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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...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hackensack, N.J. :
World Scientific,
©2006.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.
- 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.
- 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.
- 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.
- 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.