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Vibration of Mindlin Plates

Author: K.M. Liew

Publisher: Elsevier

Published: 1998-11-10

Total Pages: 412

ISBN-13: 9780080543543

Over the last several years, the four authors have jointly conducted research into the analysis of vibrating Mindlin plates as a collaborative project between Nanyang Technological University, The National University of Singapore, and The University of Queensland. The research was prompted by the fact that there is a dearth of vibration results for Mindlin plates when compared to classical thin plate solutions. To generate the vibration results, the authors have successfully employed the Ritz method for general plate shapes and boundary conditions. The Ritz method, once thought to be awkward for general plate analysis, can be automated through suitable trial functions (for displacements) that satisfy the geometric plate boundary conditions a priori. This work has been well-received by academics and researchers, as indicated by the continual requests for the authors' papers and the Ritz software codes. This monograph is written with the view to share this so-called p-Ritz method for the vibration analysis of Mindlin plates and its software codes with the research community. To the authors' knowledge, the monograph contains the first published Ritz plate software codes of its kind.

An Introduction to the Mathematical Theory of Vibrations of Elastic Plates

Author: Raymond David Mindlin

Publisher: World Scientific

Published: 2006

Total Pages: 211

ISBN-13: 9812772499

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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. 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.

Theories and Applications of Plate Analysis

Author: Rudolph Szilard

Publisher: John Wiley & Sons

Published: 2004-01-02

Total Pages: 1062

ISBN-13: 9780471429890

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This book by a renowned structural engineer offers comprehensive coverage of both static and dynamic analysis of plate behavior, including classical, numerical, and engineering solutions. It contains more than 100 worked examples showing step by step how the various types of analysis are performed.

Vibration Analysis of Plates by the Superposition Method

Author: Daniel J Gorman

Publisher: World Scientific

Published: 1999-05-21

Total Pages: 384

ISBN-13: 9814495468

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The elegance and logic of the superposition method have made it a highly attractive analytical procedure for obtaining accurate mathematical solutions to plate vibration problems. Its applicability to vast families of these problems, ranging from the dynamic behaviour of isotropic and orthotropic plates to laminated plate behaviour, is well demonstrated in the technical literature. Now, at last, a comprehensive book is made available to those who wish to use this powerful analytical technique. Beginning with a thorough and lucid introduction to the superposition method as it applies to free vibration of thin isotropic rectangular plates, with all combinations of classical boundary conditions, the book describes procedures for handling vast families of realistic practical plate vibration problems. These include orthotropic plates, point-supported plates, plates resting on elastic edge supports, plates with in-plane forces, buckling of plates, etc. The reader is subsequently introduced to utilization of the superposition method for the analysis of thick Mindlin plates as well as transverse-shear-deformable laminated plates. Particular emphasis is placed on plate free vibration analysis, with a list of pertinent publications attached to each chapter. The superposition method is unique in that all solutions obtained satisfy the governing differential equations exactly throughout the entire domain of the plate. The boundary conditions are satisfied to any desired degree of accuracy. Despite the attractive features of this analytical method, many researchers and designers have access only to published papers related to particular problems. With this new book, they have for the first time a comprehensive, illustrated description of the means of exploiting the superposition method. They will be able to prepare their own computer schemes and analyse any plate vibration problem of interest. Contents:Plate Vibration Analysis by the Method of SuperpositionThe Vibration of Orthotropic Rectangular PlatesPlates with Elastic Edge SupportPoint Supported Plates and Plates with Attached MassesVibration of Plates with Mixed Boundary ConditionsFree Vibration of Non-Rectangular Straight-Edged PlatesFree Vibration and Buckling of Plates with In-Plane ForcesThe Vibration of Mindlin PlatesFree Vibration of Laminated PlatesThe Forced Vibration of PlatesSome Additional Applications of the Superposition Method Readership: Civil and mechanical engineers. Keywords:Rectangular Plate;Vibration Superposition Method;Analytical Solutions;Eigenvalues Mode Shapes;Resonant FrequenciesReviews: “… definitely succeeds in its objective of making the ‘method available to all potential users in the field of mechanical vibrations’ and it is recommended for purchase by engineering libraries and all engineers who wish to use or evaluate the use of the superposition method.” Appl. Mech. Rev.

Introduction to Finite Element Vibration Analysis

Author: Maurice Petyt

Publisher: Cambridge University Press

Published: 1998-07-30

Total Pages: 584

ISBN-13: 9780521634175

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First time paperback of successful mechanical engineering book suitable as a textbook for graduate students in mechanical engineering.

Recent Advances in Structural Engineering

Author: Srinivasan Chandrasekaran

Publisher: Springer Nature

Published: 2021-03-31

Total Pages: 261

ISBN-13: 9813363894

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The book presents the select proceedings of National Conference on Recent Advances in Structural Engineering (NCRASE 2020). Various topics covered in this book include advanced structural materials, computational methods of structures, earthquake resistant analysis and design, analysis and design of structures against wind loads, pre-stressed concrete structures, bridge engineering, experimental methods and techniques of structures, offshore structures, composite structures, smart materials and structures, port and harbor structures, structural dynamics, high rise structures, sustainable materials in the construction technology, advanced structural analysis, extreme loads on structures, innovative structures, and special structures. The book will be useful for researchers and professional working in the field of structural engineering.

Formulas for Dynamics, Acoustics and Vibration

Author: Robert D. Blevins

Publisher: John Wiley & Sons

Published: 2016-05-03

Total Pages: 464

ISBN-13: 1119038219

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With Over 60 tables, most with graphic illustration, and over 1000 formulas, Formulas for Dynamics, Acoustics, and Vibration will provide an invaluable time-saving source of concise solutions for mechanical, civil, nuclear, petrochemical and aerospace engineers and designers. Marine engineers and service engineers will also find it useful for diagnosing their machines that can slosh, rattle, whistle, vibrate, and crack under dynamic loads.

Computational and Experimental Simulations in Engineering

Author: Hiroshi Okada

Publisher: Springer Nature

Published: 2019-11-16

Total Pages: 1278

ISBN-13: 303027053X

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This book gathers the latest advances, innovations, and applications in the field of computational engineering, as presented by leading international researchers and engineers at the 24th International Conference on Computational & Experimental Engineering and Sciences (ICCES), held in Tokyo, Japan on March 25-28, 2019. ICCES covers all aspects of applied sciences and engineering: theoretical, analytical, computational, and experimental studies and solutions of problems in the physical, chemical, biological, mechanical, electrical, and mathematical sciences. As such, the book discusses highly diverse topics, including composites; bioengineering & biomechanics; geotechnical engineering; offshore & arctic engineering; multi-scale & multi-physics fluid engineering; structural integrity & longevity; materials design & simulation; and computer modeling methods in engineering. The contributions, which were selected by means of a rigorous international peer-review process, highlight numerous exciting ideas that will spur novel research directions and foster multidisciplinary collaborations.

Vibration of Continuous Systems

Author: Singiresu S. Rao

Publisher: John Wiley & Sons

Published: 2007-02-09

Total Pages: 744

ISBN-13: 0471771716

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Broad, up-to-date coverage of advanced vibration analysis by the market-leading author Successful vibration analysis of continuous structural elements and systems requires a knowledge of material mechanics, structural mechanics, ordinary and partial differential equations, matrix methods, variational calculus, and integral equations. Fortunately, leading author Singiresu Rao has created Vibration of Continuous Systems, a new book that provides engineers, researchers, and students with everything they need to know about analytical methods of vibration analysis of continuous structural systems. Featuring coverage of strings, bars, shafts, beams, circular rings and curved beams, membranes, plates, and shells-as well as an introduction to the propagation of elastic waves in structures and solid bodies-Vibration of Continuous Systems presents: * Methodical and comprehensive coverage of the vibration of different types of structural elements * The exact analytical and approximate analytical methods of analysis * Fundamental concepts in a straightforward manner, complete with illustrative examples With chapters that are independent and self-contained, Vibration of Continuous Systems is the perfect book that works as a one-semester course, self-study tool, and convenient reference.

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

Author: Isaac E Elishakoff

Publisher: World Scientific

Published: 2019-10-29

Total Pages: 798

ISBN-13: 9813236531

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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)