Mechanical and Electromagnetic Vibrations and Waves

Tamer Bécherrawy is the author of Mechanical and Electromagnetic Vibrations and Waves, published by Wiley.

• Preface xiChapter 1. Free Oscillations11.1. Oscillations and waves, period and frequency 11.2. Simple harmonic vibrations: differential equation and linearity 21.3. Complex representation and phasor representation 51.4. Point mass subject to a force–Kx 91.5. Angular oscillations 121.6. Damped oscillations 151.7. Dissipation of the energy of a damped oscillator 191.8. Oscillating LCR circuits 201.9. Small oscillations of a system with one degree of freedom 221.10. Nonlinear oscillators 251.11. Systems with two degrees of freedom 251.12. Generalization to systems with n degrees of freedom 291.13. Normal variables for systems with n degrees of freedom* 321.14. Summary 351.15. Problem solving suggestions 381.16. Conceptual questions 391.17. Problems 40Chapter 2. Superposition of Harmonic Oscillations, Fourier Analysis 512.1. Superposition of two scalar and isochronous simple harmonic oscillations 512.2. Superposition of two perpendicular and isochronous vector oscillations, polarization 532.3. Superposition of two perpendicular and non-isochronous oscillations 572.4. Superposition of scalar non-synchronous harmonic oscillations, beats 582.5. Fourier analysis of a periodic function 602.6. Fourier analysis of a non-periodic function 652.7. Fourier analysis of a signal, uncertainty relation 672.8. Dirac delta-function 692.9. Summary 712.10. Problem solving suggestions 742.11. Conceptual questions 752.12. Problems 76Chapter 3. Forced Oscillations 833.1. Transient regime and steady regime 833.2. Case of a simple harmonic excitation force 853.3. Resonance 873.4. Impedance and energy of a forced oscillator in the steady regime 883.5. Complex impedance 923.6. Sustained electromagnetic oscillations 943.7. Excitation from a state of equilibrium* 963.8. Response to an arbitrary force, nonlinear systems 973.9. Excitation of a system of coupled oscillators 993.10. Generalization of the concepts of external force and impedance 1033.11. Some applications 1043.12. Summary 1053.13. Problem solving suggestions 1063.14. Conceptual questions 1073.15. Problems 108Chapter 4. Propagation in Infinite Media 1154.1. Propagation of one-dimensional waves 1154.2. Propagation of two- and three-dimensional waves 1174.3. Propagation of a vector wave 1214.4. Polarization of a transverse vector wave 1234.5. Monochromatic wave, wave vector and wavelength1254.6. Dispersion 1274.7. Group velocity 1294.8. Fourier analysis for waves* 1304.9. Modulation 1334.10. Energy of waves 1354.11. Other unattenuated wave equations, conserved quantities* 1374.12. Impedance of a medium* 1394.13. Attenuated waves 1404.14. Sources and observers in motion, the Doppler effect and shock waves 1434.15. Summary 1484.16. Problem solving suggestions 1504.17. Conceptual questions 1524.18. Problems 153Chapter 5. Mechanical Waves 1595.1. Transverse waves on a taut string 1595.2. Strain and stress in elastic solids 1625.3. Elastic waves in massive springs and rods 1665.4. Propagation of sound in a pipe 1685.5. Transverse waves on elastic membranes 1725.6. Mechanical waves in three dimensions 1745.7. Energy of mechanical waves 1765.8. Progressive waves, impedance and intensity 1795.9. Elements of physiological acoustics 1835.10. Infrasounds and ultrasounds 1855.11. Surface waves* 1865.12. Summary 1915.13. Problem solving suggestions 1945.14. Conceptual questions 1945.15. Problems 195Chapter 6. Electromagnetic Waves 2016.1. Principal results of the electromagnetic theory 2016.2. The propagation equations of the fields in vacuum and infinite dielectrics 2046.3. Electromagnetic simple harmonic plane waves 2056.4. Energy density and the Poynting vector 2066.5. Polarization of electromagnetic waves 2076.6. Momentum density and angular momentum density, radiation pressure* 2096.7. Electromagnetic waves in plasmas* 2126.8. Electromagnetic waves in Ohmic conductors* 2146.9. Quantization of electromagnetic radiation 2186.10. Electromagnetic spectrum 2196.11. Emission of electromagnetic radiations 2216.12. Spontaneous emission and stimulated emission 2236.13. Summary 2266.14. Problem solving suggestions 2296.15. Conceptual questions 2296.16. Problems 231Chapter 7. Reflection and Refraction of Waves 2377.1. Reflection of an elastic wave on two joined strings 2377.2. Reflection and transmission of a one-dimensional acoustic wave 2407.3. General laws of reflection and transmission of three-dimensional waves 2437.4. Reflection and refraction of a three-dimensional acoustic wave 2467.5. Reflection and refraction of an electromagnetic wave at the interface of dielectrics 2487.6. Case of attenuated waves in the second medium* 2557.7. Summary 2587.8. Problem solving suggestions 2607.9. Conceptual questions 2617.10. Problems 262Chapter 8. Interference and Diffraction 2698.1. Order and fringes of interference of two waves 2698.2. Intensity and contrast 2718.3. Interference of light waves, Young’s experiment 2738.4. Multiwave interference, conditions for interference 2778.5. Holography 2818.6. Thin film interference 2828.7. The Huygens-Fresnel principle and diffraction by an aperture 2858.8. Diffraction grating 2908.9. Diffraction of X-rays 2958.10. Summary 2978.11. Problem solving suggestions 2998.12. Conceptual questions 3008.13. Problems 301Chapter 9. Standing Waves and Guided Waves 3079.1. One-dimensional standing waves 3089.2. Standing waves on a membrane and in a rectangular cavity 3139.3. Fourier analysis of standing waves* 3169.4. Resonance and standing waves 3199.5. Sound wave guided by two parallel plates 3209.6. Guided sound waves in a rectangular pipe 3229.7. Transmission lines 3249.8. Electromagnetic waveguides* 3269.9. Waveguides formed by two plane and parallel plates* 3289.10. Guided electromagnetic waves in a hollow conductor* 3319.11. Applications of waveguides 3359.12. Summary 3379.13. Problem solving suggestions 3409.14. Conceptual questions 3419.15. Problems 342Answers to the Problems 349APPENDICES 371Appendix A. Mathematical Review 373A.1. Expansion formulas 373A.2. Logarithmic, exponential and hyperbolic functions 374A.3. Trigonometric functions 374A.4. Integrals 375A.5. Complex numbers 378A.6. Vector analysis in Cartesian coordinates 380A.7. Vector analysis in curvilinear coordinates 382Appendix B. Units in Physics 387B.1. Multiples and submultiples of units 387B.2. Fundamental and derived SI units 387B.3. Mechanical units 388B.4. Electromagnetic units 389Appendix C. Some Physical Constants 391C.1. Mechanical and thermodynamic constants 391C.2. Electromagnetic and atomic constants 392Further Reading 393Index 395

“The book employs a multi-disciplinary approach, and the students in electrical and mechanical engineering as well as in physics will find  a useful additional reading.”  (Zentralblatt MATH, 1 December 2012)