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:	9780486139579
Publisher:	Dover Publications
Publication date:	03/29/2012
Series:	Dover Books on Physics
Sold by:	Barnes & Noble
Format:	eBook
Pages:	688
File size:	53 MB
Note:	This product may take a few minutes to download.

About the Author

Karl F. Graff

Table of Contents

INTRODUCTIONI.1 General aspects of wave propagationI.2 Applications of wave phenomenaI.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.