Wave Motion in Elastic Solids,9780486667454

Wave Motion in Elastic Solids

by
ISBN13: 9780486667454
ISBN10: 0486667456
Format: Paperback
Pub. Date: 1991-06-01
Publisher(s): Dover Publications
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Summary

Comprehensive textbook for students and research workers offers self-contained coverage of a variety of topics ranging from the elementary theory of waves and vibrations in strings to the three-dimensional theory of waves in thick plates. Emphasis is on analytical and experimental results, in addition to theoretical development. Appendices contain introductory material on elasticity, transforms and experimental techniques. Over 100 problems.

Table of Contents

Introduction 1(1)
General aspects of wave propagation
1(2)
Applications of wave phenomena
3(2)
Historical background
5(4)
Waves and Vibrations in Strings
9(66)
Waves in long strings
9(20)
The governing equations
9(1)
Harmonic waves
10(3)
The D'Alembert solution
13(1)
The initial-value problem
14(3)
The initial-value problem by Fourier analysis
17(2)
Energy in a string
19(2)
Forced motion of a semi-infinite string
21(2)
Forced motion of an infinite string
23(6)
Reflection and transmission at boundaries
29(7)
Types of boundaries
29(1)
Reflection from a fixed boundary
30(1)
Reflection from an elastic boundary
31(3)
Reflection of harmonic waves
34(1)
Reflection and transmission at discontinuities
35(1)
Free vibration of a finite string
36(6)
Waves in a finite string
36(1)
Vibrations of a fixed-fixed string
37(3)
The general normal mode solution
40(2)
Forced vibrations of a string
42(9)
Solution by Green's function
43(1)
Solution by transform techniques
44(5)
Solution by normal modes
49(2)
The string on an elastic base-dispersion
51(7)
The governing equation
51(1)
Propagation of harmonic waves
51(3)
Frequency spectrum and the dispersion curve
54(2)
Harmonic and pulse excitation of a semi-infinite string
56(2)
Pulses in a dispersive media---group velocity
58(10)
The concept of group velocity
59(3)
Propagation of narrow-band pulses
62(3)
Wide-band pulses---The method of stationary phase
65(3)
The string on a viscous subgrade
68(3)
The governing equation
68(1)
Harmonic wave propagation
69(1)
Forced motion of a string
69(2)
References
71(1)
Problems
72(3)
Longitudinal Waves in Thin Rods
75(65)
Waves in long rods
76(4)
The governing equation
76(1)
Basic propagation characteristics
77(3)
Reflection and transmission at boundaries
80(4)
Reflection from free and fixed ends
80(2)
Reflection from other end conditions
82(1)
Transmission into another rod
83(1)
Waves and vibrations in a finite rod
84(11)
Waves in a finite rod---history of a stress pulse
84(2)
Free vibrations of a finite rod
86(4)
Forced vibrations of rods
90(1)
Impulse loading of a rod---two approaches
91(4)
Longitudinal impact
95(13)
Longitudinal collinear impact of two rods
95(5)
Rigid-mass impact against a rod
100(5)
Impact of an elastic sphere against a rod
105(3)
Dispersive effects in rods
108(17)
Rods of variable cross section---impedance
108(6)
Rods of variable section---horn resonance
114(2)
Effects of lateral inertia---dispersion
116(5)
Effects of lateral inertia---pulse propagation
121(4)
Torsional vibrations
125(3)
The governing equation
126(2)
Experimental studies in longitudinal waves
128(6)
Longitudinal impact of spheres on rods
128(1)
Longitudinal waves across discontinuities
128(2)
The split Hopkinson pressure bar
130(3)
Lateral inertia effects
133(1)
Some other results of longitudinal wave experiments
133(1)
References
134(2)
Problems
136(4)
Flexural Waves in Thin Rods
140(73)
Propagation and reflection characteristics
140(15)
The governing equation
140(3)
Propagation of harmonic waves
143(1)
The initial-value problem
144(4)
Forced motion of a beam
148(5)
Reflection of harmonic waves
153(2)
Free and forced vibrations of finite beams
155(15)
Natural frequencies of finite beams
155(4)
Orthogonality
159(1)
The initial-value problem
160(1)
Forced vibrations of beams---methods of analysis
160(7)
Some problems in forced vibrations of beams
167(3)
Foundation and prestress effects
170(10)
The governing equation
171(2)
The beam on an elastic foundation
173(1)
The moving load on an elastically supported beam
174(1)
The effects of prestress
175(2)
Impulse loading of a finite, prestressed, visco-elastically supported beam
177(3)
Effects of shear and rotary inertia
180(15)
The governing equations
181(3)
Harmonic waves
184(3)
Pulse propagation in a Timoshenko beam
187(8)
Wave propagation in rings
195(7)
The governing equations
195(4)
Wave propagation
199(3)
Experimental studies on beams
202(7)
Propagation of transients in straight beams
202(4)
Beam vibration experiments
206(2)
Waves in curved rings
208(1)
References
209(2)
Problems
211(2)
Waves in Membranes, Thin Plates, and Shells
213(60)
Transverse motion in membranes
213(16)
The governing equation
214(1)
Plane waves
215(2)
The initial-value problem
217(3)
Forced vibration of a membrane
220(2)
Reflection of waves from membrane boundaries
222(2)
Waves in a membrane strip
224(1)
Vibrations of finite membranes
225(4)
Flexural waves in thin plates
229(29)
The governing equations
229(5)
Boundary conditions for a plate
234(1)
Plane waves in an infinite plate
235(1)
An initial-value problem
236(3)
Forced motion of an infinite plate
239(6)
Reflection of plane waves from boundaries
245(1)
Free vibrations of finite plates
246(9)
Experimental results on waves in plates
255(3)
Waves in thin cylindrical shells
258(12)
Governing equations for a cylindrical membrane shell
259(4)
Wave propagation in the shell
263(3)
Longitudinal impact of a membrane shell
266(4)
References
270(1)
Problems
271(2)
Waves in Infinite Media
273(38)
Wave types
273(8)
The governing equations
274(2)
Dilatational and distortional waves
276(2)
Plane waves
278(3)
Waves generated by body forces
281(13)
Certain classical solutions
282(1)
The simple SH wave source
283(5)
More general body forces
288(6)
Cavity source problems
294(15)
Harmonic dilatational waves from a spherical cavity
294(3)
Dilatational waves from a step pulse
297(3)
General case of dilatational waves with spherical symmetry
300(3)
Harmonic waves from a cylindrical cavity
303(3)
Transient dilatational waves from a cylindrical cavity
306(3)
References
309(1)
Problems
310(1)
Waves in Semi-Infinite Media
311(83)
Propagation and reflection of plane waves in a half-space
311(18)
Governing equations
312(5)
Waves at oblique incidence
317(5)
Waves at grazing incidence
322(1)
Surface waves
323(5)
Wave reflection under mixed boundary conditions
328(1)
SH wave source---method of steepest descent
329(14)
The SH wave source---formal solution
330(2)
Direct evaluation of the integral
332(4)
Method of steepest descent
336(5)
SH wave source solution by steepest descent
341(2)
Surface source problems
343(32)
Waves from a harmonic, normal line force
344(9)
Other results for harmonic sources
353(3)
Transient normal loading on a half-space
356(12)
Results for transient loads on a half-space
368(7)
Waves in layered media
375(7)
Two semi-infinite media in contact---plane waves
377(3)
Waves in layered media---Love waves
380(2)
Experimental studies on waves in semi-infinite media
382(7)
Waves into a half-space from a surface source
382(2)
Surface waves on a half-space
384(2)
Other studies on surface waves
386(3)
References
389(2)
Problems
391(3)
Scattering and Diffraction of Elastic Waves
394(37)
Scattering of waves by cavities
395(14)
Scattering of SH waves by a cylindrical cavity
395(5)
Scattering of compressional waves by a spherical obstacle
400(9)
Diffraction of plane waves
409(19)
Discussion of the Green's function approach
409(1)
The Sommerfeld diffraction problem
410(17)
Geometric acoustics
427(1)
References
428(2)
Problems
430(1)
Wave Propagation in Plates and Rods
431(151)
Continuous waves in a plate
431(33)
SH waves in a plate
432(3)
Waves in a plate with mixed boundary conditions
435(5)
The Rayleigh-Lamb frequency equation for the plate
440(2)
The general frequency equation for a plate
442(4)
Analysis of the Rayleigh-Lamb equation
446(12)
Circular crested waves in a plate
458(2)
Bounded plates---SH and Lame modes
460(4)
Waves in circular rods and cylindrical shells
464(16)
The frequency equation for the solid rod
464(4)
Torsional, longitudinal, and flexural modes in a rod
468(7)
Waves in cylindrical shells
475(5)
Approximate theories for waves in plates, rods, and shells
480(52)
An approximate theory for plate flexural modes
482(12)
An approximate theory for extensional waves in plates
494(16)
Approximate theories for longitudinal waves in rods
510(11)
Approximate theories for waves in shells
521(11)
Forced motion of plates and rods
532(29)
SH waves in a plate
533(5)
Pulse propagation in an infinite rod
538(5)
Transient compressional waves in semi-infinite rods and plates
543(18)
Experimental studies on waves in rods and plates
561(14)
Multiple reflections within a waveguide
561(2)
Dispersion of a sharp pulse in a cylindrical rod
563(2)
Experimental results for step pulses
565(6)
Other studies of waves in cylindrical rods and shells
571(4)
References
575(4)
Problems
579(3)
APPENDIX A. THE ELASTICITY EQUATIONS 582(21)
A.1. Notation
582(1)
A.2. Strain
583(2)
A.3. Stress
585(1)
A.4. Conservation equations
585(3)
A.4.1. Conservation of mass
586(1)
A.4.2. Conservation of momentum
587(1)
A.4.3. Conservation of moment of momentum
587(1)
A.4.4. Conservation of energy
588(2)
A.5. Constitutive equations
590(2)
A.5.1. Green's method
590(1)
A.5.2. Cauchy's method
590(1)
A.5.3. Isotropic elastic solid
591(1)
A.6. Solution uniqueness and boundary conditions
592(2)
A.6.1. Uniqueness
592(2)
A.6.2. Boundary conditions
594(1)
A.7. Other continua
594(2)
A.8. Additional energy considerations
596(4)
A.9. Elasticity equations in curvilinear coordinates
600(3)
A.9.1. Cylindrical coordinates
600(1)
A.9.2. Spherical coordinates
601(2)
APPENDIX B. INTEGRAL TRANSFORMS 603(26)
B.1. General
603(1)
B.2. Laplace transforms
604(10)
B.2.1. Definition
604(1)
B.2.2. Transforms of derivatives
605(1)
B.2.3. The inverse transform
605(1)
B.2.4. Partial fractions
606(1)
B.2.5. Solutions of ordinary differential equations
607(1)
B.2.6. Convolution
608(2)
B.2.7. The inversion integral
610(4)
B.3. Fourier transforms
614(6)
B.3.1. Definition
614(1)
B.3.2. Transforms of derivatives
614(2)
B.3.3. The inverse transform
616(1)
B.3.4. Convolution
617(1)
B.3.5. Finite Fourier transforms
617(2)
B.3.6. The Fourier integral
619(1)
B.4. Hankel transforms
620(1)
B.4.1. Definitions
620(1)
B.4.2. Transforms of derivatives and Parseval's theorem
621(1)
B.5. Tables of transforms
621(7)
B.6. Fourier spectra of pulses
628(1)
APPENDIX C. EXPERIMENTAL METHODS IN STRESS WAVES 629(8)
C.1. Methods for producing stress waves
629(3)
C.2. Methods for detecting stress waves
632(5)
References to Appendices A, B, C.
634(3)
Author Index 637(4)
Subject Index 641

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