An introduction to the mathematical theory of vibrations of elastic plates /
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 the...
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| Format: | Electronic eBook |
| Language: | English |
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Hackensack, N.J. :
World Scientific,
©2006.
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| Subjects: | |
| Online Access: | CONNECT |
MARC
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| 100 | 1 | |a Mindlin, Raymond D. |q (Raymond David), |d 1906-1987. |1 https://id.oclc.org/worldcat/entity/E39PBJmdrKjgvXpk9XbgjQHjYP | |
| 245 | 1 | 3 | |a An introduction to the mathematical theory of vibrations of elastic plates / |c R.D. Mindlin ; edited by Jiashi Yang. |
| 260 | |a Hackensack, N.J. : |b World Scientific, |c ©2006. | ||
| 300 | |a 1 online resource (xix, 190 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 504 | |a Includes bibliographical references (pages 175-180) and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a 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. | ||
| 505 | 0 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 546 | |a English. | ||
| 500 | |a EBSCO eBook Academic Comprehensive Collection North America |5 TMurS | ||
| 500 | |a EBSCO eBook EngineeringCore |5 TMurS | ||
| 650 | 0 | |a Elastic plates and shells. | |
| 650 | 0 | |a Vibration |x Mathematical models. | |
| 650 | 0 | |a Nonlinear theories. | |
| 700 | 1 | |a Yang, Jiashi, |d 1956- |1 https://id.oclc.org/worldcat/entity/E39PCjGghw7jQD4R7KPqTWb68C | |
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| 776 | 0 | 8 | |i Print version: |a Mindlin, Raymond D. (Raymond David), 1906-1987. |t Introduction to the mathematical theory of vibrations of elastic plates. |d Hackensack, N.J. : World Scientific, ©2006 |w (DLC) 2006042124 |
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