Vadim A Krysko's Books

Deterministic Chaos In One Dimensional Continuous Systems

By: Jan Awrejcewicz,Vadim A Krysko,Irina V Papkova,Anton V Krysko

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Deterministic Chaos In One Dimensional Continuous Systems

By: Jan Awrejcewicz,Vadim A Krysko,Irina V Papkova,Anton V Krysko

This book focuses on the computational analysis of nonlinear vibrations of structural members (beams, plates, panels, shells), where the studied dynamical problems can be reduced to the consideration of one spatial variable and time. The reduction is carried out based on a formal mathematical approach aimed at reducing the problems with infinite dimension to finite ones. The process also includes a transition from governing nonlinear partial differential equations to a set of finite number of ordinary differential equations.Beginning with an overview of the recent results devoted to the analysis and control of nonlinear dynamics of structural members, placing emphasis on stability, buckling, bifurcation and deterministic chaos, simple chaotic systems are briefly discussed. Next, bifurcation and chaotic dynamics of the Euler-Bernoulli and Timoshenko beams including the geometric and physical nonlinearity as well as the elastic-plastic deformations are illustrated. Despite the employed classical numerical analysis of nonlinear phenomena, the various wavelet transforms and the four Lyapunov exponents are used to detect, monitor and possibly control chaos, hyper-chaos, hyper-hyper-chaos and deep chaos exhibited by rectangular plate-strips and cylindrical panels.The book is intended for post-graduate and doctoral students, applied mathematicians, physicists, teachers and lecturers of universities and companies dealing with a nonlinear dynamical system, as well as theoretically inclined engineers of mechanical and civil engineering.

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Page Count

577

Publisher

World Scientific

Published Date

ISBN 10

9814719714

ISBN 13

9789814719711

Mathematical Modelling and Numerical Analysis of Size-Dependent Structural Members in Temperature Fields

Regular and Chaotic Dynamics of Micro/Nano Beams, and Cylindrical Panels

By: Jan Awrejcewicz,Anton V. Krysko,Maxim V. Zhigalov,Vadim A. Krysko

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Mathematical Modelling and Numerical Analysis of Size-Dependent Structural Members in Temperature Fields

Regular and Chaotic Dynamics of Micro/Nano Beams, and Cylindrical Panels

By: Jan Awrejcewicz,Anton V. Krysko,Maxim V. Zhigalov,Vadim A. Krysko

This book is devoted to researchers and teachers, as well as graduate students, undergraduates and bachelors in engineering mechanics, nano-mechanics, nanomaterials, nanostructures and applied mathematics. It presents a collection of the latest developments in the field of nonlinear (chaotic) dynamics of mass distributed-parameter nanomechanical structures, providing a rigorous and comprehensive study of modeling nonlinear phenomena. It is written in a unique pedagogical style particularly suitable for independent study and self-education. In addition, the book achieves a good balance between Western and Eastern extensive studies of the mathematical problems of nonlinear vibrations of structural members.

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Page Count

419

Publisher

Springer Nature

Published Date

ISBN 10

3030559939

ISBN 13

9783030559939

Chaos in Structural Mechanics

By: Jan Awrejcewicz,Vadim Anatolevich Krys'ko

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Chaos in Structural Mechanics

By: Jan Awrejcewicz,Vadim Anatolevich Krys'ko

This volume introduces new approaches to modeling strongly nonlinear behaviour of structural mechanical units: beams, plates and shells or composite systems. The text draws on bifurcation theory and chaos, emphasizing control and stability of objects and systems.

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Page Count

424

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540776761

ISBN 13

9783540776765

Nonclassical Thermoelastic Problems in Nonlinear Dynamics of Shells

Applications of the Bubnov-Galerkin and Finite Difference Numerical Methods

By: Jan Awrejcewicz,Vadim A. Krysko

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Nonclassical Thermoelastic Problems in Nonlinear Dynamics of Shells

Applications of the Bubnov-Galerkin and Finite Difference Numerical Methods

By: Jan Awrejcewicz,Vadim A. Krysko

From the reviews: "A unique feature of this book is the nice blend of engineering vividness and mathematical rigour. [...] The authors are to be congratulated for their valuable contribution to the literature in the area of theoretical thermoelasticity and vibration of plates." Journal of Sound and Vibration

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Page Count

432

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642556779

ISBN 13

9783642556777

Nonlinear Dynamics of Continuous Elastic Systems

By: Jan Awrejcewicz,Vadim Anatolevich Krys'ko,Alexander F. Vakakis

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Nonlinear Dynamics of Continuous Elastic Systems

By: Jan Awrejcewicz,Vadim Anatolevich Krys'ko,Alexander F. Vakakis

This monograph is devoted to recent advances in nonlinear dynamics of continuous elastic systems. A major part of the book is dedicated to the analysis of non-homogeneous continua, e.g. plates and shells characterized by sudden changes in their thickness, possessing holes in their bodies or/and edges, made from different materials with diverse dynamical characteristics and complicated boundary conditions. New theoretical and numerical approaches for analyzing the dynamics of such continua are presented, such as the method of added masses and the method of proper orthogonal decomposition. The presented hybrid approach leads to results that cannot be obtained by other standard theories in the field. The demonstrated methods are illustrated by numerous examples of application.

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Page Count

351

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3662089920

ISBN 13

9783662089927

Thermo-Dynamics of Plates and Shells

By: Jan Awrejcewicz,Vadim Anatolevich Krys'ko,Anton V. Krys'ko

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Thermo-Dynamics of Plates and Shells

By: Jan Awrejcewicz,Vadim Anatolevich Krys'ko,Anton V. Krys'ko

This monograph is devoted to nonlinear dynamics of thin plates and shells with thermosensitive excitation. Because of the variety of sizes and types of mathematical models in current use, there is no prospect of solving them analytically. However, the book emphasizes a rigorous mathematical treatment of the obtained differential equations, since it helps efficiently in further developing of various suitable numerical algorithms to solve the stated problems.

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Page Count

785

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540342621

ISBN 13

9783540342625

Elastic and Thermoelastic Problems in Nonlinear Dynamics of Structural Members

Applications of the Bubnov-Galerkin and Finite Difference Methods

By: Jan Awrejcewicz,Vadim A. Krysko

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Elastic and Thermoelastic Problems in Nonlinear Dynamics of Structural Members

Applications of the Bubnov-Galerkin and Finite Difference Methods

By: Jan Awrejcewicz,Vadim A. Krysko

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Page Count

615

Publisher

Springer Nature

Published Date

ISBN 10

303037663X

ISBN 13

9783030376635

Mathematical Models of Higher Orders

Shells in Temperature Fields

By: Vadim A. Krysko,Jan Awrejcewicz,Maxim V. Zhigalov,Valeriy F. Kirichenko,Anton V. Krysko

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Mathematical Models of Higher Orders

Shells in Temperature Fields

By: Vadim A. Krysko,Jan Awrejcewicz,Maxim V. Zhigalov,Valeriy F. Kirichenko,Anton V. Krysko

This book offers a valuable methodological approach to the state-of-the-art of the classical plate/shell mathematical models, exemplifying the vast range of mathematical models of nonlinear dynamics and statics of continuous mechanical structural members. The main objective highlights the need for further study of the classical problem of shell dynamics consisting of mathematical modeling, derivation of nonlinear PDEs, and of finding their solutions based on the development of new and effective numerical techniques. The book is designed for a broad readership of graduate students in mechanical and civil engineering, applied mathematics, and physics, as well as to researchers and professionals interested in a rigorous and comprehensive study of modeling non-linear phenomena governed by PDEs.

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Page Count

477

Publisher

Springer

Published Date

ISBN 10

3030047148

ISBN 13

9783030047146

Book's by Vadim A Krysko

Deterministic Chaos In One Dimensional Continuous Systems

Deterministic Chaos In One Dimensional Continuous Systems

Mathematical Modelling and Numerical Analysis of Size-Dependent Structural Members in Temperature Fields

Mathematical Modelling and Numerical Analysis of Size-Dependent Structural Members in Temperature Fields

Chaos in Structural Mechanics

Chaos in Structural Mechanics

Nonclassical Thermoelastic Problems in Nonlinear Dynamics of Shells

Nonclassical Thermoelastic Problems in Nonlinear Dynamics of Shells

Nonlinear Dynamics of Continuous Elastic Systems

Nonlinear Dynamics of Continuous Elastic Systems

Thermo-Dynamics of Plates and Shells

Thermo-Dynamics of Plates and Shells

Elastic and Thermoelastic Problems in Nonlinear Dynamics of Structural Members

Elastic and Thermoelastic Problems in Nonlinear Dynamics of Structural Members

Mathematical Models of Higher Orders

Mathematical Models of Higher Orders

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