Leonid Isaakovich Manevich's Books

The Mechanics of Nonlinear Systems with Internal Resonances

By: Arkadiy I. Manevich,Leonid Isaakovich Manevich

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The Mechanics of Nonlinear Systems with Internal Resonances

By: Arkadiy I. Manevich,Leonid Isaakovich 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.

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Page Count

278

Publisher

World Scientific

Published Date

ISBN 10

1860945104

ISBN 13

9781860945106

Solitons in Macromolecular Systems

By: Leonid Isaakovich Manevich,V. V. Simmons

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Solitons in Macromolecular Systems

By: Leonid Isaakovich Manevich,V. V. Simmons

This book addresses the issue of non-linear problems that have dominated the forefront of physics. To analyse these problems, it is necessary to develop mathematical methods to match new concepts. In this connection, for the first time in a long time, the same key notions have attracted the attention of physicists and mathematicians. This book discusses how the role of such excitations in essentially non-linear systems is similar to that of harmonic oscillations and waves in linear physical models.

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Page Count

142

Publisher

Nova Publishers

Published Date

ISBN 10

160456265X

ISBN 13

9781604562651

Mechanics of Periodically Heterogeneous Structures

By: Leonid Isaakovich Manevich,I.V. Andrianov,V.G. Oshmyan

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Mechanics of Periodically Heterogeneous Structures

By: Leonid Isaakovich Manevich,I.V. Andrianov,V.G. Oshmyan

Rigorous presentation of Mathematical Homogenization Theory is the subject of numerous publications. This book, however, is intended to fill the gap in the analytical and numerical performance of the corresponding asymptotic analysis of the static and dynamic behaviors of heterogenous systems. Numerous concrete applications to composite media, heterogeneous plates and shells are considered. A lot of details, numerical results for cell problem solutions, calculations of high-order terms of asymptotic expansions, boundary layer analysis etc., are included.

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Page Count

294

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540416307

ISBN 13

9783540416302

Asymptotical Mechanics of Thin-Walled Structures

A Handbook

By: Igor V. Andrianov,Jan Awrejcewicz,Leonid Isaakovich Manevich

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Asymptotical Mechanics of Thin-Walled Structures

A Handbook

By: Igor V. Andrianov,Jan Awrejcewicz,Leonid Isaakovich Manevich

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 its 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

548

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540408762

ISBN 13

9783540408765

Book's by Leonid Isaakovich Manevich

The Mechanics of Nonlinear Systems with Internal Resonances

The Mechanics of Nonlinear Systems with Internal Resonances

Solitons in Macromolecular Systems

Solitons in Macromolecular Systems

Mechanics of Periodically Heterogeneous Structures

Mechanics of Periodically Heterogeneous Structures

Asymptotical Mechanics of Thin-Walled Structures

Asymptotical Mechanics of Thin-Walled Structures

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