nonstationary non-resonance processes described exactly or approximately by the combinations of the non-resonant normal modes. Thus, the role of LPTs in understanding and analyzing of intense resonance energy transfer is similar to the role of NNMs for the stationary processes. The book is a valuable resource for engineers needing to deal effectively with the problems arising in the fields of mechanical and physical applications, when the natural physical model is quite complicated. At the same time, the mathematical analysis means that it is of interest to researchers working on the theory and numerical investigation of nonlinear oscillations.

Keywords

Limiting Phase Trajectories Nonlinear Oscillations Resonance Energy Transport Resonance Energy Exchange Non-resonant Normal Modes

Authors and affiliations

  • Leonid I. Manevitch
    • 1
  • Agnessa Kovaleva
    • 2
  • Valeri Smirnov
    • 3
  • Yuli Starosvetsky
    • 4
  1. 1.Institute of Chemical PhysicsRussian Academy of ScienceMoscowRussia
  2. 2.Space Research InstituteRussian Academy of ScienceMoscowRussia
  3. 3.Institute of Chemical PhysicsRussian Academy of ScienceMoscowRussia
  4. 4.Technion—Israel Institute of TechnologyFaculty of Mechanical EngineeringHaifaIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-981-10-4666-7
  • Copyright Information Springer Nature Singapore Pte Ltd. 2018
  • Publisher Name Springer, Singapore
  • eBook Packages Engineering
  • Print ISBN 978-981-10-4665-0
  • Online ISBN 978-981-10-4666-7
  • Series Print ISSN 1612-1384
  • Series Online ISSN 1860-6237
  • About this book