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BL
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| Record Number
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968062
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b722432
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| Main Entry
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Mindlin, Raymond D., (Raymond David),1906-1987.
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| Title & Author
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An introduction to the mathematical theory of vibrations of elastic plates /\ R.D. Mindlin ; edited by Jiashi Yang.
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| Publication Statement
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Hackensack, N.J. :: World Scientific,, ©2006.
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| Page. NO
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1 online resource (xix, 190 pages) :: illustrations
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| ISBN
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1281373230
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: 6611373233
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: 9781281373236
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: 9786611373238
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: 9789812772497
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: 9812772499
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9789812703811
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9812703810
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| Bibliographies/Indexes
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Includes bibliographical references (pages 175-180) and index.
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| Contents
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Foreword; Preface; Contents; Chapter 1: Elements of the Linear Theory of Elasticity; 1.01 Notation; 1.02 Principle of Conservation of Energy; 1.03 Hooke's Law; 1.04 Constants of Elasticity; 1.05 Uniqueness of Solutions; 1.06 Variational Equation of Motion; 1.07 Displacement-Equations of Motion; Chapter 2: Solutions of the Three-Dimensional Equations; 2.01 Introductory; 2.02 Simple Thickness-Modes in an Infinite Plate; 2.03 Simple Thickness-Modes in an Infinite, Isotropic Plate; 2.04 Simple Thickness-Modes in an Infinite, Monoclinic Plate.
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2.05 Simple Thickness-Modes in an Infinite, Triclinic Plate2.06 Plane Strain in an Isotropic Body; 2.07 Equivoluminal Modes; 2.08 Wave-Nature of Equivoluminal Modes; 2.09 Infinite, Isotropic Plate Held between Smooth, Rigid Surfaces (Plane Strain); 2.10 Infinite, Isotropic Plate Held between Smooth, Elastic Surfaces (Plane Strain); 2.11 Coupled Dilatational and Equivoluminal Modes in an Infinite, Isotropic Plate with Free Faces (Plane Strain); 2.12 Three-Dimensional Coupled Dilatational and Equivoluminal Modes in an Infinite Isotropic Plate with Free Faces.
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2.13 Solutions in Cylindrical Coordinates2.14 Additional Boundaries; Chapter 3: Infinite Power Series of Two-Dimensional Equations; 3.01 Introductory; 3.02 Stress-Equations of Motion; 3.03 Strain; 3.04 Stress-Strain Relations; 3.05 Strain-Energy and Kinetic Energy; 3.06 Uniqueness of Solutions; 3.07 Plane Tensors; Chapter 4: Zero-Order Approximation; 4.01 Separation of Zero-Order Terms from Series; 4.02 Uniqueness of Solutions; 4.03 Stress-Strain Relations; 4.04 Displacement-Equations of Motion; 4.05 Useful Range of Zero-Order Approximation; Chapter 5: First-Order Approximation.
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5.01 Separation of Zero- and First-Order Terms from Series5.02 Adjustment of Upper Modes; 5.03 Uniqueness of Solutions; 5.04 Stress-Strain Relations; 5.05 Stress-Displacement Relations; 5.06 Displacement-Equations of Motion; 5.07 Useful Range of First-Order Approximation; Chapter 6: Intermediate Approximations; 6.01 Introductory; 6.02 Thickness-Shear, Thickness-Flexure and Face-Extension; 6.03 Thickness-Shear and Thickness-Flexure; 6.04 Classical Theory of Low-Frequency Vibrations of Thin Plates; 6.05 Moderately-High-Frequency Vibrations of Thin Plates; References.
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Appendix Applications of the First-Order ApproximationBiographical Sketch of R.D. Mindlin; Students of R.D. Mindlin; Presidential Medal for Merit; National Medal of Science; Handwritten Equations from the 1955 Monograph; Index.
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| Abstract
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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.
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| Subject
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Elastic plates and shells.
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| Subject
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Nonlinear theories.
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Vibration-- Mathematical models.
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Elastic plates and shells.
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Nonlinear theories.
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| Subject
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TECHNOLOGY ENGINEERING-- Structural.
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| Subject
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Vibration-- Mathematical models.
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| Dewey Classification
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624.1/776
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| LC Classification
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QA935.M84 2006eb
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| Added Entry
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Yang, Jiashi,1956-
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