An Introduction To The Mathematical Theory Of Vibrations Of Elastic Plates

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An Introduction to the Mathematical Theory of Vibrations of Elastic Plates

Author : Raymond David Mindlin
Publisher : World Scientific
ISBN 13 : 9812703810
Total Pages : 211 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis An Introduction to the Mathematical Theory of Vibrations of Elastic Plates by : Raymond David Mindlin

Download or read book An Introduction to the Mathematical Theory of Vibrations of Elastic Plates written by Raymond David Mindlin and published by World Scientific. This book was released on 2006 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book by the late R D Mindlin is destined to become a classic introduction to the mathematical aspects of two-dimensional theories of elastic plates. It systematically derives the two-dimensional theories of anisotropic elastic plates from the variational formulation of the three-dimensional theory of elasticity by power series expansions. The uniqueness of two-dimensional problems is also examined from the variational viewpoint. The accuracy of the two-dimensional equations is judged by comparing the dispersion relations of the waves that the two-dimensional theories can describe with prediction from the three-dimensional theory. Discussing mainly high-frequency dynamic problems, it is also useful in traditional applications in structural engineering as well as provides the theoretical foundation for acoustic wave devices.

Introduction To The Mathematical Theory Of Vibrations Of Elastic Plates, An - By R D Mindlin

Author : Jiashi Yang
Publisher : World Scientific
ISBN 13 : 9814476544
Total Pages : 211 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Introduction To The Mathematical Theory Of Vibrations Of Elastic Plates, An - By R D Mindlin by : Jiashi Yang

Download or read book Introduction To The Mathematical Theory Of Vibrations Of Elastic Plates, An - By R D Mindlin written by Jiashi Yang and published by World Scientific. This book was released on 2006-12-29 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book by the late R D Mindlin is destined to become a classic introduction to the mathematical aspects of two-dimensional theories of elastic plates. It systematically derives the two-dimensional theories of anisotropic elastic plates from the variational formulation of the three-dimensional theory of elasticity by power series expansions. The uniqueness of two-dimensional problems is also examined from the variational viewpoint. The accuracy of the two-dimensional equations is judged by comparing the dispersion relations of the waves that the two-dimensional theories can describe with prediction from the three-dimensional theory. Discussing mainly high-frequency dynamic problems, it is also useful in traditional applications in structural engineering as well as provides the theoretical foundation for acoustic wave devices.

An Introduction to the Mathematical Theory of Vibrations of Elastic Plates

Author : Raymond David Mindlin
Publisher : World Scientific
ISBN 13 : 9812772499
Total Pages : 211 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis An Introduction to the Mathematical Theory of Vibrations of Elastic Plates by : Raymond David Mindlin

Vibrations of Elastic Plates

Author : Yi-Yuan Yu
Publisher : Springer Science & Business Media
ISBN 13 : 1461223385
Total Pages : 234 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Vibrations of Elastic Plates by : Yi-Yuan Yu

Download or read book Vibrations of Elastic Plates written by Yi-Yuan Yu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on my experiences as a teacher and as a researcher for more than four decades. When I started teaching in the early 1950s, I became interested in the vibrations of plates and shells. Soon after I joined the Polytechnic Institute of Brooklyn as a professor, I began working busily on my research in vibrations of sandwich and layered plates and shells, and then teaching a graduate course on the same subject. Although I tried to put together my lecture notes into a book, I never finished it. Many years later, I came to the New Jersey Institute of Technology as the dean of engineering. When I went back to teaching and looked for some research areas to work on, I came upon laminated composites and piezoelectric layers, which appeared to be natural extensions of sandwiches. Working on these for the last several years has brought me a great deal of joy, since I still am able to find my work relevant. At least I can claim that I still am pursuing life-long learning as it is advocated by educators all over the country. This book is based on the research results I accumulated during these two periods of my work, the first on vibrations and dynamical model ing of sandwiches, and the second on laminated composites and piezoelec tric layers.

Stationary Oscillations of Elastic Plates

Author : Gavin R. Thomson
Publisher : Springer Science & Business Media
ISBN 13 : 0817682414
Total Pages : 230 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Stationary Oscillations of Elastic Plates by : Gavin R. Thomson

Download or read book Stationary Oscillations of Elastic Plates written by Gavin R. Thomson and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems in mathematical physics rely heavily on the use of elliptical partial differential equations, and boundary integral methods play a significant role in solving these equations. Stationary Oscillations of Elastic Plates studies the latter in the context of stationary vibrations of thin elastic plates. The techniques presented here reduce the complexity of classical elasticity to a system of two independent variables, modeling problems of flexural-vibrational elastic body deformation with the aid of eigenfrequencies and simplifying them to manageable, uniquely solvable integral equations. The book is intended for an audience with a knowledge of advanced calculus and some familiarity with functional analysis. It is a valuable resource for professionals in pure and applied mathematics, and for theoretical physicists and mechanical engineers whose work involves elastic plates. Graduate students in these fields can also benefit from the monograph as a supplementary text for courses relating to theories of elasticity or flexural vibrations.

Wave Motion in Elastic Solids

Author : Karl F. Graff
Publisher : Courier Corporation
ISBN 13 : 0486139573
Total Pages : 688 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Wave Motion in Elastic Solids by : Karl F. Graff

Download or read book Wave Motion in Elastic Solids written by Karl F. Graff and published by Courier Corporation. This book was released on 2012-04-26 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt: Self-contained coverage of topics ranging from elementary theory of waves and vibrations in strings to three-dimensional theory of waves in thick plates. Over 100 problems.

R.D. Mindlin and Applied Mechanics

Author : George Herrmann
Publisher : Elsevier
ISBN 13 : 1483155544
Total Pages : 304 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis R.D. Mindlin and Applied Mechanics by : George Herrmann

Download or read book R.D. Mindlin and Applied Mechanics written by George Herrmann and published by Elsevier. This book was released on 2013-10-22 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: R. D. Mindlin and Applied Mechanics is a collection of studies in the development of Applied Mechanics dedicated to Professor Raymond D. Mindlin by his former students. This book contains the development of specific areas of Mechanics of Solids to which Mindlin has contributed most. Organized into eight chapters, this text first discusses the past, present and likely future of photoelasticity. Subsequent chapters explore the development of the three-dimensional theory of elasticity; generalized elastic continua; bodies in contact with applications to granular media; and waves and vibrations in isotropic and anisotropic plates. Other chapters discuss the vibrations and wave propagation in rods, piezoelectric crystals, and electro-elasticity. Lastly, the lattice theories and continuum mechanics are described.

The History of the Theory of Structures

Author : Karl-Eugen Kurrer
Publisher : John Wiley & Sons
ISBN 13 : 3433601348
Total Pages : 864 pages
Book Rating : 4.4/5 (336 download)

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Book Synopsis The History of the Theory of Structures by : Karl-Eugen Kurrer

Download or read book The History of the Theory of Structures written by Karl-Eugen Kurrer and published by John Wiley & Sons. This book was released on 2012-01-09 with total page 864 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book traces the evolution of theory of structures and strength of materials - the development of the geometrical thinking of the Renaissance to become the fundamental engineering science discipline rooted in classical mechanics. Starting with the strength experiments of Leonardo da Vinci and Galileo, the author examines the emergence of individual structural analysis methods and their formation into theory of structures in the 19th century. For the first time, a book of this kind outlines the development from classical theory of structures to the structural mechanics and computational mechanics of the 20th century. In doing so, the author has managed to bring alive the differences between the players with respect to their engineering and scientific profiles and personalities, and to create an understanding for the social context. Brief insights into common methods of analysis, backed up by historical details, help the reader gain an understanding of the history of structural mechanics from the standpoint of modern engineering practice. A total of 175 brief biographies of important personalities in civil and structural engineering as well as structural mechanics plus an extensive bibliography round off this work.

A Treatise on the Mathematical Theory of Elasticity

Author : A. E. H. Love
Publisher : Cambridge University Press
ISBN 13 : 1107618096
Total Pages : 663 pages
Book Rating : 4.1/5 (76 download)

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Book Synopsis A Treatise on the Mathematical Theory of Elasticity by : A. E. H. Love

Download or read book A Treatise on the Mathematical Theory of Elasticity written by A. E. H. Love and published by Cambridge University Press. This book was released on 2013-01-03 with total page 663 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1927, this is a classic account of the mathematical theory of elasticity by English mathematician A. E. H. Love. The text provides a detailed explanation of the topic in its various aspects, revealing important relationships with general physics and applications to engineering.

Applied Mechanics Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 1006 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 1960 with total page 1006 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Hygro-Thermo-Magneto-Electro-Elastic Theory of Anisotropic Doubly-Curved Shells

Author : Francesco Tornabene
Publisher : Società Editrice Esculapio
ISBN 13 :
Total Pages : 1073 pages
Book Rating : 4.2/5 (224 download)

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Book Synopsis Hygro-Thermo-Magneto-Electro-Elastic Theory of Anisotropic Doubly-Curved Shells by : Francesco Tornabene

Download or read book Hygro-Thermo-Magneto-Electro-Elastic Theory of Anisotropic Doubly-Curved Shells written by Francesco Tornabene and published by Società Editrice Esculapio. This book was released on 2023-10-13 with total page 1073 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to present in depth several Higher-order Shear Deformation Theories (HSDTs) by means of a unified approach for studying the Hygro-Thermo-Magneto-Electro- Elastic Theory of Anisotropic Doubly-Curved Shells. In particular, a general coupled multifield theory regarding anisotropic shell structures is provided. The three-dimensional multifield problem is reduced in a two-dimensional one following the principles of the Equivalent Single Layer (ESL) approach and the Equivalent Layer-Wise (ELW) approach, setting a proper configuration model. According to the adopted configuration assumptions, several Higher-order Shear Deformation Theories (HSDTs) are obtained. Furthermore, the strong and weak formulations of the corresponding governing equations are discussed and illustrated. The approach presented in this volume is completely general and represents a valid tool to investigate the physical behavior of many arbitrarily shaped structures. An isogeometric mapping procedure is also illustrated to this aim. Special attention is given also to advanced and innovative constituents, such as Carbon Nanotubes (CNTs), Variable Angle Tow (VAT) composites and Functionally Graded Materials (FGMs). In addition, several numerical applications are used to support the theoretical models. Accurate, efficient and reliable numerical techniques able to approximate both derivatives and integrals are considered, which are respectively the Differential Quadrature (DQ) and Integral Quadrature (IQ) methods. The Theory of Composite Thin Shells is derived in a simple and intuitive manner from the theory of thick and moderately thick shells (First-order Shear Deformation Theory or Reissner- Mindlin Theory). In particular, the Kirchhoff-Love Theory and the Membrane Theory for composite shells are shown. Furthermore, the Theory of Composite Arches and Beams is also exposed. In particular, the equations of the Timoshenko Theory and the Euler-Bernoulli Theory are directly deducted from the equations of singly-curved shells of translation and of plates.

Mechanics Of Piezoelectric Structures (Second Edition)

Author : Jiashi Yang
Publisher : World Scientific
ISBN 13 : 9811226814
Total Pages : 315 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Mechanics Of Piezoelectric Structures (Second Edition) by : Jiashi Yang

Download or read book Mechanics Of Piezoelectric Structures (Second Edition) written by Jiashi Yang and published by World Scientific. This book was released on 2020-09-18 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a continuation of the author's previous book An Introduction to the Theory of Piezoelectricity (Springer, New York, 2005) on the three-dimensional theory of piezoelectricity, this book covers one- and two-dimensional theories of piezoelectric structures including rods, beams, plates and shells. In addition to the so-called low-frequency motions of extension and bending, high-frequency motions of thickness shear and thickness stretch are also considered for certain applications unique in resonant piezoelectric devices. Both single-layer and multi-layer structures are treated. Nonlinear effects due to large deflection or large shear deformation are also discussed. The emphasis in on the development of structural theories with various levels of sophistication for different applications in piezoelectric devices.The book is heavily influenced by R D Mindlin's early contributions to this field. It is destined to be one of the most systematic and comprehensive books on piezoelectric structures. This second edition is a major reorganization of the first edition with multiple additions as well as deletion of chapters and sections.

Handbook On Timoshenko-ehrenfest Beam And Uflyand- Mindlin Plate Theories

Author : Isaac E Elishakoff
Publisher : World Scientific
ISBN 13 : 9813236531
Total Pages : 798 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Handbook On Timoshenko-ehrenfest Beam And Uflyand- Mindlin Plate Theories by : Isaac E Elishakoff

Download or read book Handbook On Timoshenko-ehrenfest Beam And Uflyand- Mindlin Plate Theories written by Isaac E Elishakoff and published by World Scientific. This book was released on 2019-10-29 with total page 798 pages. Available in PDF, EPUB and Kindle. Book excerpt: The refined theory of beams, which takes into account both rotary inertia and shear deformation, was developed jointly by Timoshenko and Ehrenfest in the years 1911-1912. In over a century since the theory was first articulated, tens of thousands of studies have been performed utilizing this theory in various contexts. Likewise, the generalization of the Timoshenko-Ehrenfest beam theory to plates was given by Uflyand and Mindlin in the years 1948-1951.The importance of these theories stems from the fact that beams and plates are indispensable, and are often occurring elements of every civil, mechanical, ocean, and aerospace structure.Despite a long history and many papers, there is not a single book that summarizes these two celebrated theories. This book is dedicated to closing the existing gap within the literature. It also deals extensively with several controversial topics, namely those of priority, the so-called 'second spectrum' shear coefficient, and other issues, and shows vividly that the above beam and plate theories are unnecessarily overcomplicated.In the spirit of Einstein's dictum, 'Everything should be made as simple as possible but not simpler,' this book works to clarify both the Timoshenko-Ehrenfest beam and Uflyand-Mindlin plate theories, and seeks to articulate everything in the simplest possible language, including their numerous applications.This book is addressed to graduate students, practicing engineers, researchers in their early career, and active scientists who may want to have a different look at the above theories, as well as readers at all levels of their academic or scientific career who want to know the history of the subject. The Timoshenko-Ehrenfest Beam and Uflyand-Mindlin Plate Theories are the key reference works in the study of stocky beams and thick plates that should be given their due and remain important for generations to come, since classical Bernoulli-Euler beam and Kirchhoff-Love theories are applicable for slender beams and thin plates, respectively.Related Link(s)

Linear Theories of Elasticity and Thermoelasticity

Author : Clifford Truesdell
Publisher : Springer
ISBN 13 : 3662397765
Total Pages : 755 pages
Book Rating : 4.6/5 (623 download)

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Book Synopsis Linear Theories of Elasticity and Thermoelasticity by : Clifford Truesdell

Download or read book Linear Theories of Elasticity and Thermoelasticity written by Clifford Truesdell and published by Springer. This book was released on 2013-12-17 with total page 755 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Advances in Continuum Mechanics and Thermodynamics of Material Behavior

Author : Donald E. Carlson
Publisher : Springer Science & Business Media
ISBN 13 : 9401007284
Total Pages : 431 pages
Book Rating : 4.4/5 (1 download)

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Book Synopsis Advances in Continuum Mechanics and Thermodynamics of Material Behavior by : Donald E. Carlson

Download or read book Advances in Continuum Mechanics and Thermodynamics of Material Behavior written by Donald E. Carlson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers included in this volume were presented at the Symposium on Advances in the Continuum Mechanics and Thermodynamics of Material Behavior, held as part of the 1999 Joint ASME Applied Mechanics and Materials Summer Conference at Virginia Tech on June 27-30, 1999. The Symposium was held in honor of Professor Roger L. Fosdick on his 60th birthday. The papers are written by prominent researchers in the fields of mechanics, thermodynamics, materials modeling, and applied mathematics. They address open questions and present the latest development in these and related areas. This volume is a valuable reference for researchers and graduate students in universities and research laboratories.

Anisotropic Doubly-Curved Shells

Author : Francesco Tornabene
Publisher : Società Editrice Esculapio
ISBN 13 : 8835328993
Total Pages : 1199 pages
Book Rating : 4.8/5 (353 download)

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Book Synopsis Anisotropic Doubly-Curved Shells by : Francesco Tornabene

Download or read book Anisotropic Doubly-Curved Shells written by Francesco Tornabene and published by Società Editrice Esculapio. This book was released on 2019-11-01 with total page 1199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to present in depth several Higher-order Shear Deformation Theories (HSDTs) by means of a unified approach for the mechanical analysis of doubly-curved shell structures made of anisotropic and composite materials. In particular, the strong and weak formulations of the corresponding governing equations are discussed and illustrated. The approach presented in this volume is completely general and represents a valid tool to investigate the structural behavior of many arbitrarily shaped structures. An isogeometric mapping procedure is also illustrated to this aim. Special attention is given also to advanced and innovative constituents, such as Carbon Nanotubes (CNTs), Variable Angle Tow (VAT) composites and Functionally Graded Materials (FGMs). In addition, several numerical applications are developed to support the theoretical models. Accurate, efficient and reliable numerical techniques able to approximate both derivatives and integrals are presented, which are respectively the Differential Quadrature (DQ) and Integral Quadrature (IQ) methods. Finally, two numerical techniques, named Strong Formulation Finite Element Method (SFEM) and Weak Formulation Finite Element Method (WFEM), are developed to deal with multi-element domains characterized by arbitrary shapes and discontinuities.

Piezoelectric Shells

Author : Hornsen (HS) Tzou
Publisher : Springer
ISBN 13 : 9402412581
Total Pages : 456 pages
Book Rating : 4.4/5 (24 download)

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Book Synopsis Piezoelectric Shells by : Hornsen (HS) Tzou

Download or read book Piezoelectric Shells written by Hornsen (HS) Tzou and published by Springer. This book was released on 2018-12-06 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introduction to piezoelectric shells and distributed sensing, energy harvesting and control applications. It familiarizes readers with a generic approach of piezoelectric shells and fundamental electromechanics of distributed piezoelectric sensors, energy harvesters and actuators applied to shell structures. The book is divided into two major parts, the first of which focuses on piezoelectric shell continua, while the second examines distributing sensing, energy harvesting and control of elastic continua, e.g., shells and plates. The exploitation of new, advanced multifunctional smart structures and structronic systems has been one of the mainstream research and development activities over the years. In the search for innovative structronics technologies, piezoelectric materials have proved to be very versatile in both sensor and actuator applications. Consequently, the piezoelectric technology has been applied to a broad range of practical applications, from small-scale nano- and micro-sensors/actuators to large-scale airplane and space structures and systems. The book provides practicing engineers and researchers with an introduction to advanced piezoelectric shell theories and distributed sensor/energy harvester/actuator technologies in the context of structural identification, energy harvesting and precision control. The book can also be used as a textbook for graduate students. This second edition contains substantial new materials, especially energy harvesting and experimental components, and has been updated and corrected for a new generation of readers.