Wave Motion in Elastic Solids

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ISBN: 9780486667454 | 0486667456
Cover: Paperback
Copyright: 6/1/1991

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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.

Introduction

(1)

General aspects of wave propagation

(2)

Applications of wave phenomena

(2)

Historical background

(4)

Waves and Vibrations in Strings

(66)

Waves in long strings

(20)

The governing equations

(1)

Harmonic waves

(3)

The D'Alembert solution

(1)

The initial-value problem

(3)

The initial-value problem by Fourier analysis

(2)

Energy in a string

(2)

Forced motion of a semi-infinite string

(2)

Forced motion of an infinite string

(6)

Reflection and transmission at boundaries

(7)

Types of boundaries

(1)

Reflection from a fixed boundary

(1)

Reflection from an elastic boundary

(3)

Reflection of harmonic waves

(1)

Reflection and transmission at discontinuities

(1)

Free vibration of a finite string

(6)

Waves in a finite string

(1)

Vibrations of a fixed-fixed string

(3)

The general normal mode solution

(2)

Forced vibrations of a string

(9)

Solution by Green's function

(1)

Solution by transform techniques

(5)

Solution by normal modes

(2)

The string on an elastic base-dispersion

(7)

The governing equation

(1)

Propagation of harmonic waves

(3)

Frequency spectrum and the dispersion curve

(2)

Harmonic and pulse excitation of a semi-infinite string

(2)

Pulses in a dispersive media---group velocity

(10)

The concept of group velocity

(3)

Propagation of narrow-band pulses

(3)

Wide-band pulses---The method of stationary phase

(3)

The string on a viscous subgrade

(3)

The governing equation

(1)

Harmonic wave propagation

(1)

Forced motion of a string

(2)

References

(1)

Problems

(3)

Longitudinal Waves in Thin Rods

(65)

Waves in long rods

(4)

The governing equation

(1)

Basic propagation characteristics

(3)

Reflection and transmission at boundaries

(4)

Reflection from free and fixed ends

(2)

Reflection from other end conditions

(1)

Transmission into another rod

(1)

Waves and vibrations in a finite rod

(11)

Waves in a finite rod---history of a stress pulse

(2)

Free vibrations of a finite rod

(4)

Forced vibrations of rods

(1)

Impulse loading of a rod---two approaches

(4)

Longitudinal impact

(13)

Longitudinal collinear impact of two rods

(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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Wave Motion in Elastic Solids

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