Overview
- Suggests a new common approach to the study of resonance energy transport based on the concept of Limiting Phase Trajectories
- Discusses applications to significant nonlinear problems from different fields of physics and mechanics
- Includes careful mathematical analysis, which is of interest to researchers working on the theory of nonlinear oscillations or algorithms
- Includes supplementary material: sn.pub/extras
Part of the book series: Foundations of Engineering Mechanics (FOUNDATIONS)
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Table of contents (15 chapters)
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Front Matter
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Extensions to Non-conservative Systems
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Front Matter
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Applications
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Front Matter
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Back Matter
Keywords
About this book
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 a
re 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.Authors and Affiliations
Bibliographic Information
Book Title: Nonstationary Resonant Dynamics of Oscillatory Chains and Nanostructures
Authors: Leonid I. Manevitch, Agnessa Kovaleva, Valeri Smirnov, Yuli Starosvetsky
Series Title: Foundations of Engineering Mechanics
DOI: https://doi.org/10.1007/978-981-10-4666-7
Publisher: Springer Singapore
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer Nature Singapore Pte Ltd. 2018
Hardcover ISBN: 978-981-10-4665-0Published: 03 August 2017
Softcover ISBN: 978-981-13-5195-2Published: 12 January 2019
eBook ISBN: 978-981-10-4666-7Published: 25 July 2017
Series ISSN: 1612-1384
Series E-ISSN: 1860-6237
Edition Number: 1
Number of Pages: XXII, 436
Number of Illustrations: 78 b/w illustrations, 116 illustrations in colour
Topics: Vibration, Dynamical Systems, Control, Solid State Physics, Nanotechnology, Engineering Thermodynamics, Heat and Mass Transfer