A Generalization Of The Lame And Somigliana Stress Functions For The Dynamic Theory Of Linear Viscoelastic Solids

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A Generalization of the Lame and Somigliana Stress Functions for the Dynamic Theory of Linear Voscoelastic Solids

Author : W. S. Edelstein
Publisher :
ISBN 13 :
Total Pages : 17 pages
Book Rating : 4.:/5 (227 download)

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Book Synopsis A Generalization of the Lame and Somigliana Stress Functions for the Dynamic Theory of Linear Voscoelastic Solids by : W. S. Edelstein

Download or read book A Generalization of the Lame and Somigliana Stress Functions for the Dynamic Theory of Linear Voscoelastic Solids written by W. S. Edelstein and published by . This book was released on 1964 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: A study is made of solutions of the displacement equations of motion appropriate to the dynamic linear theory of homogeneous isotropic, viscoelastic solids. These equations are derived from the fundamental system of field equations. In the absence of body forces, the divergence and curl of the displacement field (or the field itself, provided it is either irrotational or solenoidal) satisfy hereditary wave equations. Such an equation is simply the classical wave equation with the square of the wave velocity replaced by an integral operator of the Volterra type. It also follows that the displacement, strain, and stress fields satisfy iterated hereditary wave equations. Generalizations are introduced to viscoelasticity of the Lame and Somigliana stress function solutions of elastodynamics. By an adaptation of arguments the completeness of the generalized Lame functions is established, and, using this result, the completeness of the viscoelastic Somigliana solution is proved. Next, it is found that every displacement field can be decomposed into the sum of a solenoidal and an irrotational vector, each of which satisfies an hereditary wave equation. (Author).

A Generalization of the Lamé and Somigliana Stress Functions for the Dynamic Theory of Linear Viscoelastic Solids

Author : Warren Stanley Edelstein
Publisher :
ISBN 13 :
Total Pages : 32 pages
Book Rating : 4.:/5 (513 download)

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Book Synopsis A Generalization of the Lamé and Somigliana Stress Functions for the Dynamic Theory of Linear Viscoelastic Solids by : Warren Stanley Edelstein

Download or read book A Generalization of the Lamé and Somigliana Stress Functions for the Dynamic Theory of Linear Viscoelastic Solids written by Warren Stanley Edelstein and published by . This book was released on 1964 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:

U.S. Government Research Reports

Author :
Publisher :
ISBN 13 :
Total Pages : 286 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis U.S. Government Research Reports by :

Download or read book U.S. Government Research Reports written by and published by . This book was released on 1964 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Scientific and Technical Aerospace Reports

Author :
Publisher :
ISBN 13 :
Total Pages : 932 pages
Book Rating : 4.:/5 (319 download)

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Book Synopsis Scientific and Technical Aerospace Reports by :

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1964 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Applied Mechanics Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 666 pages
Book Rating : 4.:/5 (26 download)

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Book Synopsis Applied Mechanics Reviews by :

Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1964 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Viscoelastic Solids (1998)

Author : Roderic S. Lakes
Publisher : CRC Press
ISBN 13 : 1351355643
Total Pages : 476 pages
Book Rating : 4.3/5 (513 download)

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Book Synopsis Viscoelastic Solids (1998) by : Roderic S. Lakes

Download or read book Viscoelastic Solids (1998) written by Roderic S. Lakes and published by CRC Press. This book was released on 2017-11-22 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Viscoelastic Solids covers the mathematical theory of viscoelasticity and physical insights, causal mechanisms, and practical applications. The book: presents a development of the theory, addressing both transient and dynamic aspects as well as emphasizing linear viscoelasticity synthesizes the structure of the theory with the aim of developing physical insight illustrates the methods for the solution of stress analysis problems in viscoelastic objects explores experimental methods for the characterization of viscoelastic materials describes the phenomenology of viscoelasticity in a variety of materials, including polymers, metals, high damping alloys, rock, piezoelectric materials, cellular solids, dense composite materials, and biological materials analyzes high damping and extremely low damping provides the theory of viscoelastic composite materials, including examples of various types of structure and the relationships between structure and mechanical properties contains examples on the use of viscoelastic materials in preventing and alleviating human suffering Viscoelastic Solids also demonstrates the use of viscoelasticity for diverse applications, such as earplugs, gaskets, computer disks, satellite stability, medical diagnosis, injury prevention, vibration abatement, tire performance, sports, spacecraft explosions, and music.

Stress Function Theory for Linearly Viscoelastic Solids

Author : A. S. Elder
Publisher :
ISBN 13 :
Total Pages : 30 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Stress Function Theory for Linearly Viscoelastic Solids by : A. S. Elder

Download or read book Stress Function Theory for Linearly Viscoelastic Solids written by A. S. Elder and published by . This book was released on 1960 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Theory of Viscoelasticity

Author : R. M. Christensen
Publisher : Courier Corporation
ISBN 13 : 0486318966
Total Pages : 384 pages
Book Rating : 4.4/5 (863 download)

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Book Synopsis Theory of Viscoelasticity by : R. M. Christensen

Download or read book Theory of Viscoelasticity written by R. M. Christensen and published by Courier Corporation. This book was released on 2013-04-26 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Theory of Linear Viscoelasticity

Author : D. R. Bland
Publisher : Courier Dover Publications
ISBN 13 : 0486816389
Total Pages : 145 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis The Theory of Linear Viscoelasticity by : D. R. Bland

Download or read book The Theory of Linear Viscoelasticity written by D. R. Bland and published by Courier Dover Publications. This book was released on 2016-10-05 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Phenomenological Theory of Linear Viscoelastic Behavior

Author : Nicholas W. Tschoegl
Publisher : Springer Science & Business Media
ISBN 13 : 3642736025
Total Pages : 791 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis The Phenomenological Theory of Linear Viscoelastic Behavior by : Nicholas W. Tschoegl

Download or read book The Phenomenological Theory of Linear Viscoelastic Behavior written by Nicholas W. Tschoegl and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 791 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lectures on Viscoelasticity Theory

Author : A.C. Pipkin
Publisher : Springer Science & Business Media
ISBN 13 : 146121078X
Total Pages : 199 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Lectures on Viscoelasticity Theory by : A.C. Pipkin

Download or read book Lectures on Viscoelasticity Theory written by A.C. Pipkin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Bollettino della Unione matematica italiana

Author :
Publisher :
ISBN 13 :
Total Pages : 1152 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis Bollettino della Unione matematica italiana by :

Download or read book Bollettino della Unione matematica italiana written by and published by . This book was released on 1981 with total page 1152 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Berichte der Deutschen Rheologischen Gesellschaft e.V. mit Dokumentation Rheologie

Author : Deutsche Rheologische Gesellschaft
Publisher :
ISBN 13 :
Total Pages : 874 pages
Book Rating : 4.:/5 (5 download)

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Book Synopsis Berichte der Deutschen Rheologischen Gesellschaft e.V. mit Dokumentation Rheologie by : Deutsche Rheologische Gesellschaft

Download or read book Berichte der Deutschen Rheologischen Gesellschaft e.V. mit Dokumentation Rheologie written by Deutsche Rheologische Gesellschaft and published by . This book was released on 1967 with total page 874 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Problems in Linear Viscoelasticity

Author : Mauro Fabrizio
Publisher : SIAM
ISBN 13 : 0898712661
Total Pages : 210 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Mathematical Problems in Linear Viscoelasticity by : Mauro Fabrizio

Download or read book Mathematical Problems in Linear Viscoelasticity written by Mauro Fabrizio and published by SIAM. This book was released on 1992-01-01 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes general mathematical modeling of viscoelastic materials as systems with fading memory. Discusses the interrelation between topics such as existence, uniqueness, and stability of initial boundary value problems, variational and extremum principles, and wave propagation. Demonstrates the deep connection between the properties of the solution to initial boundary value problems and the requirements of the general physical principles. Discusses special techniques and new methods, including Fourier and Laplace transforms, extremum principles via weight functions, and singular surfaces and discontinuity waves.

Creep and Relaxation of Nonlinear Viscoelastic Materials

Author : William Nichols Findley
Publisher : Courier Dover Publications
ISBN 13 :
Total Pages : 404 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Creep and Relaxation of Nonlinear Viscoelastic Materials by : William Nichols Findley

Download or read book Creep and Relaxation of Nonlinear Viscoelastic Materials written by William Nichols Findley and published by Courier Dover Publications. This book was released on 1989 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pioneering presentation of basic theory, experimental methods and results, solution of boundary value problems. Six appendices. Updated bibliography.

Viscoelasticity

Author : Wilhelm Flügge
Publisher : Springer Science & Business Media
ISBN 13 : 3662022761
Total Pages : 204 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Viscoelasticity by : Wilhelm Flügge

Download or read book Viscoelasticity written by Wilhelm Flügge and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: No mathematical theory can completely describe the complex world around us. Every theory is aimed at a certain class of phenomena, formulates their essential features, and disregards what is of minor importance. The theory meets its limits of applicability where a dis regarded influence becomes important. Thus, rigid-body dynamics describes in many cases the motion of actual bodies with high accu racy, but it fails to produce more than a few general statements in the case of impact, because elastic or anelastic deformation, no matter how local or how small, attains a dominating influence. For a long time mechanics of deformable bodies has been based upon Hooke's law - that is, upon thE" assumption of linear elasticity. It was well known that most engineering materials like metals, con crde, wood, soil, are not linearly elastic or, are so within limits too narrow to cover tne range of pl'actical intcrest. Nevertheless, almost all routine stress analysis is still based on Hooke T s law be cause of its simplicity. In the course of time engineers have become increasingly con scious of the importance of the anelastic behavior of many materials, and mathematical formulations have been attempted and applied to practical problems. Outstanding among them are the theories of ide ally plastic and of viscoelastic materials. While plastic behavior is essentially nonlinear (piecewise linear at best), viscoelasticity, like elasticity, permits a linear theory. This theory of linear visco elasticity is the subject of tbe present book.

On the Completeness of Certain Stress Functions in the Linear Theory of Elasticity

Author : Eli Sternberg
Publisher :
ISBN 13 :
Total Pages : 1 pages
Book Rating : 4.:/5 (227 download)

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Book Synopsis On the Completeness of Certain Stress Functions in the Linear Theory of Elasticity by : Eli Sternberg

Download or read book On the Completeness of Certain Stress Functions in the Linear Theory of Elasticity written by Eli Sternberg and published by . This book was released on 1961 with total page 1 pages. Available in PDF, EPUB and Kindle. Book excerpt: The comple ne of certain solutions in terms of stress functions to t e displac ment equation of motion nd equilibrium in classical ela ticity theory is treat d. PECIFICALLY, DEAL WIT THE STRESS FUNCTIONS OF Lame and of Somigliana in elastodynamics, as well as with ose of Galerkin and Papkovich in the equilibrium theory. The four of stress function cited are apt to be the mos sig ificant from t vi poi t of applicatio s and the present method for establishing their completen ss appears to be specially economical. (Author).