Leonid I. Manevitch's Books

Asymptotic Approaches in Nonlinear Dynamics

New Trends and Applications

By: Jan Awrejcewicz,Igor V. Andrianov,Leonid I. Manevitch

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Asymptotic Approaches in Nonlinear Dynamics

New Trends and Applications

By: Jan Awrejcewicz,Igor V. Andrianov,Leonid I. Manevitch

This book covers developments in the theory of oscillations from diverse viewpoints, reflecting the fields multidisciplinary nature. It introduces the state-of-the-art in the theory and various applications of nonlinear dynamics. It also offers the first treatment of the asymptotic and homogenization methods in the theory of oscillations in combination with Pad approximations. With its wealth of interesting examples, this book will prove useful as an introduction to the field for novices and as a reference for specialists.

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Page Count

321

Publisher

Springer Science & Business Media

Published Date

ISBN 10

364272079X

ISBN 13

9783642720796

Normal Modes and Localization in Nonlinear Systems

By: Alexander F. Vakakis,Leonid I. Manevitch,Yuri V. Mikhlin,Valery N. Pilipchuk,Alexandr A. Zevin

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Normal Modes and Localization in Nonlinear Systems

By: Alexander F. Vakakis,Leonid I. Manevitch,Yuri V. Mikhlin,Valery N. Pilipchuk,Alexandr A. Zevin

This landmark book deals with nonlinear normal modes (NNMs) and nonlinear mode localization. Offers an analysis which enables the study of various nonlinear phenomena having no counterpart in linear theory. On a more theoretical level, the concept of NNMs will be shown to provide an excellent framework for understanding a variety of distinctively nonlinear phenomena such as mode bifurcations and standing or traveling solitary waves.

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Page Count

552

Publisher

John Wiley & Sons

Published Date

ISBN 10

3527617876

ISBN 13

9783527617876

Asymptotology

Ideas, Methods, and Applications

By: Igor V. Andrianov,Leonid I. Manevitch

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Asymptotology

Ideas, Methods, and Applications

By: Igor V. Andrianov,Leonid I. Manevitch

Asymptotic methods belong to the, perhaps, most romantic area of modern mathematics. They are widely known and have been used in me chanics, physics and other exact sciences for many, many decades. But more than this, asymptotic ideas are found in all branches of human knowledge, indeed in all areas of life. In this broader context they have not and perhaps cannot be fully formalized. However, they are mar velous, they leave room for fantasy, guesses and intuition; they bring us very near to the border of the realm of art. Many books have been written and published about asymptotic meth ods. Most of them presume a mathematically sophisticated reader. The authors here attempt to describe asymptotic methods on a more accessi ble level, hoping to address a wider range of readers. They have avoided the extreme of banishing formulae entirely, as done in some popular science books that attempt to describe mathematical methods with no mathematics. This is impossible (and not wise). Rather, the authors have tried to keep the mathematics at a moderate level. At the same time, using simple examples, they think they have been able to illustrate all the key ideas of asymptotic methods and approaches, to depict in de tail the results of their application to various branches of knowledg- from astronomy, mechanics, and physics to biology, psychology and art. The book is supplemented by several appendices, one of which con tains the profound ideas of R. G.

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Page Count

262

Publisher

Springer Science & Business Media

Published Date

ISBN 10

144199162X

ISBN 13

9781441991621

Asymptotical Mechanics of Thin-Walled Structures

By: Igor V. Andrianov,Jan Awrejcewicz,Leonid I. Manevitch

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Asymptotical Mechanics of Thin-Walled Structures

By: Igor V. Andrianov,Jan Awrejcewicz,Leonid I. Manevitch

In this book a detailed and systematic treatment of asymptotic methods in the theory of plates and shells is presented. The main features of the book are the basic principles of asymptotics and their applications, traditional approaches such as regular and singular perturbations, as well as new approaches such as the composite equations approach. The book introduces the reader to the field of asymptotic simplification of the problems of the theory of plates and shells and will be useful as a handbook of methods of asymptotic integration. Providing a state-of-the-art review of asymptotic applications, this book will be useful as an introduction to the field for novices as well as a reference book for specialists.

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Page Count

527

Publisher

Springer Science & Business Media

Published Date

ISBN 10

354045246X

ISBN 13

9783540452461

Tractable Models of Solid Mechanics

Formulation, Analysis and Interpretation

By: Oleg V. Gendelman,Leonid I. Manevitch

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Tractable Models of Solid Mechanics

Formulation, Analysis and Interpretation

By: Oleg V. Gendelman,Leonid I. Manevitch

This book describes significant tractable models used in solid mechanics - classical models used in modern mechanics as well as new ones. The models are selected to illustrate the main ideas which allow scientists to describe complicated effects in a simple manner and to clarify basic notations of solid mechanics. A model is considered to be tractable if it is based on clear physical assumptions which allow the selection of significant effects and relatively simple mathematical formulations. The first part of the book briefly reviews classical tractable models for a simple description of complex effects developed from the 18th to the 20th century and widely used in modern mechanics. The second part describes systematically the new tractable models used today for the treatment of increasingly complex mechanical objects – from systems with two degrees of freedom to three-dimensional continuous objects.

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Page Count

310

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642153720

ISBN 13

9783642153723

Nonstationary Resonant Dynamics of Oscillatory Chains and Nanostructures

By: Leonid I. Manevitch,Agnessa Kovaleva,Valeri Smirnov,Yuli Starosvetsky

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Nonstationary Resonant Dynamics of Oscillatory Chains and Nanostructures

By: Leonid I. Manevitch,Agnessa Kovaleva,Valeri Smirnov,Yuli Starosvetsky

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.

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Page Count

448

Publisher

Springer

Published Date

ISBN 10

9811046662

ISBN 13

9789811046667

The Mechanics Of Nonlinear Systems With Internal Resonances

By: Leonid Manevitch,Arkadiy I Manevich

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The Mechanics Of Nonlinear Systems With Internal Resonances

By: Leonid Manevitch,Arkadiy I Manevich

One of the most important features of nonlinear systems with several degrees of freedom is the presence of internal resonances at certain relations between natural frequencies of different modes. This monograph is the first book devoted predominantly to internal resonances in different mechanical systems including those of practical importance.The main purpose is to consider the internal resonances from the general point of view and to elucidate their role in applied nonlinear dynamics by using an efficient approach based on introducing the complex representation of equations of motion (together with the multiple scale method). Considered here are autonomous and nonautonomous discrete two-degree-of-freedom systems, infinite chains of particles, and continuous systems, including circular rings and cylindrical shells. Specific attention is paid to the case of one-to-one internal resonance in systems with cubic nonlinearities. Steady-state and nonstationary regimes of motion, interaction of the internal and external resonances at forced oscillations, and bifurcations of steady-state modes and their stability are systematically studied./a

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Page Count

276

Publisher

World Scientific

Published Date

ISBN 10

1783260440

ISBN 13

9781783260447

Book's by Leonid I. Manevitch

Asymptotic Approaches in Nonlinear Dynamics

Asymptotic Approaches in Nonlinear Dynamics

Normal Modes and Localization in Nonlinear Systems

Normal Modes and Localization in Nonlinear Systems

Asymptotology

Asymptotology

Asymptotical Mechanics of Thin-Walled Structures

Asymptotical Mechanics of Thin-Walled Structures

Tractable Models of Solid Mechanics

Tractable Models of Solid Mechanics

Nonstationary Resonant Dynamics of Oscillatory Chains and Nanostructures

Nonstationary Resonant Dynamics of Oscillatory Chains and Nanostructures

The Mechanics Of Nonlinear Systems With Internal Resonances

The Mechanics Of Nonlinear Systems With Internal Resonances

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