04158nam 2200673 a 450 991078460160332120230829001350.01-281-37323-09786611373238981-277-249-9(CKB)1000000000399061(EBL)1681615(OCoLC)879074330(SSID)ssj0000183009(PQKBManifestationID)11170406(PQKBTitleCode)TC0000183009(PQKBWorkID)10173307(PQKB)11133771(MiAaPQ)EBC1681615(WSP)00006309(Au-PeEL)EBL1681615(CaPaEBR)ebr10201378(CaONFJC)MIL137323(EXLCZ)99100000000039906120061101d2006 uy 0engurbuu|||uu|||txtccrAn introduction to the mathematical theory of vibrations of elastic plates[electronic resource] /R.D. Mindlin ; edited by Jiashi YangHackensack, N.J. World Scientificc20061 online resource (212 p.)Description based upon print version of record.981-270-381-0 Includes bibliographical references (p. 175-180) and index.Contents; Foreword; Preface; 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 Motion1.07 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 Coordinates; 2.14 Additional Boundaries; Chapter 3: Infinite Power Series of Two-Dimensional Equations; 3.01 Introductory3.02 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 Series4.02 Uniqueness of SolutionsThis 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 prElastic plates and shellsVibrationMathematical modelsNonlinear theoriesElastic plates and shells.VibrationMathematical models.Nonlinear theories.624.1/776Mindlin Raymond D(Raymond David),1906-1987.1499066Yang Jiashi1956-476573MiAaPQMiAaPQMiAaPQBOOK9910784601603321An introduction to the mathematical theory of vibrations of elastic plates3724878UNINA