# Linear Theory

## 1st Edition

**eBook ISBN:**9781483276717

**Imprint:**Academic Press

**Published Date:**28th September 1975

**Page Count:**675

## Description

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.

## Table of Contents

Preface

Acknowledgments

Contents of Volume I

Chapter V. Fundamentals of Linear Elastodynamics

5.1 Scope of the Chapter

5.2 Resume of Basic Equations of Linear Elasticity

5.3 Displacement Formulation of Elastodynamics

5.4 Displacement Potentials

5.5 Stress Formulation of Elastodynamics

5.6 Convoluted Forms of the Field Equations

5.7 Uniqueness Theorem of Elastodynamics

5.8 Reciprocal Theorem

5.9 Some Properties of the Wave Equation

5.10 Fundamental Singular Solution of Elastodynamics

5.11 Integral Representation Theorems

5.12 Two-Dimensional Representation Theorem

5.13 Radiation Conditions

5.14 Integral Equation Formulation of Boundary-Value Problems

5.15 Green's Functions of Elastodynamic States

5.16 Reduced Elastodynamic Equations

5.17 Solution of Elastodynamic Equations by Eigenfunction Expansions

5.18 Variational Principles for Linear Elastodynamics

Chapter VI. One-Dimensional Motions

6.1 Scope of the Chapter

6.2 One-Dimensional Elastodynamic Equations

6.3 D'Alembert Solution

6.4 Propagation of Longitudinal Waves in Half-Space

6.5 Initial-Value Problem for a Finite Strip

6.6 Finite Strip Fixed at One End and Subject to Dynamical Tractions at the Other

6.7 Propagation of Spherical Waves

6.8 Spherical Cavity Subject to Dynamical Pressure

6.9 Eigenfunctions for Spherical Domains

6.10 Propagation of Cylindrical Waves

6.11 Cylindrical Cavity Subject to Dynamical Pressure

6.12 Eigenfunctions for Cylindrical Domains

6.13 Initial-Value Problem for Cylindrical Waves

Chapter VII. Two-Dimensional Motions

7.1 Scope of the Chapter

7.2 Fundamental Equations

7.3 Lame Potentials

7.4 Propagation of Plane Harmonic Waves

7.5 Plane Elastic Waves in a Half-Space with a Free Boundary

7.6 Harmonic Surface Waves on a Half-Space

7.7 Waves in Layered Media

7.8 Dispersion and Group Velocity

7.9 Elastic Waves in Infinite Plates

7.10 Solutions by Complex Functions

7.11 Moving Line Load on the Surface of a Half-Space

7.12 Moving Griffith Crack

7.13 Moving Punch on a Half-Space

7.14 Self-Similar Solutions of Plane Problems

7.15 Similarity Solutions for the Half-Space

7.16 Line Impulse on the Surface of a Half-Space

7.17 Miscellaneous Stress Boundary-Value Problems in Half-Space

7.18 A Dynamic Contact Problem in Half-Space

7.19 Some Remarks—Other Solutions

7.20 Integral Transform Methods

7.21 Lamb's Problem

7.22 Transient Solution of the Problem of Buried Pressure Line Source in Half-Space

7.23 Impulsive Buried Line Force

7.24 Transient Motion of a Surface Line Load

7.25 Infinite Slab under Surface Loads

7.26 Antiplane Motion of a Slab Subject to End Loads

7.27 Plane-Strain Vibrations of Circular Cylinders

7.28 Circular Cylinder Subjected to Dynamical Tractions

7.29 Dynamic Tractions in a Circular Cavity

Chapter VIII. Three-Dimensional Solutions

8.1 Scope of the Chapter

8.2 Basic Equations in Curvilinear Coordinates

8.3 Infinite Elastic Space Subjected to Dynamical Loads

8.4 Finite Line Source in Infinite Elastic Space

8.5 Half-Space Subjected to Surface Twist

8.6 Lamb's Problem

8.7 Half-Space under Moving Load

8.8 Self-Similar Solutions of Axisymmetric Problems

8.9 The Circular Cylinder Problem

8.10 Vibrations of a Circular Cylinder

8.11 Propagation of Waves in a Hollow Circular Cylinder

8.12 Infinite Cylinder under Surface Tractions

8.13 The Sphere Problem

8.14 Free Vibrations of an Elastic Sphere

8.15 Elastic Sphere and Spherical Cavity Subjected to Dynamical Surface Loads

8.16 Torsion of Sphere

8.17 Elastic Sphere under Polar Traction

8.18 Incompressible Elastic Sphere

Chapter IX. Diffraction of Elastic Waves

9.1 Scope of the Chapter

9.2 Methods of Solution

9.3 Scattering of SH-Waves by a Rigid Cylinder

9.4 Diffraction of a Plane SH-Pulse by a Rigid Half-Plane

9.5 Diffraction of a Plane SH-Pulse by a Semi-Infinite Crack

9.6 Diffraction of P-Waves by a Rigid Half-Plane

9.7 Scattering of SH-Waves by a Circular Cylinder

9.8 Scattering of P-Waves by a Cylinder

9.9 Scattering of SV-Waves by a Cylinder

9.10 Oblique Plane Waves Incident to a Cylinder

9.11 Scattering of Plane Pulses

9.12 Scattering of Plane Waves from a Sphere

9.13 Scattering of Harmonic Waves of Arbitrary Shape by a Sphere

9.14 General Solution of the Scalar Wave Equation in Elliptic Coordinates

9.15 Scattering of SH-Waves by an Elliptic Cylinder

9.16 Scattering of P- and SV-Waves by an Elliptic Cylinder

9.17 Diffraction of Elastic Waves by a Rigid Strip

9.18 Diffraction of Elastic Waves by a Crack

9.19 Asymptotic Solutions for the Diffraction of Scalar Waves

9.20 Asymptotic Theory of Elastic Waves

References

Index

## Details

- No. of pages:
- 675

- Language:
- English

- Copyright:
- © Academic Press 1975

- Published:
- 28th September 1975

- Imprint:
- Academic Press

- eBook ISBN:
- 9781483276717