Wave Motion in Elastic Solids

by Karl F. Graff

Overview

This highly useful textbook presents comprehensive intermediate-level coverage of nearly all major topics of elastic wave propagation in solids. The subjects range from the elementary theory of waves and vibrations in strings to the three-dimensional theory of waves in thick plates. The book is designed not only for a wide audience of engineering students, but also as a general reference for workers in vibrations and acoustics.
Chapters 1–4 cover wave motion in the simple structural shapes, namely strings, longitudinal rod motion, beams and membranes, plates and (cylindrical) shells. Chapters 5–8 deal with wave propagation as governed by the three-dimensional equations of elasticity and cover waves in infinite media, waves in half-space, scattering and diffraction, and waves in thick rods, plates, and shells.
To make the book as self-contained as possible, three appendices offer introductory material on elasticity equations, integral transforms and experimental methods in stress waves. In addition, the author has presented fairly complete development of a number of topics in the mechanics and mathematics of the subject, such as simple transform solutions, orthogonality conditions, approximate theories of plates and asymptotic methods.
Throughout, emphasis has been placed on showing results, drawn from both theoretical and experimental studies, as well as theoretical development of the subject. Moreover, there are over 100 problems distributed throughout the text to help students grasp the material. The result is an excellent resource for both undergraduate and graduate courses and an authoritative reference and review for research workers and professionals.

Product Details

ISBN-13:	9780486667454
Publisher:	Dover Publications
Publication date:	06/01/1991
Series:	Dover Books on Physics
Edition description:	Revised ed.
Pages:	688
Product dimensions:	5.50(w) x 8.50(h) x (d)

Table of Contents

INTRODUCTION
I.1 General aspects of wave propagation
I.2 Applications of wave phenomena
I.3 Historical background
1. WAVES AND VIBRATIONS IN STRINGS
1.1. Waves in long strings
1.1.1. The governing equations
1.1.2. Harmonic waves
1.1.3. The D'Alembert solution
1.1.4. The initial-value problem
1.1.5. The initial-value problem by Fourier analysis
1.1.6. Energy in a string
1.1.7. Forced motion of a semi-infinite string
1.1.8. Forced motion of an infinite string
1.2. Reflection and transmission at boundaries
1.2.1. Types of boundaries
1.2.2. Reflection from a fixed boundary
1.2.3. Reflection from an elastic boundary
1.2.4. Reflection of harmonic waves
1.2.5. Reflection and transmission at discontinuities
1.3. Free vibration of a finite string
1.3.1. Waves in a finite string
1.3.2. Vibrations of a fixed-fixed string
1.3.3. The general normal mode solution
1.4. Forced vibrations of a string
1.4.1. Solution by Green's function
1.4.2. Solution by transform techniques
1.4.3. Solution by normal modes
1.5. The string on an elastic base-dispersion
1.5.1. The governing equation
1.5.2. Propagation of harmonic waves
1.5.3. Frequency spectrum and the dispersion curve
1.5.4 Harmonic and pulse exitation of a semi-infinite string
1.6. Pulses in a dispersive media-group velocity
1.6.1. The concept of group velocity
1.6.2. Propagation of narrow-band pulses
1.6.3. Wide-band pulses-The method of stationary phase
1.7. The string on a viscous subgrade
1.7.1 The governing equation
1.7.2 Harmonic wave propagation
1.7.3 Forced motion of a string
2. LONGITUDINAL WAVES IN THIN RODS
2.1. Waves in long rods
2.1.1. The governing equation
2.1.2. Basic propagation characteristics
2.2. Reflection and transmission at boundaries
2.2.1. Reflection from free and fixed ends
2.2.2. Reflection from other end conditions
2.2.3. Transmission into another rod
2.3. Waves and vibration in a finite rod
2.3.1. Waves in a finite rod-history of a stress pulse
2.3.2. Free vibrations of a finite rod
2.3.3. Forced vibrations of rods
2.3.4. Impulse loading of a rod-two approaches
2.4. Longitudinal impact
2.4.1. Longitudinal collinear impact of two rods
2.4.2. Rigid-mass impact against a rod
2.4.3. Impact of an elastic sphere against a rod
2.5. Dispersive effects in rods
2.5.1. Rods of variable cross section-impedance
2.5.2. Rods of variable section-horn resonance
2.5.3. Effects of lateral inertia-dispersion
2.5.4. Effects of lateral inertia-pulse propagation
2.6. Torsional vibrations
2.6.1. The governing equation
2.7. Experimental studies in longitudinal waves
2.7.1. Longitudinal impact of spheres on rods
2.7.2. Longitudinal wave across discontinuities
2.7.3. The split Hopkinson pressure bar
2.7.4. Lateral inertia effects
2.7.5. Some other results of longitudinal wave experiments
References
Problems
3. FLEXURAL WAVES IN THIN RODS
3.1. Propagation and reflection characteristics
3.1.1. The governing equation
3.1.2. Propagation of harmonic waves
3.1.3. The initial-value problem
3.1.4. Forced motion of a beam
3.1.5 Reflection of harmonic view
3.2. Free and forced vibrations of finite beams
3.2.1. Natural frequencies of finite beams
3.2.2. Orthogonality
3.2.3. The initial-value problem
3.2.4. Forced vibrations of beams-methods of analysis
3.2.5 Some problems in forced vibrations of beams
3.3. Foundation and prestress effects
3.3.1 The governing equation
3.3.2. The beam on an elastic foundation
3.3.3. The moving load on a elastically supported beam
3.3.4. The effects of prestress
3.3.5 "Impulse loading of a finite, prestressed, visco-elastically supported beam"
3.4. Effects of shear and rotary inertia
3.4.1. The governing equations
3.4.2. Harmonic waves
3.4.3. Pulse propagation in a Timeoshenko beam
3.5. Wave propagation in rings
3.5.1. The governing equations
3.5.2. Wave propagation
3.6. Experimental studies on beams
3.6.1. Propagation of transients in straight beams
3.6.2. Beam vibration experiments
3.6.3. Waves in curved rings
References
Problems
4. "WAVES IN MEMBRANES, THIN PLATES, AND SHELLS"
4.1. Transverse motion in membranes
4.1.1. The governing equation
4.1.2. Plane waves
4.1.3. The initial-value problem
4.1.4 Forced vibration of a membrane
4.1.5 Reflection of waves from membrane boundaries
4.1.6. Waves in a membrane strip
4.1.7. Vibrations of finite membranes
4.2. Flexural waves in thin plates
4.2.1. The governing equations
4.2.2. Boundary conditions for a plate
4.2.3. Plane waves in an infinite plate
4.2.4. An initial-value problem
4.2.5. Forced motion of an infinite plate
4.2.6. Reflection of plane waves from boundaries
4.2.7. Free vibrations of finite plates
4.2.8 Experimental results on waves in plates
4.3. Waves in the cylindrical shells
4.3.1. Governing equations for a cylindrical membrane shell
4.3.2. Wave propagation in the shell
&n
6.4.2. Waves in layered media-Love waves
6.5. Experimental studies on waves in semi-infinite media
6.5.1. Waves into a half-space from a surface source
6.5.2. Surface waves on a half-space
6.5.3. Other studies on surface waves
References
Problems
7. SCATTERING AND DIFFRACTION OF ELASTIC WAVES
7.1. Scattering of waves by cavities
7.1.1. Scattering of SH waves by a cylindrical cavity
7.1.2 Scattering of compressional waves by a spherical obstacle
7.2. Diffraction of plane waves
7.2.1. Discussion of the Green's function approach
7.2.2. The Sommerfield diffraction problem
7.2.3. Geometric acoustics
References
Problems
8. WAVE PROPOGATION IN PLATES AND RODS
8.1. Continuous waves in a plate
8.1.1. SH waves in a plate
8.1.2. Waves in a plate with mixed boundary conditions
8.1.3. The Rayleigh-Lamb frequency equation for the plate
8.1.4. The general frequency equation for a plate
8.1.5. Analysis of the Raleigh-Lamb equation
8.1.6. Circular crested waves in a plate
8.1.7 Bound plates-SH and Lamè modes
8.2. Waves in circular rods and cylindrical shells
8.2.1. The frequency equation for the solid rod
8.2.2. "Torsional, longitudinal, and flexural modes in a rod"
8.2.3. Waves in cylindrical shells
8.3. "Approximate theories for waves in plates, rods, and shells"
8.3.1. An approximate theory for plate flexural modes
8.3.2. An approximate theory for extensional waves in plates
8.3.3. Approximate theories for longitudinal waves in rods
8.3.4. Approximate theories for waves in shells
8.4. Forced motion of plates and rods
8.4.1. SH waves in a plate
8.4.2. Pulse propagation in a infinite rod
8.4.3. Transient compressional wave in semi-infinite rods and plates
8.5. Experimental studies on waves in rods and plates
8.5.1. Multiple reflections within a waveguide
8.5.2. Dispersion of a sharp pulse in a cylindrical rod
8.5.3. Experimental results for step pulses
8.5.4. Other studies of waves in cylindrical rods and shells
References
Problems
APPENDIX A. THE ELASTICITY EQUATIONS
A.1. Notation
A.2. Strain
A.3. Stress
A.4. Conservation equations
A.4.1. Conservation of mass
A.4.2. Conservation of momentum
A.4.3. Conservation of moment of momentum
A.4.4. Conservation of energy
A.5. Constitutive equations
A.5.1. Green's method
A.5.2. Cauchy's method
A.5.3. Isotropic elastic solid
A.6. Solution uniqueness and boundary conditions
A.6.1. Uniqueness
A.6.2. Boundary conditions
A.7. Other continua
A.8. Additional energy consideration
A.9. Elasticity equations in curvilinear coordinates
A.9.1. Cylindrical coordinates
A.9.2. Spherical coordinates
APPENDIX B. INTEGRAL TRANSFORMS
B.1. General
B.2. Laplace transforms
B.2.1. Definition
B.2.2. Transforms of derivatives
B.2.3. The inverse transform
B.2.4. Partial fractions
B.2.5. Solutions of ordinary differential equations
B.2.6. Convolution
B.2.7 The inversion integral
B.3. Fourier transforms
B.3.1. Definition
B.3.2. Transforms of derivatives
B.3.3. The inverse transform
B.3.4. Convolution
B.3.5. Finite Fourier transforms
B.3.6. The Fourier integral
B.4. Hankel transforms
B.4.1. Definitions
B.4.2. Transforms of derivatives and Parseval's theorem
B.5. Tables of transforms
B.6. Fourier spectra of pulses
APPENDDIX C. EXPERIMENTAL METHODS IN STRESS WAVES
C.1. Methods for producing stress waves
C.2. Methods for detecting stress waves
"References to Appendices A, B, C."
AUTHOR INDEX
SUBJECT INDEX