Wave Motion in Elastic Solids

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 Lam