An Introduction to the Mathematical Theory of Vibrations of Elastic Plates

An Introduction to the Mathematical Theory of Vibrations of Elastic Plates
Author: Raymond David Mindlin,Jiashi Yang
Publsiher: World Scientific
Total Pages: 211
Release: 2006
Genre: Technology & Engineering
ISBN: 9789812703811

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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.

Vibrations of Elastic Plates

Vibrations of Elastic Plates
Author: Yi-Yuan Yu
Publsiher: Springer Science & Business Media
Total Pages: 234
Release: 2012-12-06
Genre: Technology & Engineering
ISBN: 9781461223382

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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.

Vibration of Plates

Vibration of Plates
Author: Arthur W. Leissa
Publsiher: Unknown
Total Pages: 380
Release: 1969
Genre: Plates (Engineering)
ISBN: STANFORD:36105113766153

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An Introduction to the Mathematical Theory of Vibrations of Elastic Plates

An Introduction to the Mathematical Theory of Vibrations of Elastic Plates
Author: Raymond David Mindlin,Jiashi Yang
Publsiher: World Scientific
Total Pages: 211
Release: 2006
Genre: Technology & Engineering
ISBN: 9789812772497

Download An Introduction to the Mathematical Theory of Vibrations of Elastic Plates Book in PDF, Epub and Kindle

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. Sample Chapter(s). Chapter 1: Elements of the Linear Theory of Elasticity (416 KB). Contents: Elements of the Linear Theory of Elasticity; Solutions of the Three-Dimensional Equations; Infinite Power Series of Two-Dimensional Equations; Zero-Order Approximation; First-Order Approximation; Intermediate Approximations. Readership: Researchers in mechanics, civil and mechanical engineering and applied mathematics.

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

Introduction To The Mathematical Theory Of Vibrations Of Elastic Plates  An   By R D Mindlin
Author: Jiashi Yang
Publsiher: World Scientific
Total Pages: 211
Release: 2006-12-29
Genre: Technology & Engineering
ISBN: 9789814476546

Download Introduction To The Mathematical Theory Of Vibrations Of Elastic Plates An By R D Mindlin Book in PDF, Epub and Kindle

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.

Vibrations of Shells and Plates

Vibrations of Shells and Plates
Author: Werner Soedel
Publsiher: CRC Press
Total Pages: 594
Release: 2004-08-11
Genre: Mathematics
ISBN: 9780203026304

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With increasingly sophisticated structures involved in modern engineering, knowledge of the complex vibration behavior of plates, shells, curved membranes, rings, and other complex structures is essential for today‘s engineering students, since the behavior is fundamentally different than that of simple structures such as rods and beams. Now in its

Vibrations of Elastic Systems

Vibrations of Elastic Systems
Author: Edward B. Magrab
Publsiher: Springer Science & Business Media
Total Pages: 499
Release: 2012-01-19
Genre: Technology & Engineering
ISBN: 9789400726710

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This work presents a unified approach to the vibrations of elastic systems as applied to MEMS devices, mechanical components, and civil structures. Applications include atomic force microscopes, energy harvesters, and carbon nanotubes and consider such complicating effects as squeeze film damping, viscous fluid loading, in-plane forces, and proof mass interactions with their elastic supports. These effects are analyzed as single degree-of-freedom models and as more realistic elastic structures. The governing equations and boundary conditions for beams, plates, and shells with interior and boundary attachments are derived by applying variational calculus to an expression describing the energy of the system. The advantages of this approach regarding the generation of orthogonal functions and the Rayleigh-Ritz method are demonstrated. A large number of graphs and tables are given to show the impact of various factors on the systems’ natural frequencies, mode shapes, and responses.

Linear Piezoelectric Plate Vibrations

Linear Piezoelectric Plate Vibrations
Author: Henry Frank Tiersten
Publsiher: Springer
Total Pages: 216
Release: 2013-11-11
Genre: Science
ISBN: 9781489964533

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