Jan Awrejcewicz's Books

Approximate Models of Mechanics of Composites

An Asymptotic Approach

By: Igor V. Andrianov,Jan Awrejcewicz,Galina A. Starushenko

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Approximate Models of Mechanics of Composites

An Asymptotic Approach

By: Igor V. Andrianov,Jan Awrejcewicz,Galina A. Starushenko

Approximate Models of Mechanics of Composites: An Asymptotic Approach is an essential guide to constructing asymptotic models and mathematical methods to correctly identify the mechanical behavior of composites. It provides methodology for predicting and evaluating composite behavior in various structures, leading to accurate mathematical and physical assessments. The book estimates the error of approximations through comparing asymptotic solutions with the results of numerical and analytical solutions to gain a holistic view of the data. The authors have developed asymptotic models based on mathematical and physical rigorous approaches, which include three-phase models of fibrous composites, a modernized three-phase composite model with cylindrical inclusions, and models of two-dimensional composites of hexagonal structure. Also covered are two-phase models of composites related to the Maxwell formula and a percolation transition model for elastic problems based on the self-consistency method and Padé approximations. By obtaining analytical expressions to effectively characterize composite materials, their physical and geometric parameters can be accurately assessed. This book suits engineers and students working in material science, mechanical engineering, physics, and mathematics, as well as composite materials in industries such as construction, transport, aerospace, and chemical engineering.

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441

Publisher

CRC Press

Published Date

ISBN 10

1000890309

ISBN 13

9781000890303

Dynamics Of Mechatronics Systems: Modeling, Simulation, Control, Optimization And Experimental Investigations

By: Jan Awrejcewicz,Donat Lewandowski,Pawel Olejnik

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Dynamics Of Mechatronics Systems: Modeling, Simulation, Control, Optimization And Experimental Investigations

By: Jan Awrejcewicz,Donat Lewandowski,Pawel Olejnik

This book describes the interplay of mechanics, electronics, electrotechnics, automation and biomechanics. It provides a broad overview of mechatronics systems ranging from modeling and dimensional analysis, and an overview of magnetic, electromagnetic and piezo-electric phenomena. It also includes the investigation of the pneumo-fluid-mechanical, as well as electrohydraulic servo systems, modeling of dynamics of an atom/particle embedded in the magnetic field, integrity aspects of the Maxwell's equations, the selected optimization problems of angular velocity control of a DC motor subjected to chaotic disturbances with and without stick-slip dynamics, and the analysis of a human chest adjacent to the elastic backrest aimed at controlling force to minimize relative compression of the chest employing the LQR.This book provides a theoretical background on the analysis of various kinds of mechatronics systems, along with their computational analysis, control, optimization as well as laboratory investigations.

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357

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World Scientific

Published Date

ISBN 10

9813146567

ISBN 13

9789813146563

Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions

By: Igor Andrianov,Jan Awrejcewicz,Vladyslav Danishevs'kyy,Andrey Ivankov

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Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions

By: Igor Andrianov,Jan Awrejcewicz,Vladyslav Danishevs'kyy,Andrey Ivankov

Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions comprehensively covers the theoretical background of asymptotic approaches and their use in solving mechanical engineering-oriented problems of structural members, primarily plates (statics and dynamics) with mixed boundary conditions. The first part of this book introduces the theory and application of asymptotic methods and includes a series of approaches that have been omitted or not rigorously treated in the existing literature. These lesser known approaches include the method of summation and construction of the asymptotically equivalent functions, methods of small and large delta, and the homotopy perturbations method. The second part of the book contains original results devoted to the solution of the mixed problems of the theory of plates, including statics, dynamics and stability of the studied objects. In addition, the applicability of the approaches presented to other related linear or nonlinear problems is addressed. Key features: • Includes analytical solving of mixed boundary value problems • Introduces modern asymptotic and summation procedures • Presents asymptotic approaches for nonlinear dynamics of rods, beams and plates • Covers statics, dynamics and stability of plates with mixed boundary conditions • Explains links between the Adomian and homotopy perturbation approaches Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions is a comprehensive reference for researchers and practitioners working in the field of Mechanics of Solids and Mechanical Engineering, and is also a valuable resource for graduate and postgraduate students from Civil and Mechanical Engineering.

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Page Count

281

Publisher

John Wiley & Sons

Published Date

ISBN 10

111872514X

ISBN 13

9781118725146

Classical Mechanics

Dynamics

By: Jan Awrejcewicz

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Classical Mechanics

Dynamics

By: Jan Awrejcewicz

This is the second volume of three books devoted to Mechanics. In this book, dynamical and advanced mechanics problems are stated, illustrated, and discussed, including a few novel concepts in comparison to standard text books and monographs. Apart from being addressed to a wide spectrum of graduate students, postgraduate students, researchers, and teachers from the fields of mechanical and civil engineering, this volume is also intended to be used as a self-contained material for applied mathematicians and physical scientists and researchers.

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475

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461437407

ISBN 13

9781461437406

Classical Mechanics

Kinematics and Statics

By: Jan Awrejcewicz

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Classical Mechanics

Kinematics and Statics

By: Jan Awrejcewicz

This is the first volume of three, devoted to Mechanics. This book contains classical mechanics problems including kinematics and statics. It is recommended as a supplementary textbook for undergraduate and graduate students from mechanical and civil engineering, as well as for physical scientists and engineers. It contains a basic introduction to classical mechanics, including fundamental principles, statics, and the geometry of masses, as well as thorough discussion on kinematics.

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453

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Springer Science & Business Media

Published Date

ISBN 10

1461437911

ISBN 13

9781461437918

Classical Mechanics

Dynamics

By: Jan Awrejcewicz

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Classical Mechanics

Dynamics

By: Jan Awrejcewicz

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475

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Springer Science & Business Media

Published Date

ISBN 10

1461437407

ISBN 13

9781461437406

Classical Mechanics

Applied Mechanics and Mechatronics

By: Jan Awrejcewicz,Zbigniew Koruba

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Classical Mechanics

Applied Mechanics and Mechatronics

By: Jan Awrejcewicz,Zbigniew Koruba

This is the last book of three devoted to Mechanics, and uses the theoretical background presented in Classical Mechanics: Kinematics and Statics and Classical Mechanics: Dynamics. It focuses on exhibiting a unique approach, rooted in the classical mechanics, to study mechanical and electromagnetic processes occurring in Mechatronics. Contrary to the majority of the books devoted to Applied Mechanics, this volume places a particular emphasis on theory, modeling, analysis, and control of gyroscopic devices, including the military applications. This volume provides practicing mechanical/mechatronic engineers and designers, researchers, graduate and postgraduate students with a knowledge of mechanics focused directly on advanced applications.

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271

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Springer Science & Business Media

Published Date

ISBN 10

1461439787

ISBN 13

9781461439783

Ordinary Differential Equations and Mechanical Systems

By: Jan Awrejcewicz

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Ordinary Differential Equations and Mechanical Systems

By: Jan Awrejcewicz

This book applies a step-by-step treatment of the current state-of-the-art of ordinary differential equations used in modeling of engineering systems/processes and beyond. It covers systematically ordered problems, beginning with first and second order ODEs, linear and higher-order ODEs of polynomial form, theory and criteria of similarity, modeling approaches, phase plane and phase space concepts, stability optimization and ending on chaos and synchronization. Presenting both an overview of the theory of the introductory differential equations in the context of applicability and a systematic treatment of modeling of numerous engineering and physical problems through linear and non-linear ODEs, the volume is self-contained, yet serves both scientific and engineering interests. The presentation relies on a general treatment, analytical and numerical methods, concrete examples and engineering intuition. The scientific background used is well balanced between elementary and advanced level, making it as a unique self-contained source for both theoretically and application oriented graduate and doctoral students, university teachers, researchers and engineers of mechanical, civil and mechatronic engineering.

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621

Publisher

Springer

Published Date

ISBN 10

3319076590

ISBN 13

9783319076591

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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351

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3662089920

ISBN 13

9783662089927

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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424

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Springer Science & Business Media

Published Date

ISBN 10

3540776761

ISBN 13

9783540776765

Approximate Models of Mechanics of Composites

An Asymptotic Approach

By: Igor V. Andrianov,Jan Awrejcewicz,Galina A. Starushenko

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Approximate Models of Mechanics of Composites

An Asymptotic Approach

By: Igor V. Andrianov,Jan Awrejcewicz,Galina A. Starushenko

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441

Publisher

CRC Press

Published Date

ISBN 10

1000890309

ISBN 13

9781000890303

Bifurcation and Chaos in Nonsmooth Mechanical Systems

By: Jan Awrejcewicz,Claude-Henri Lamarque

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Bifurcation and Chaos in Nonsmooth Mechanical Systems

By: Jan Awrejcewicz,Claude-Henri Lamarque

This book presents the theoretical frame for studying lumped nonsmooth dynamical systems: the mathematical methods are recalled, and adapted numerical methods are introduced (differential inclusions, maximal monotone operators, Filippov theory, Aizerman theory, etc.). Tools available for the analysis of classical smooth nonlinear dynamics (stability analysis, the Melnikov method, bifurcation scenarios, numerical integrators, solvers, etc.) are extended to the nonsmooth frame. Many models and applications arising from mechanical engineering, electrical circuits, material behavior and civil engineering are investigated to illustrate theoretical and computational developments.

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564

Publisher

World Scientific

Published Date

ISBN 10

9812384596

ISBN 13

9789812384591

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

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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615

Publisher

Springer Nature

Published Date

ISBN 10

303037663X

ISBN 13

9783030376635

Nonlinear Dynamics of a Wheeled Vehicle

By: Ryszard Andrzejewski,Jan Awrejcewicz

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Nonlinear Dynamics of a Wheeled Vehicle

By: Ryszard Andrzejewski,Jan Awrejcewicz

On average, 60% of the world's people and cargo is transported by vehicle that move on rubber tires over roadways of various construction, composition, and quality. The number of such vehicles, including automobiles and all manner of trucks, increases continually with a growing positive impact on accessibility and a growing negative impact on interactions among humans and their relationship to the surrounding environment. This multiplicity of vehicles, through their physical impact and their emissions, is responsible for, among other negative results: waste of energy, pollution through emission of harmful compounds, degradation of road surfaces, crowding of roads leading to waste of time and increase of social stress, and decrease in safety and comfort. In particular, the safety of vehicular traffic depends on a man-vehicle-road system that includes both active and passive security controls. In spite of the drawbacks mentioned above, the governments of almost every country in the world not only expect but facilitate improvements in vehicular transport performance in order to increase such parameters as load capacity and driving velocity, while decreasing such parameters as costs to passengers, energy resources investments, fuel consumption, etc. Some of the problems have clear, if not always easily attainable, solutions.

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344

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387243585

ISBN 13

9780387243580

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

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

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424

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Springer Science & Business Media

Published Date

ISBN 10

3540776761

ISBN 13

9783540776765

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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527

Publisher

Springer Science & Business Media

Published Date

ISBN 10

354045246X

ISBN 13

9783540452461

Asymptotic Multiple Scale Method in Time Domain

Multi-Degree-of-Freedom Stationary and Nonstationary Dynamics

By: Jan Awrejcewicz,Roman Starosta,Grażyna Sypniewska-Kamińska

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Asymptotic Multiple Scale Method in Time Domain

Multi-Degree-of-Freedom Stationary and Nonstationary Dynamics

By: Jan Awrejcewicz,Roman Starosta,Grażyna Sypniewska-Kamińska

This book offers up novel research which uses analytical approaches to explore nonlinear features exhibited by various dynamic processes. Relevant to disciplines across engineering and physics, the asymptotic method combined with the multiple scale method is shown to be an efficient and intuitive way to approach mechanics. Beginning with new material on the development of cutting-edge asymptotic methods and multiple scale methods, the book introduces this method in time domain and provides examples of vibrations of systems. Clearly written throughout, it uses innovative graphics to exemplify complex concepts such as nonlinear stationary and nonstationary processes, various resonances and jump pull-in phenomena. It also demonstrates the simplification of problems through using mathematical modelling, by employing the use of limiting phase trajectories to quantify nonlinear phenomena. Particularly relevant to structural mechanics, in rods, cables, beams, plates and shells, as well as mechanical objects commonly found in everyday devices such as mobile phones and cameras, the book shows how each system is modelled, and how it behaves under various conditions. It will be of interest to engineers and professionals in mechanical engineering and structural engineering, alongside those interested in vibrations and dynamics. It will also be useful to those studying engineering maths and physics.

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506

Publisher

CRC Press

Published Date

ISBN 10

1000581276

ISBN 13

9781000581270

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

310

Publisher

Springer

Published Date

ISBN 10

3642720803

ISBN 13

9783642720802

Smooth And Nonsmooth High Dimensional Chaos And The Melnikov-type Methods

By: Jan Awrejcewicz,Mariusz M Holicke

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Smooth And Nonsmooth High Dimensional Chaos And The Melnikov-type Methods

By: Jan Awrejcewicz,Mariusz M Holicke

This book focuses on the development of Melnikov-type methods applied to high dimensional dynamical systems governed by ordinary differential equations. Although the classical Melnikov's technique has found various applications in predicting homoclinic intersections, it is devoted only to the analysis of three-dimensional systems (in the case of mechanics, they represent one-degree-of-freedom nonautonomous systems). This book extends the classical Melnikov's approach to the study of high dimensional dynamical systems, and uses simple models of dry friction to analytically predict the occurrence of both stick-slip and slip-slip chaotic orbits, research which is very rarely reported in the existing literature even on one-degree-of-freedom nonautonomous dynamics.This pioneering attempt to predict the occurrence of deterministic chaos of nonlinear dynamical systems will attract many researchers including applied mathematicians, physicists, as well as practicing engineers. Analytical formulas are explicitly formulated step-by-step, even attracting potential readers without a rigorous mathematical background.

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Page Count

318

Publisher

World Scientific

Published Date

ISBN 10

9814474649

ISBN 13

9789814474641

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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785

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540342621

ISBN 13

9783540342625

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

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432

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Springer Science & Business Media

Published Date

ISBN 10

3642556779

ISBN 13

9783642556777

Asymptotical Mechanics of Composites

Modelling Composites without FEM

By: Igor V. Andrianov,Jan Awrejcewicz,Vladyslav V. Danishevskyy

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Asymptotical Mechanics of Composites

Modelling Composites without FEM

By: Igor V. Andrianov,Jan Awrejcewicz,Vladyslav V. Danishevskyy

In this book the authors show that it is possible to construct efficient computationally oriented models of multi-parameter complex systems by using asymptotic methods, which can, owing to their simplicity, be directly used for controlling processes arising in connection with composite material systems. The book focuses on this asymptotic-modeling-based approach because it allows us to define the most important out of numerous parameters describing the system, or, in other words, the asymptotic methods allow us to estimate the sensitivity of the system parameters. Further, the book addresses the construction of nonlocal and higher-order homogenized models. Local fields on the micro-level and the influence of so-called non-ideal contact between the matrix and inclusions are modeled and investigated. The book then studies composites with non-regular structure and cluster type composite conductivity, and analyzes edge effects in fiber composite materials. Transition of load from a fiber to a matrix for elastic and viscoelastic composites, various types of fiber composite fractures, and buckling of fibers in fiber-reinforced composites is also investigated. Last but not least, the book includes studies on perforated membranes, plates, and shells, as well as the asymptotic modeling of imperfect nonlinear interfaces.

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333

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Springer

Published Date

ISBN 10

3319657860

ISBN 13

9783319657868

Dynamics Of Mechatronics Systems: Modeling, Simulation, Control, Optimization And Experimental Investigations

By: Jan Awrejcewicz,Donat Lewandowski,Pawel Olejnik

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Dynamics Of Mechatronics Systems: Modeling, Simulation, Control, Optimization And Experimental Investigations

By: Jan Awrejcewicz,Donat Lewandowski,Pawel Olejnik

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357

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World Scientific

Published Date

ISBN 10

9813146567

ISBN 13

9789813146563

Nonsmooth Dynamics of Contacting Thermoelastic Bodies

By: Jan Awrejcewicz,Yuriy Pyr'yev

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Nonsmooth Dynamics of Contacting Thermoelastic Bodies

By: Jan Awrejcewicz,Yuriy Pyr'yev

This work is devoted to an intensive study in contact mechanics, treating the nonsmooth dynamics of contacting bodies. Mathematical modeling is illustrated and discussed in numerous examples of engineering objects working in different kinematic and dynamic environments. Topics covered in five self-contained chapters examine non-steady dynamic phenomena which are determined by key factors: i.e., heat conduction, thermal stresses, and the amount of wearing. New to this monograph is the importance of the inertia factor, which is considered on par with thermal stresses. Nonsmooth Dynamics of Contacting Thermoelastic Bodies is an engaging accessible practical reference for engineers (civil, mechanical, industrial) and researchers in theoretical and applied mechanics, applied mathematics, physicists, and graduate students.

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256

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387096531

ISBN 13

9780387096537

Bifurcation and Chaos in Coupled Oscillators

By: Jan Awrejcewicz

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Bifurcation and Chaos in Coupled Oscillators

By: Jan Awrejcewicz

This book develops a general methodological approach to investigate complex physical systems presented by the author in a previous book. The nonlinear dynamics of coupled oscillators is investigated numerically and analytically. Three different mechanical, and one biomechanical, examples are used to demonstrate a general systematical approach to the study of dissipative dynamical systems. Many original examples of special chaotic behavior are discussed and illustrated.

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Page Count

266

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World Scientific

Published Date

ISBN 10

9810205791

ISBN 13

9789810205799

Classical Mechanics

Hamiltonian and Lagrangian Formalism

By: Alexei Deriglazov

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Classical Mechanics

Hamiltonian and Lagrangian Formalism

By: Alexei Deriglazov

The revised edition of this advanced textbook provides the reader with a solid grounding in the formalism of classical mechanics, underlying a number of powerful mathematical methods that are widely used in modern theoretical and mathematical physics. It reviews the fundamentals of Lagrangian and Hamiltonian mechanics, and goes on to cover related topics such as canonical transformations, integral invariants, potential motion in geometric setting, symmetries, the Noether theorem and systems with constraints. While in some cases the formalism is developed beyond the traditional level adopted in the standard textbooks on classical mechanics, only elementary mathematical methods are used in the exposition of the material. New material for the revised edition includes additional sections on the Euler-Lagrange equation, the Cartan two-form in Lagrangian theory, and Newtonian equations of motion in context of general relativity. Also new for this edition is the inclusion of problem sets and solutions to aid in the understanding of the material presented. The mathematical constructions involved are explicitly described and explained, so the book is a good starting point for the student new to this field. Where possible, intuitive motivations are replaced by explicit proofs and direct computations, preserving the level of rigor that makes the book useful for more advanced students intending to work in one of the branches of the vast field of theoretical physics. To illustrate how classical-mechanics formalism works in other branches of theoretical physics, examples related to electrodynamics, as well as to relativistic and quantum mechanics, are included.

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Page Count

455

Publisher

Springer

Published Date

ISBN 10

3319441477

ISBN 13

9783319441474

Bifurcation And Chaos In Simple Dynamical Systems

By: Jan Awrejcewicz

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Bifurcation And Chaos In Simple Dynamical Systems

By: Jan Awrejcewicz

This book presents a detailed analysis of bifurcation and chaos in simple non-linear systems, based on previous works of the author. Practical examples for mechanical and biomechanical systems are discussed. The use of both numerical and analytical approaches allows for a deeper insight into non-linear dynamical phenomena. The numerical and analytical techniques presented do not require specific mathematical knowledge.

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138

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World Scientific

Published Date

ISBN 10

9814520055

ISBN 13

9789814520058

Perspectives in Dynamical Systems II: Mathematical and Numerical Approaches

DSTA, Łódź, Poland December 2–5, 2019

By: Jan Awrejcewicz

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Perspectives in Dynamical Systems II: Mathematical and Numerical Approaches

DSTA, Łódź, Poland December 2–5, 2019

By: Jan Awrejcewicz

This volume is part of collection of contributions devoted to analytical and experimental techniques of dynamical systems, presented at the 15th International Conference “Dynamical Systems: Theory and Applications”, held in Łódź, Poland on December 2-5, 2019. The wide selection of material has been divided into three volumes, each focusing on a different field of applications of dynamical systems. The broadly outlined focus of both the conference and these books includes bifurcations and chaos in dynamical systems, asymptotic methods in nonlinear dynamics, dynamics in life sciences and bioengineering, original numerical methods of vibration analysis, control in dynamical systems, optimization problems in applied sciences, stability of dynamical systems, experimental and industrial studies, vibrations of lumped and continuous systems, non-smooth systems, engineering systems and differential equations, mathematical approaches to dynamical systems, and mechatronics.

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Page Count

297

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Springer Nature

Published Date

ISBN 10

3030773108

ISBN 13

9783030773106

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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577

Publisher

World Scientific

Published Date

ISBN 10

9814719714

ISBN 13

9789814719711

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