Modeling Nonlinear Problems In The Mechanics Of Strings And Rods

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Modeling Nonlinear Problems in the Mechanics of Strings and Rods

Oliver M. O'Reilly
Modeling Nonlinear Problems in the Mechanics of Strings and Rods Book PDF

Author : Oliver M. O'Reilly
Publisher : Springer
Page : 425 pages
File Size : 46,5 Mb
Release : 2017-03-10
Category : Mathematics
ISBN : 9783319505985

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Modeling Nonlinear Problems in the Mechanics of Strings and Rods by Oliver M. O'Reilly Pdf

This book presents theories of deformable elastic strings and rods and their application to broad classes of problems. Readers will gain insights into the formulation and analysis of models for mechanical and biological systems. Emphasis is placed on how the balance laws interplay with constitutive relations to form a set of governing equations. For certain classes of problems, it is shown how a balance of material momentum can play a key role in forming the equations of motion. The first half of the book is devoted to the purely mechanical theory of a string and its applications. The second half of the book is devoted to rod theories, including Euler’s theory of the elastica, Kirchhoff ’s theory of an elastic rod, and a range of Cosserat rod theories. A variety of classic and recent applications of these rod theories are examined. Two supplemental chapters, the first on continuum mechanics of three-dimensional continua and the second on methods from variational calculus, are included to provide relevant background for students. This book is suited for graduate-level courses on the dynamics of nonlinearly elastic rods and strings.

A Primer on the Kinematics of Discrete Elastic Rods

M. Khalid Jawed,Alyssa Novelia,Oliver M. O'Reilly
A Primer on the Kinematics of Discrete Elastic Rods Book PDF

Author : M. Khalid Jawed,Alyssa Novelia,Oliver M. O'Reilly
Publisher : Springer
Page : 118 pages
File Size : 53,6 Mb
Release : 2018-05-04
Category : Technology & Engineering
ISBN : 9783319769653

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A Primer on the Kinematics of Discrete Elastic Rods by M. Khalid Jawed,Alyssa Novelia,Oliver M. O'Reilly Pdf

This primer discusses a numerical formulation of the theory of an elastic rod, known as a discrete elastic rod, that was recently developed in a series of papers by Miklós Bergou et al. Their novel formulation of discrete elastic rods represents an exciting new method to simulate and analyze the behavior of slender bodies that can be modeled using an elastic rod. The formulation has been extensively employed in computer graphics and is highly cited. In the primer, we provide relevant background from both discrete and classical differential geometry so a reader familiar with classic rod theories can appreciate, comprehend, and use Bergou et al.’s computational efficient formulation of a nonlinear rod theory. The level of coverage is suitable for graduate students in mechanics and engineering sciences.

Graph-Based Modelling in Science, Technology and Art

Stanisław Zawiślak,Jacek Rysiński
Graph Based Modelling in Science Technology and Art Book PDF

Author : Stanisław Zawiślak,Jacek Rysiński
Publisher : Springer Nature
Page : 311 pages
File Size : 41,7 Mb
Release : 2021-08-01
Category : Technology & Engineering
ISBN : 9783030767877

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Graph-Based Modelling in Science, Technology and Art by Stanisław Zawiślak,Jacek Rysiński Pdf

This book presents interdisciplinary, cutting-edge and creative applications of graph theory and modeling in science, technology, architecture and art. Topics are divided into three parts: the first one examines mechanical problems related to gears, planetary gears and engineering installations; the second one explores graph-based methods applied to medical analyses as well as biological and chemical modeling; and the third part includes various topics e.g. drama analysis, aiding of design activities and network visualisation. The authors represent several countries in Europe and America, and their contributions show how different, useful and fruitful the utilization of graphs in modelling of engineering systems can be. The book has been designed to serve readers interested in the subject of graph modelling and those with expertise in related areas, as well as members of the worldwide community of graph modelers.

IUTAM Symposium on Exploiting Nonlinear Dynamics for Engineering Systems

Ivana Kovacic,Stefano Lenci
IUTAM Symposium on Exploiting Nonlinear Dynamics for Engineering Systems Book PDF

Author : Ivana Kovacic,Stefano Lenci
Publisher : Springer
Page : 316 pages
File Size : 51,6 Mb
Release : 2019-07-24
Category : Technology & Engineering
ISBN : 9783030236922

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IUTAM Symposium on Exploiting Nonlinear Dynamics for Engineering Systems by Ivana Kovacic,Stefano Lenci Pdf

This is the proceedings of the IUTAM Symposium on Exploiting Nonlinear Dynamics for Engineering Systems that was held in Novi Sad, Serbia, from July 15th to 19th, 2018. The appearance of nonlinear phenomena used to be perceived as dangerous, with a general tendency to avoid them or control them. This perception has led to intensive research using various approaches and tailor-made tools developed over decades. However, the Nonlinear Dynamics of today is experiencing a profound shift of paradigm since recent investigations rely on a different strategy which brings good effects of nonlinear phenomena to the forefront. This strategy has a positive impact on different fields in science and engineering, such as vibration isolation, energy harvesting, micro/nano-electro-mechanical systems, etc. Therefore, the ENOLIDES Symposium was devoted to demonstrate the benefits and to unlock the potential of exploiting nonlinear dynamical behaviour in these but also in other emerging fields of science and engineering. This proceedings is useful for researchers in the fields of nonlinear dynamics of mechanical systems and structures, and in Mechanical and Civil Engineering.

50+ Years of AIMETA

Giuseppe Rega
50 Years of AIMETA Book PDF

Author : Giuseppe Rega
Publisher : Springer Nature
Page : 505 pages
File Size : 44,7 Mb
Release : 2022-06-04
Category : Technology & Engineering
ISBN : 9783030941956

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50+ Years of AIMETA by Giuseppe Rega Pdf

The book retraces the history of the Italian Association of Theoretical and Applied Mechanics (AIMETA) since its establishment in 1965. AIMETA is the official Italian association of mechanics adhering to IUTAM (International Union of Theoretical and Applied Mechanics), which organizes and coordinates a meaningful number of research activities, the most important of which are the biennial National Congress and the internationally renowned journal “Meccanica”, published by Springer. Besides collecting and organizing all related important data and information, as far as possible, by distinguishing among the five scientific areas – general mechanics, solids, structures, fluids, machines – encompassed by AIMETA, the history of the association is assumed as a proper perspective to overview the evolution of theoretical and applied mechanics in Italy over about the last fifty years. This is accomplished in the first part of the book. with also a specific focus on the mechanics of solids and structures, where the biographies of a meaningful number of recognized Italian scholars of mechanics in all areas are also provided, along with testimonials and memories by a few senior people meaningfully involved with AIMETA and Italian mechanics. The second part gives an account, although unavoidably incomplete, of recent developments of mechanical sciences in Italy, as reflected also in the activities of AIMETA and with reference to the international context. Contributions by a number of invited senior scholars, still very active, consist of overviews on some scientific themes in the various areas, summaries of achievements of research groups, expressions of research viewpoints, prospects for future developments.

Nonlinear Problems of Elasticity

S.S Antman
Nonlinear Problems of Elasticity Book PDF

Author : S.S Antman
Publisher : Springer
Page : 752 pages
File Size : 40,6 Mb
Release : 2012-12-22
Category : Mathematics
ISBN : 1475741480

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Nonlinear Problems of Elasticity by S.S Antman Pdf

The scientists of the seventeenth and eighteenth centuries, led by Jas. Bernoulli and Euler, created a coherent theory of the mechanics of strings and rods undergoing planar deformations. They introduced the basic con cepts of strain, both extensional and flexural, of contact force with its com ponents of tension and shear force, and of contact couple. They extended Newton's Law of Motion for a mass point to a law valid for any deformable body. Euler formulated its independent and much subtler complement, the Angular Momentum Principle. (Euler also gave effective variational characterizations of the governing equations. ) These scientists breathed life into the theory by proposing, formulating, and solving the problems of the suspension bridge, the catenary, the velaria, the elastica, and the small transverse vibrations of an elastic string. (The level of difficulty of some of these problems is such that even today their descriptions are sel dom vouchsafed to undergraduates. The realization that such profound and beautiful results could be deduced by mathematical reasoning from fundamental physical principles furnished a significant contribution to the intellectual climate of the Age of Reason. ) At first, those who solved these problems did not distinguish between linear and nonlinear equations, and so were not intimidated by the latter. By the middle of the nineteenth century, Cauchy had constructed the basic framework of three-dimensional continuum mechanics on the founda tions built by his eighteenth-century predecessors.

Nonlinear Problems of Elasticity

Stuart Antman
Nonlinear Problems of Elasticity Book PDF

Author : Stuart Antman
Publisher : Springer Science & Business Media
Page : 762 pages
File Size : 49,5 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475741476

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Nonlinear Problems of Elasticity by Stuart Antman Pdf

The scientists of the seventeenth and eighteenth centuries, led by Jas. Bernoulli and Euler, created a coherent theory of the mechanics of strings and rods undergoing planar deformations. They introduced the basic con cepts of strain, both extensional and flexural, of contact force with its com ponents of tension and shear force, and of contact couple. They extended Newton's Law of Motion for a mass point to a law valid for any deformable body. Euler formulated its independent and much subtler complement, the Angular Momentum Principle. (Euler also gave effective variational characterizations of the governing equations. ) These scientists breathed life into the theory by proposing, formulating, and solving the problems of the suspension bridge, the catenary, the velaria, the elastica, and the small transverse vibrations of an elastic string. (The level of difficulty of some of these problems is such that even today their descriptions are sel dom vouchsafed to undergraduates. The realization that such profound and beautiful results could be deduced by mathematical reasoning from fundamental physical principles furnished a significant contribution to the intellectual climate of the Age of Reason. ) At first, those who solved these problems did not distinguish between linear and nonlinear equations, and so were not intimidated by the latter. By the middle of the nineteenth century, Cauchy had constructed the basic framework of three-dimensional continuum mechanics on the founda tions built by his eighteenth-century predecessors.

Nonlinear Problems of Elasticity

S.S Antman
Nonlinear Problems of Elasticity Book PDF

Author : S.S Antman
Publisher : Springer
Page : 0 pages
File Size : 46,6 Mb
Release : 2012-02-25
Category : Mathematics
ISBN : 0387501029

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Nonlinear Problems of Elasticity by S.S Antman Pdf

Enlarged, updated, and extensively revised, this second edition illuminates specific problems of nonlinear elasticity, emphasizing the role of nonlinear material response. Opening chapters discuss strings, rods, and shells, and applications of bifurcation theory and the calculus of variations to problems for these bodies. Subsequent chapters cover tensors, three-dimensional continuum mechanics, three-dimensional elasticity , general theories of rods and shells, and dynamical problems. Each chapter includes interesting, challenging, and tractable exercises.

Mechanics of Generalized Continua

Gérard A. Maugin,Andrei V. Metrikine
Mechanics of Generalized Continua Book PDF

Author : Gérard A. Maugin,Andrei V. Metrikine
Publisher : Springer Science & Business Media
Page : 337 pages
File Size : 49,7 Mb
Release : 2010-03-24
Category : Mathematics
ISBN : 9781441956958

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Mechanics of Generalized Continua by Gérard A. Maugin,Andrei V. Metrikine Pdf

In their 1909 publication Théorie des corps déformables, Eugène and François Cosserat made a historic contribution to materials science by establishing the fundamental principles of the mechanics of generalized continua. The chapters collected in this volume showcase the many areas of continuum mechanics that grew out of the foundational work of the Cosserat brothers. The included contributions provide a detailed survey of the most recent theoretical developments in the field of generalized continuum mechanics and can serve as a useful reference for graduate students and researchers in mechanical engineering, materials science, applied physics and applied mathematics.

Dynamics of Rods

Valery A. Svetlitsky
Dynamics of Rods Book PDF

Author : Valery A. Svetlitsky
Publisher : Springer Science & Business Media
Page : 472 pages
File Size : 47,7 Mb
Release : 2005-04-14
Category : Science
ISBN : 3540242848

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Dynamics of Rods by Valery A. Svetlitsky Pdf

This is the first and only monograph on this subject, and provides a systematic presentation of theoretical fundamentals of the mechanics of rods as well as numerical methods used for practical purposes. Includes problems and solutions for self-study.

Nonlinear Problems of Elasticity

Stuart Antman
Nonlinear Problems of Elasticity Book PDF

Author : Stuart Antman
Publisher : Springer Science & Business Media
Page : 845 pages
File Size : 45,7 Mb
Release : 2005-11-24
Category : Mathematics
ISBN : 9780387276496

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Nonlinear Problems of Elasticity by Stuart Antman Pdf

Enlarged, updated, and extensively revised, this second edition illuminates specific problems of nonlinear elasticity, emphasizing the role of nonlinear material response. Opening chapters discuss strings, rods, and shells, and applications of bifurcation theory and the calculus of variations to problems for these bodies. Subsequent chapters cover tensors, three-dimensional continuum mechanics, three-dimensional elasticity , general theories of rods and shells, and dynamical problems. Each chapter includes interesting, challenging, and tractable exercises.

Nonlinear Problems of Elasticity

Stuart S. Antman
Nonlinear Problems of Elasticity Book PDF

Author : Stuart S. Antman
Publisher : Springer
Page : 0 pages
File Size : 53,6 Mb
Release : 2023-08-28
Category : Mathematics
ISBN : 3031313143

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Nonlinear Problems of Elasticity by Stuart S. Antman Pdf

Enlarged, updated, and extensively revised, this second edition illuminates specific problems of nonlinear elasticity, emphasizing the role of nonlinear material response. Opening chapters discuss strings, rods, and shells, and applications of bifurcation theory and the calculus of variations to problems for these bodies. Subsequent chapters cover tensors, three-dimensional continuum mechanics, three-dimensional elasticity , general theories of rods and shells, and dynamical problems. Each chapter includes interesting, challenging, and tractable exercises.

Asymptotic Multiple Scale Method in Time Domain

Jan Awrejcewicz,Roman Starosta,Grażyna Sypniewska-Kamińska
Asymptotic Multiple Scale Method in Time Domain Book PDF

Author : Jan Awrejcewicz,Roman Starosta,Grażyna Sypniewska-Kamińska
Publisher : CRC Press
Page : 411 pages
File Size : 51,8 Mb
Release : 2022-05-10
Category : Mathematics
ISBN : 9781000581256

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Asymptotic Multiple Scale Method in Time Domain by Jan Awrejcewicz,Roman Starosta,Grażyna Sypniewska-Kamińska Pdf

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.

Nonlinear Dynamics and Stochastic Mechanics

Wolfgang Kliemann
Nonlinear Dynamics and Stochastic Mechanics Book PDF

Author : Wolfgang Kliemann
Publisher : CRC Press
Page : 560 pages
File Size : 43,8 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9781351083508

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Nonlinear Dynamics and Stochastic Mechanics by Wolfgang Kliemann Pdf

Engineering systems have played a crucial role in stimulating many of the modern developments in nonlinear and stochastic dynamics. After 20 years of rapid progress in these areas, this book provides an overview of the current state of nonlinear modeling and analysis for mechanical and structural systems. This volume is a coherent compendium written by leading experts from the United States, Canada, Western and Eastern Europe, and Australia. The 22 articles describe the background, recent developments, applications, and future directions in bifurcation theory, chaos, perturbation methods, stochastic stability, stochastic flows, random vibrations, reliability, disordered systems, earthquake engineering, and numerics. The book gives readers a sophisticated toolbox that will allow them to tackle modeling problems in mechanical systems that use stochastic and nonlinear dynamics ideas. An extensive bibliography and index ensure this volume will remain a reference standard for years to come.

Mechanics and Model-Based Control of Advanced Engineering Systems

Alexander K. Belyaev,Hans Irschik,Michael Krommer
Mechanics and Model Based Control of Advanced Engineering Systems Book PDF

Author : Alexander K. Belyaev,Hans Irschik,Michael Krommer
Publisher : Springer Science & Business Media
Page : 317 pages
File Size : 51,8 Mb
Release : 2013-12-12
Category : Technology & Engineering
ISBN : 9783709115718

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Mechanics and Model-Based Control of Advanced Engineering Systems by Alexander K. Belyaev,Hans Irschik,Michael Krommer Pdf

Mechanics and Model-Based Control of Advanced Engineering Systems collects 32 contributions presented at the International Workshop on Advanced Dynamics and Model Based Control of Structures and Machines, which took place in St. Petersburg, Russia in July 2012. The workshop continued a series of international workshops, which started with a Japan-Austria Joint Workshop on Mechanics and Model Based Control of Smart Materials and Structures and a Russia-Austria Joint Workshop on Advanced Dynamics and Model Based Control of Structures and Machines. In the present volume, 10 full-length papers based on presentations from Russia, 9 from Austria, 8 from Japan, 3 from Italy, one from Germany and one from Taiwan are included, which represent the state of the art in the field of mechanics and model based control, with particular emphasis on the application of advanced structures and machines.