Eringen / Suhubi Linear Theory

1. Auflage 2013
ISBN: 978-1-4832-7671-7
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 675 Seiten, Web PDF

Elastodynamics, Volume II: Linear Theory is a continuation of Volume I and discusses the dynamical theory of linear isotropic elasticity. The volume deals with the fundamental theorems regarding elastodynamics and the different mathematical methods of solution and their employment in one, two, and three dimensions. The text outlines the fundamentals of linear elastodynamics and explains basic equations, displacement formulation, stress formulation, and the uniqueness theorem of elastodynamics. The book also investigates elastodynamic problems involving one-space dimension in governing boundaries, equations, and initial conditions. The book then compares two-dimensional problems as being subject to more precise mathematical analysis compared to three-dimensional situations by using scalar wave equations. The text then analyzes elastodynamic problems in three space dimensions when the solution depends on the condition of separability of the vector wave equation and the satisfaction of the boundary conditions. The diffraction of elastic waves is also described using two approaches: the integral equation method or the Eigen function technique. The book can prove valuable to researchers and practitioners whose work involves advanced statistics, general physics, and thermodynamics.

Autoren/Hrsg.

Eringen, A. Cemal

Suhubi, Erdogan S.

Inhaltsverzeichnis

1;Front Cover;1
2;Linear Theory;4
3;Copyright Page;5
4;Table of Contents;6
5;Preface;10
6;Acknowledgments;12
7;Contents of Volume I;15
8;Chapter V. Fundamentals of Linear Elastodynamics;16
8.1;5.1 Scope of the Chapter;16
8.2;5.2 Resume of Basic Equations of Linear Elasticity;17
8.3;5.3 Displacement Formulation of Elastodynamics;20
8.4;5.4 Displacement Potentials;21
8.5;5.5 Stress Formulation of Elastodynamics;29
8.6;5.6 Convoluted Forms of the Field Equations;30
8.7;5.7 Uniqueness Theorem of Elastodynamics;33
8.8;5.8 Reciprocal Theorem;40
8.9;5.9 Some Properties of the Wave Equation;42
8.10;5.10 Fundamental Singular Solution of Elastodynamics;63
8.11;5.11 Integral Representation Theorems;77
8.12;5.12 Two-Dimensional Representation Theorem;82
8.13;5.13 Radiation Conditions;87
8.14;5.14 Integral Equation Formulation of Boundary-Value Problems;94
8.15;5.15 Green's Functions of Elastodynamic States;98
8.16;5.16 Reduced Elastodynamic Equations;103
8.17;5.17 Solution of Elastodynamic Equations by Eigenfunction Expansions;110
8.18;5.18 Variational Principles for Linear Elastodynamics;115
9;Chapter VI. One-Dimensional Motions;127
9.1;6.1 Scope of the Chapter;127
9.2;6.2 One-Dimensional Elastodynamic Equations;128
9.3;6.3 D'Alembert Solution;130
9.4;6.4 Propagation of Longitudinal Waves in Half-Space;135
9.5;6.5 Initial-Value Problem for a Finite Strip;140
9.6;6.6 Finite Strip Fixed at One End and Subject to Dynamical Tractions at the Other;143
9.7;6.7 Propagation of Spherical Waves;147
9.8;6.8 Spherical Cavity Subject to Dynamical Pressure;148
9.9;6.9 Eigenfunctions for Spherical Domains;157
9.10;6.10 Propagation of Cylindrical Waves;161
9.11;6.11 Cylindrical Cavity Subject to Dynamical Pressure;163
9.12;6.12 Eigenfunctions for Cylindrical Domains;165
9.13;6.13 Initial-Value Problem for Cylindrical Waves;169
10;Chapter VII Two-Dimensional Motions;173
10.1;7.1 Scope of the Chapter;173
10.2;7.2 Fundamental Equations;174
10.3;7.3 Lame Potentials;176
10.4;7.4 Propagation of Plane Harmonic Waves;177
10.5;7.5 Plane Elastic Waves in a Half-Space with a Free Boundary;181
10.6;7.6 Harmonic Surface Waves on a Half-Space;198
10.7;7.7 Waves in Layered Media;203
10.8;7.8 Dispersion and Group Velocity;223
10.9;7.9 Elastic Waves in Infinite Plates;231
10.10;7.10 Solutions by Complex Functions;238
10.11;7.11 Moving Line Load on the Surface of a Half-Space;247
10.12;7.12 Moving Grifiith Crack;257
10.13;7.13 Moving Punch on a Half-Space;264
10.14;7.14 Self-Similar Solutions of Plane Problems;273
10.15;7.15 Similarity Solutions for the Half-Space;284
10.16;7.16 Line Impulse on the Surface of a Half-Space;287
10.17;7.17 Miscellaneous Stress Boundary-Value Problems in Half-Space;299
10.18;7.18 A Dynamic Contact Problem in Half-Space;302
10.19;7.19 Some Remarks—Other Solutions;316
10.20;7.20 Integral Transform Methods;317
10.21;7.21 Lamb's Problem;325
10.22;7.22 Transient Solution of the Problem of Buried Pressure Line Source in Half-Space;326
10.23;7.23 Impulsive Buried Line Force;338
10.24;7.24 Transient Motion of a Surface Line Load;347
10.25;7.25 Infinite Slab under Surface Loads;360
10.26;7.26 Antiplane Motion of a Slab Subject to End Loads;363
10.27;7.27 Plane-Strain Vibrations of Circular Cylinders;366
10.28;7.28 Circular Cylinder Subjected to Dynamical Tractions;373
10.29;7.29 Dynamic Tractions in a Circular Cavity;381
11;Chapter VIII. Three-Dimensional Solutions;390
11.1;8.1 Scope of the Chapter;390
11.2;8.2 Basic Equations in Curvilinear Coordinates;391
11.3;8.3 Infinite Elastic Space Subjected to Dynamical Loads;396
11.4;8.4 Finite Line Source in Infinite Elastic Space;400
11.5;8.5 Half-Space Subjected to Surface Twist;407
11.6;8.6 Lamb's Problem;414
11.7;8.7 Half-Space under Moving Load;425
11.8;8.8 Self-Similar Solutions of Axisymmetric Problems;433
11.9;8.9 The Circular Cylinder Problem;445
11.10;8.10 Vibrations of a Circular Cylinder;452
11.11;8.11 Propagation of Waves in a Hollow Circular Cylinder;465
11.12;8.12 Infinite Cylinder under Surface Tractions;475
11.13;8.13 The Sphere Problem;477
11.14;8.14 Free Vibrations of an Elastic Sphere;485
11.15;8.15 Elastic Sphere and Spherical Cavity Subjected to Dynamical Surface Loads;506
11.16;8.16 Torsion of Sphere;513
11.17;8.17 Elastic Sphere under Polar Traction;518
11.18;8.18 Incompressible Elastic Sphere;523
12;Chapter IX. Diffraction of Elastic Waves;536
12.1;9.1 Scope of the Chapter;536
12.2;9.2 Methods of Solution;537
12.3;9.3 Scattering of SH-Waves by a Rigid Cylinder;542
12.4;9.4 Diffraction of a Plane SH-Pulse by a Rigid Half-Plane;544
12.5;9.5 Diffraction of a Plane SH-Pulse by a Semi-Infinite Crack;550
12.6;9.6 Diffraction of P-Waves by a Rigid Half-Plane;553
12.7;9.7 Scattering of SH-Waves by a Circular Cylinder;562
12.8;9.8 Scattering of P-Waves by a Cylinder;571
12.9;9.9 Scattering of SV-Waves by a Cylinder;576
12.10;9.10 Oblique Plane Waves Incident to a Cylinder;579
12.11;9.11 Scattering of Plane Pulses;581
12.12;9.12 Scattering of Plane Waves from a Sphere;584
12.13;9.13 Scattering of Harmonic Waves of Arbitrary Shape by a Sphere;590
12.14;9.14 General Solution of the Scalar Wave Equation in Elliptic Coordinates;592
12.15;9.15 Scattering of SH-Waves by an Elliptic Cylinder;598
12.16;9.16 Scattering of P- and SV-Waves by an Elliptic Cylinder;602
12.17;9.17 Diffraction of Elastic Waves by a Rigid Strip;605
12.18;9.18 Diffraction of Elastic Waves by a Crack;617
12.19;9.19 Asymptotic Solutions for the Diffraction of Scalar Waves;629
12.20;9.20 Asymptotic Theory of Elastic Waves;642
13;References;650
14;Index;670