Lectures On Viscoelasticity Theory

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Lectures on Viscoelasticity Theory

Allen C. Pipkin
Lectures on Viscoelasticity Theory Book PDF

Author : Allen C. Pipkin
Publisher : Springer Science & Business Media
Page : 190 pages
File Size : 51,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461599708

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Lectures on Viscoelasticity Theory by Allen C. Pipkin Pdf

This book contains notes for a one-semester course on viscoelasticity given in the Division of Applied Mathematics at Brown University. The course serves as an introduction to viscoelasticity and as a workout in the use of various standard mathematical methods. The reader will soon find that he needs to do some work on the side to fill in details that are omitted from the text. These are notes, not a completely de tailed explanation. Furthermore, much of the content of the course is in the prob lems assigned for solution by the student. The reader who does not at least try to solve a good many of the problems is likely to miss most of the point. Much that is known about viscoelasticity is not discussed in these notes, and references to original sources are usually not given, so it will be difficult or impossible to use this book as a reference for looking things up. Readers wanting something more like a treatise should see Ferry's Viscoelastic Properties of Polymers, Lodge's Elastic Liquids, the volumes edited by Eirich on Rheology, or any issue of the Transactions of the Society of Rheology. These works emphasize physical aspects of the subject. On the mathematical side, Gurtin and Sternberg's long paper On the Linear Theory of Viscoelasticity (ARMA~, 291(1962)) remains the best reference for proofs of theorems.

Lectures on Viscoelasticity Theory

A.C. Pipkin
Lectures on Viscoelasticity Theory Book PDF

Author : A.C. Pipkin
Publisher : Springer
Page : 188 pages
File Size : 49,9 Mb
Release : 2011-09-27
Category : Science
ISBN : 1461210798

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Lectures on Viscoelasticity Theory by A.C. Pipkin Pdf

This book contains notes for a one-semester course on viscoelasticity given in the Division of Applied Mathematics at Brown University. The course serves as an introduction to viscoelasticity and as a workout in the use of various standard mathematical methods. The reader will soon find that he needs to do some work on the side to fill in details that are omitted from the text. These are notes, not a completely detailed explanation. Furthermore, much of the content of the course is in the problems assigned for solution by the student. The reader who does not at least try to solve a good many of the problems is likely to miss most of the point. Much that is known about viscoelasticity is not discussed in these notes, and references to original sources are usually not give, so it will be difficult or impossible to use this book as a reference for looking things up. Readers wanting something more like a treatise should see Ferry's Viscoelastic Properties of Polymers, Lodge's Elastic Liquids, the volumes edited by Eirich on Rheology, or any issue of the Transactions of the Society of Rheology. These works emphasize physical aspects of the subject. On the mathematical side, Gurtin and Sternberg's long paper On the Linear Theory of Viscoelasticity (ARMA II, 291 (I962» remains the best reference for proofs of theorems.

Theory of Viscoelasticity

R. M. Christensen
Theory of Viscoelasticity Book PDF

Author : R. M. Christensen
Publisher : Courier Corporation
Page : 384 pages
File Size : 40,7 Mb
Release : 2013-04-26
Category : Technology & Engineering
ISBN : 9780486318967

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Theory of Viscoelasticity by R. M. Christensen Pdf

Integration of theoretical developments offers complete description of linear theory of viscoelastic behavior of materials, with theoretical formulations derived from continuum mechanics viewpoint and discussions of problem solving. 1982 edition.

The Phenomenological Theory of Linear Viscoelastic Behavior

Nicholas W. Tschoegl
The Phenomenological Theory of Linear Viscoelastic Behavior Book PDF

Author : Nicholas W. Tschoegl
Publisher : Springer Science & Business Media
Page : 791 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642736025

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The Phenomenological Theory of Linear Viscoelastic Behavior by Nicholas W. Tschoegl Pdf

One of the principal objects of theoretical research in any department of knowledge is to find the point of view from which the subject appears in its greatest simplicity. J. Willard Gibbs This book is an outgrowth of lectures I have given, on and off over some sixteen years, in graduate courses at the California Institute of Technology, and, in abbreviated form, elsewhere. It is, nevertheless, not meant to be a textbook. I have aimed at a full exposition of the phenomenological theory of linear viscoelastic behavior for the use of the practicing scientist or engineer as well as the academic teacher or student. The book is thus primarily a reference work. In accord with the motto above, I have chosen to describe the theory of linear viscoelastic behavior through the use of the Laplace transformation. The treatment oflinear time-dependent systems in terms of the Laplace transforms of the relations between the excitation add response variables has by now become commonplace in other fields. With some notable exceptions, it has not been widely used in viscoelasticity. I hope that the reader will find this approach useful.

The Theory of Linear Viscoelasticity

D. R. Bland
The Theory of Linear Viscoelasticity Book PDF

Author : D. R. Bland
Publisher : Courier Dover Publications
Page : 144 pages
File Size : 55,9 Mb
Release : 2016-10-05
Category : Technology & Engineering
ISBN : 9780486816388

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The Theory of Linear Viscoelasticity by D. R. Bland Pdf

This concise introduction to the concepts of viscoelasticity focuses on stress analysis. Three detailed sections present examples of stress-related problems, including sinusoidal oscillation problems, quasi-static problems, and dynamic problems. 1960 edition.

Fluid Dynamics of Viscoelastic Liquids

Daniel D. Joseph
Fluid Dynamics of Viscoelastic Liquids Book PDF

Author : Daniel D. Joseph
Publisher : Springer Science & Business Media
Page : 772 pages
File Size : 40,7 Mb
Release : 2013-11-27
Category : Science
ISBN : 9781461244622

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Fluid Dynamics of Viscoelastic Liquids by Daniel D. Joseph Pdf

This book is about two special topics in rheological fluid mechanics: the elasticity of liquids and asymptotic theories of constitutive models. The major emphasis of the book is on the mathematical and physical consequences of the elasticity of liquids; seventeen of twenty chapters are devoted to this. Constitutive models which are instantaneously elastic can lead to some hyperbolicity in the dynamics of flow, waves of vorticity into rest (known as shear waves), to shock waves of vorticity or velocity, to steady flows of transonic type or to short wave instabilities which lead to ill-posed problems. Other kinds of models, with small Newtonian viscosities, give rise to perturbed instantaneous elasticity, associated with smoothing of discontinuities as in gas dynamics. There is no doubt that liquids will respond like elastic solids to impulses which are very rapid compared to the time it takes for the molecular order associated with short range forces in the liquid, to relax. After this, all liquids look viscous with signals propagating by diffusion rather than by waves. For small molecules this time of relaxation is estimated as lQ-13 to 10-10 seconds depending on the fluids. Waves associated with such liquids move with speeds of 1 QS cm/s, or even faster. For engineering applications the instantaneous elasticity of these fluids is of little interest; the practical dynamics is governed by diffusion, ·say, by the Navier-Stokes equations. On the other hand, there are other liquids which are known to have much longer times of relaxation.

Polymer Viscoelasticity

Evaristo Riande,Ricardo Diaz-Calleja,Margarita Prolongo,Rosa Masegosa,Catalina Salom
Polymer Viscoelasticity Book PDF

Author : Evaristo Riande,Ricardo Diaz-Calleja,Margarita Prolongo,Rosa Masegosa,Catalina Salom
Publisher : CRC Press
Page : 904 pages
File Size : 40,6 Mb
Release : 1999-11-05
Category : Technology & Engineering
ISBN : 9781482293241

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Polymer Viscoelasticity by Evaristo Riande,Ricardo Diaz-Calleja,Margarita Prolongo,Rosa Masegosa,Catalina Salom Pdf

Showcasing vital engineering applications to transient and dynamic pertubations of macromolecular materials, structural recovery's role in mechanical responses in the glassy state, and viscoelastic parameters that condition the non-Newtonian behaviour of polymers, this work presents a systematic account of the responses of macromolecular materials

Boundary Value Problems in Linear Viscoelasticity

John M. Golden,George A.C. Graham
Boundary Value Problems in Linear Viscoelasticity Book PDF

Author : John M. Golden,George A.C. Graham
Publisher : Springer Science & Business Media
Page : 276 pages
File Size : 47,7 Mb
Release : 2013-04-17
Category : Science
ISBN : 9783662061565

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Boundary Value Problems in Linear Viscoelasticity by John M. Golden,George A.C. Graham Pdf

The classical theories of Linear Elasticity and Newtonian Fluids, though trium phantly elegant as mathematical structures, do not adequately describe the defor mation and flow of most real materials. Attempts to characterize the behaviour of real materials under the action of external forces gave rise to the science of Rheology. Early rheological studies isolated the phenomena now labelled as viscoelastic. Weber (1835, 1841), researching the behaviour of silk threats under load, noted an instantaneous extension, followed by a further extension over a long period of time. On removal of the load, the original length was eventually recovered. He also deduced that the phenomena of stress relaxation and damping of vibrations should occur. Later investigators showed that similar effects may be observed in other materials. The German school referred to these as "Elastische Nachwirkung" or "the elastic aftereffect" while the British school, including Lord Kelvin, spoke ofthe "viscosityofsolids". The universal adoption of the term "Viscoelasticity", intended to convey behaviour combining proper ties both of a viscous liquid and an elastic solid, is of recent origin, not being used for example by Love (1934), though Alfrey (1948) uses it in the context of polymers. The earliest attempts at mathematically modelling viscoelastic behaviour were those of Maxwell (1867) (actually in the context of his work on gases; he used this model for calculating the viscosity of a gas) and Meyer (1874).

Solid Mechanics, Theory of Elasticity and Creep

Holm Altenbach,Suren Manuk Mkhitaryan,Vahram Hakobyan,Avetik Varazdat Sahakyan
Solid Mechanics Theory of Elasticity and Creep Book PDF

Author : Holm Altenbach,Suren Manuk Mkhitaryan,Vahram Hakobyan,Avetik Varazdat Sahakyan
Publisher : Springer Nature
Page : 384 pages
File Size : 41,5 Mb
Release : 2023-02-06
Category : Science
ISBN : 9783031185649

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Solid Mechanics, Theory of Elasticity and Creep by Holm Altenbach,Suren Manuk Mkhitaryan,Vahram Hakobyan,Avetik Varazdat Sahakyan Pdf

This book presents fundamental theoretical and experimental studies of well-known scientists in solid mechanics, hydromechanics, aeromechanics, biomechanics, etc. These studies relate to contact and mixed problems of the theory of elasticity and viscoelasticity, tribology, fracture mechanics, electroelasticity, magnetoelasticity, as well as to the theory of anisotropic shells and plates and are aimed at application in various areas of engineering practice. The book is devoted to the 110th birthday of academician N.Kh. Arutunyan.

Bifurcation Theory

Hansjörg Kielhöfer
Bifurcation Theory Book PDF

Author : Hansjörg Kielhöfer
Publisher : Springer Science & Business Media
Page : 355 pages
File Size : 40,6 Mb
Release : 2006-04-10
Category : Mathematics
ISBN : 9780387216331

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Bifurcation Theory by Hansjörg Kielhöfer Pdf

In the past three decades, bifurcation theory has matured into a well-established and vibrant branch of mathematics. This book gives a unified presentation in an abstract setting of the main theorems in bifurcation theory, as well as more recent and lesser known results. It covers both the local and global theory of one-parameter bifurcations for operators acting in infinite-dimensional Banach spaces, and shows how to apply the theory to problems involving partial differential equations. In addition to existence, qualitative properties such as stability and nodal structure of bifurcating solutions are treated in depth. This volume will serve as an important reference for mathematicians, physicists, and theoretically-inclined engineers working in bifurcation theory and its applications to partial differential equations.

Introduction to Spectral Theory

P.D. Hislop,I.M. Sigal
Introduction to Spectral Theory Book PDF

Author : P.D. Hislop,I.M. Sigal
Publisher : Springer Science & Business Media
Page : 331 pages
File Size : 46,6 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461207412

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Introduction to Spectral Theory by P.D. Hislop,I.M. Sigal Pdf

The intention of this book is to introduce students to active areas of research in mathematical physics in a rather direct way minimizing the use of abstract mathematics. The main features are geometric methods in spectral analysis, exponential decay of eigenfunctions, semi-classical analysis of bound state problems, and semi-classical analysis of resonance. A new geometric point of view along with new techniques are brought out in this book which have both been discovered within the past decade. This book is designed to be used as a textbook, unlike the competitors which are either too fundamental in their approach or are too abstract in nature to be considered as texts. The authors' text fills a gap in the marketplace.

Theory of Multicomponent Fluids

Donald A. Drew,Stephen L. Passman
Theory of Multicomponent Fluids Book PDF

Author : Donald A. Drew,Stephen L. Passman
Publisher : Springer Science & Business Media
Page : 311 pages
File Size : 54,6 Mb
Release : 2006-05-10
Category : Mathematics
ISBN : 9780387226378

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Theory of Multicomponent Fluids by Donald A. Drew,Stephen L. Passman Pdf

An exposition of the derivation and use of equations of motion for two-phase flow. The approach taken derives the equations of motion using ensemble averaging, and compares them with those derived from control volume methods. Closure for dispersed flows is discussed, and some fundamental solutions are given. The work focuses on the fundamental aspects of two-phase flow, and is intended to give the reader a background for understanding the dynamics as well as a system of equations that can be used in predictions of the behavior of dispersed two-phase flows. The exposition in terms of ensemble averaging is new, and combining it with modern continuum mechanics concepts makes this book unique. Intended for engineering, mathematics and physics researchers and advanced graduate students working in the field.

Elements of Applied Bifurcation Theory

Yuri Kuznetsov
Elements of Applied Bifurcation Theory Book PDF

Author : Yuri Kuznetsov
Publisher : Springer Science & Business Media
Page : 594 pages
File Size : 55,5 Mb
Release : 2008-01-10
Category : Mathematics
ISBN : 9780387227108

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Elements of Applied Bifurcation Theory by Yuri Kuznetsov Pdf

Providing readers with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems, the focus here is on efficient numerical implementations of the developed techniques. The book is designed for advanced undergraduates or graduates in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the first while updating the context to incorporate recent theoretical developments, in particular new and improved numerical methods for bifurcation analysis.

Nonlinear Theory of Shallow Shells

Iosif I. Vorovich
Nonlinear Theory of Shallow Shells Book PDF

Author : Iosif I. Vorovich
Publisher : Springer Science & Business Media
Page : 404 pages
File Size : 54,6 Mb
Release : 2008-01-08
Category : Technology & Engineering
ISBN : 9780387227764

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Nonlinear Theory of Shallow Shells by Iosif I. Vorovich Pdf

This book presents rigorous treatment of boundary value problems in nonlinear theory of shallow shells. The consideration of the problems is carried out using methods of nonlinear functional analysis.

Robust Control Theory in Hilbert Space

Avraham Feintuch
Robust Control Theory in Hilbert Space Book PDF

Author : Avraham Feintuch
Publisher : Springer Science & Business Media
Page : 234 pages
File Size : 51,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461205913

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Robust Control Theory in Hilbert Space by Avraham Feintuch Pdf

An operator theoretic approach to robust control analysis for linear time-varying systems, with the emphasis on the conceptual similarity with the H control theory for time-invariant systems. It clarifies the major difficulties confronted in the time varying case and all the necessary operator theory is developed from first principles, making the book as self-contained as possible. After presenting the necessary results from the theories of Toeplitz operators and nest algebras, linear systems are defined as input-output operators and the relationship between stabilisation and the existence of co-prime factorisations is described. Uniform optimal control problems are formulated as model-matching problems and are reduced to four block problems, while robustness is considered both from the point of view of fractional representations and the "time varying gap" metric, as is the relationship between these types of uncertainties. The book closes with the solution of the orthogonal embedding problem for time-varying contractive systems. As such, this book is useful to both mathematicians and to control engineers.