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E-grāmata: Wave Propagation

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(Massachusetts Institute of Technology)
  • Formāts: EPUB+DRM
  • Sērija : The MIT Press
  • Izdošanas datums: 31-Dec-2019
  • Izdevniecība: MIT Press
  • Valoda: eng
  • ISBN-13: 9780262353113
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Wave PropagationPalielināt
  • Formāts: EPUB+DRM
  • Sērija : The MIT Press
  • Izdošanas datums: 31-Dec-2019
  • Izdevniecība: MIT Press
  • Valoda: eng
  • ISBN-13: 9780262353113
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An engineering-oriented introduction to wave propagation by an award-winning MIT professor, with highly accessible expositions and mathematical details—many classical but others not heretofore published.

A wave is a traveling disturbance or oscillation—intentional or unintentional—that usually transfers energy without a net displacement of the medium in which the energy travels. Wave propagation is any of the means by which a wave travels. This book offers an engineering-oriented introduction to wave propagation that focuses on wave propagation in one-dimensional models that are anchored by the classical wave equation. The text is written in a style that is highly accessible to undergraduates, featuring extended and repetitive expositions and displaying and explaining mathematical and physical details—many classical but others not heretofore published. The formulations are devised to provide analytical foundations for studying more advanced topics of wave propagation.

After a precalculus summary of rudimentary wave propagation and an introduction of the classical wave equation, the book presents solutions for the models of systems that are dimensionally infinite, semi-infinite, and finite. Chapters typically begin with a vignette based on some aspect of wave propagation, drawing on a diverse range of topics. The book provides more than two hundred end-of-chapter problems (supplying answers to most problems requiring a numerical result or brief analytical expression). Appendixes cover equations of motion for strings, rods, and circular shafts; shear beams; and electric transmission lines.



An engineering-oriented introduction to wave propagation by an award-winning MIT professor, with highly accessible expositions and mathematical details—many classical but others not heretofore published.
Dedication iii
About the Author v
Acknowledgments vii
Preface xi
1 Introduction to Waves and Their Propagation
1(22)
1-1 Some Fundamental Concepts of Wave Propagation
1(2)
1-2 Modeling in Mechanical Dynamics
3(2)
Example 1-1 Is a Steel Coil a Mass or a Spring?
4(1)
1-3 Generation and Propagation of Waves
5(1)
1-4 Rudimentary Quantitative Wave Analysis
6(3)
1-5 Examples of Rudimentary Wave Propagation
9(6)
Example 1-2 Period of Longitudinal Wave in Glass Rod
11(1)
Example 1-3 Elastic Modulus of Rod
12(1)
Example 1-4 Frequency of Electromagnetic Radio Wave
12(1)
Example 1-5 Tension in String
12(1)
Example 1-6 Bandwidth of Human Hearing
13(2)
Problems for
Chapter One
15(6)
Vignette I Is There a Smallest Quantity of Energy?
21(2)
2 The Classical Wave Equation
23(30)
2-1 A Bit of History
23(2)
2-2 One-dimensional Continua Modeled by the Classical Wave Equation
25(2)
2-3 Wave Motion Governed by the Classical Wave Equation
27(3)
2-4 Partial Derivatives of Wave Functions
30(1)
2-5 Sample Functions and Wave Functions
31(3)
Example 2-1 Bell-shaped Traveling Wave
31(3)
2-6 Principle of Superposition
34(3)
Example 2-2 Superposition of Two Waves
35(2)
Problems for
Chapter Two
37(13)
Vignette II Gravitational Waves and LIGO
50(3)
3 Wave Propagation in Infinite Media
53(102)
3-1 Introduction
53(1)
3-2 Determination of Waveforms from Initial Conditions
53(7)
Example 3-1 Longitudinal Waves Propagating in Two Directions Due to Initial Displacement
56(4)
3-3 Characteristics
60(6)
Example 3-2 Reexamination of Example 3-1
60(6)
3-4 Determination of Waveforms Due to Single Functional Initial Conditions
66(10)
Example 3-3 Displacement and Particle Velocity Waves in Shear Beam Due to Nonzero Initial Displacement
66(4)
Example 3-4 Displacement and Particle Velocity Waves in Shear Beam Due to Nonzero Initial Particle Velocity
70(5)
Example 3-5 Initial Conditions Yielding a Rightward-Only Single Wave
75(1)
3-5 Domain of Dependence
76(7)
Example 3-6 Displacement and Particle Velocity in Rod at Specific Location and Time Due to Initial Conditions
78(5)
3-6 Range of Influence
83(5)
Example 3-7 Range of Influence of Space-Time Point in Aluminum Rod
86(2)
Vignette III NDE Using Ultrasonic and Thermographic Waves for Residual Life Characterizations of Composite Materials and Structures
88(2)
3-7 Harmonic Waves
90(11)
3-7.1 Definitions of Fundamental Quantities of Harmonic Waves
90(3)
3-7.2 Relationships among Fundamental Quantities of Harmonic Waves
93(2)
3-7.3 Examples
95(1)
Example 3-8 Evaluation of Tension in String
95(1)
Example 3-9 Material of Elastic Rod
96(1)
Example 3-10 Wavelength of Transverse Wave in String
96(1)
Example 3-11 Period of Torsional Wave in Cast-iron Alloy
97(1)
Example 3-12 Wave Speed and Wavelength of Harmonic Wave in Electric Transmission Line
98(1)
Example 3-13 String with Cosinusoidal Initial Displacement
98(3)
3-8 Another Look at Harmonic Traveling Waves
101(2)
3-9 Displacement, Force, and Particle Velocity in Elastic Rod
103(5)
3-10 Transmission of Energy
108(12)
3-10.1 Transmission of Energy by Arbitrary (General) Waveform
108(3)
Example 3-14 Power Transmission in Strings, Circular Shafts, Shear Beams, and Electric Transmission Lines
111(3)
3-10.2 Summary and Generic Expressions for Power Transmission
114(1)
Example 3-15 Power Transmission by Displacement Wave in Shear Beam
114(2)
3-10.3 Power Transmission by Harmonic Waves
116(2)
Example 3-16 Power Transmission by Harmonic Wave in Steel Rod
118(2)
3-11 Dispersion
120(3)
3-12 Relatively Advanced Examples
123(15)
Example 3-17 Periodic Function and Periodic Wave
123(5)
Example 3-18 Tone Burst Function and Tone Burst Wave
128(3)
Example 3-19 Attenuation of Tone Burst Wave
131(3)
Example 3-20 Ultrasonic NDE of Residual Static Strength of Impact-Damaged Graphite Fiber Composite Using Tone Burst Waves
134(2)
Example 3-21 Ultrasonic NDE of Residual Fatigue Strength of As-fabricated Graphite Fiber Composite Using Tone Burst Waves
136(2)
Problems for
Chapter Three
138(15)
Vignette IV Sound Waves and Sound Channels in the Ocean
153(2)
4 Wave Propagation in Semi-infinite Media
155(90)
4-1 Introduction
155(1)
4-2 Junctions between Two Media
155(32)
4-2.1 Displacements in Reflected and Transmitted Waves in Rods
158(3)
Example 4-1 Reflection and Transmission at Junction of Aluminum and Graphite Epoxy Rods
161(3)
Example 4-2 Displacement Reflection and Transmission Coefficients as Functions of Rod Properties
164(7)
4-2.2 Particle Velocities in Reflected and Transmitted Waves in Rods
171(1)
4-2.3 Forces in Reflected and Transmitted Waves in Rods
172(1)
4-2.4 Power in Reflected and Transmitted Waves in Rods
173(1)
4-2.5 Summary and Discussion of Reflection and Transmission Coefficients in Rods
174(4)
4-2.6 Examples of Reflection and Transmission in Other Media
178(1)
Example 4-3 Reflection and Transmission of Transverse Waves at Junction Joining Two Strings
178(3)
Example 4-4 Reflection and Transmission of Transverse Waves at Junction Joining Two Circular Shafts
181(2)
Example 4-5 Reflection and Transmission of Charge Waves at Junction Joining Two Electric Transmission Lines
183(4)
4-2.7 Analogy among Various Media
187(1)
4-3 Characteristic Impedances
187(7)
4-3.1 Characteristic Impedances of Various One-dimensional Media
188(1)
Example 4-6 Characteristic Impedances of Strings, Circular Shafts, Shear Beams, and Electric Transmission Lines
189(2)
4-3.2 Reflection and Transmission Coefficients in Terms of Characteristic Impedances for Rods, Strings, Circular Shafts, Shear Beams, and Electric Transmission Lines
191(3)
4-4 General Reflection and Transmission Coefficients versus Impedance
194(9)
Example 4-7 Junction between Semi-infinite Elastic Rod and Viscous Dashpot
199(4)
4-5 Reflection at Clamped and Free Ends
203(14)
4-5.1 Clamped End
204(5)
4-5.2 Free End
209(3)
4-5.3 Alternative Paths to Reflection Coefficients for Clamped and Free Ends
212(2)
Example 4-8 Reflection of Compressive Axial Force Pulse at Free End of Elastic Rod
214(3)
4-6 External Forcing of Semi-infinite Rod
217(10)
Example 4-9 Radiation Damping in Spring-Mass-Rod System
222(5)
Problems for
Chapter Four
227(16)
Vignette V Domino Waves
243(2)
5 Wave Propagation in Finite Media
245(144)
5-1 Introduction
245(1)
5-2 One-dimensional Wave Motion Parameters in Finite Media
245(17)
Example 5-1 Frequency of Longitudinal Wave
245(1)
Example 5-2 Length of Titanium Shaft
246(1)
Example 5-3 Capacitances of Electric Transmission Lines
246(2)
Example 5-4 Location of Break in Electric Transmission Line
248(2)
Example 5-5 Length of Microcylindrical Electric Transmission Line
250(2)
Example 5-6 Power Transmission through Graphite Fiber Epoxy Shear Beam
252(2)
Example 5-7 Pulse-echo Nondestructive Evaluation (NDE) of Specific Segment of Compound Rod
254(2)
Example 5-8 Ultrasonic Determination of Temperature
256(2)
Example 5-9 Ultrasonic Determination of Length in Multiple-Temperature Structure
258(2)
Example 5-10 Wave Motion in Finite-Length Shear Beam
260(2)
Vignette VI Falling Slinky
262(2)
5-3 One-dimensional Wave Propagation Fields in Finite Media
264(99)
Example 5-11 Wave Motion in Clamped-Clamped Rod
265(6)
Example 5-12 Wave Motion in Clamped-Free Rod
271(21)
Example 5-13 Time Dependence of Displacements in Clamped-Free Rod
292(3)
Example 5-14 Wave Motion in Free-Free Rod
295(11)
Example 5-15 Collision of Elastic Rods
306(31)
Example 5-16 Modal Analysis of Clamped-Free Rod
337(6)
Example 5-17 Time Dependence of Displacements in Clamped-Free Rod via Modal Analysis
343(3)
Example 5-18 Equivalence of Modal Analysis and Wave Analysis for Clamped-Free Rod
346(5)
Example 5-19 Falling Elastic Rod
351(12)
Problems for
Chapter Five
363(24)
General References
387(2)
Appendix A Equations of Motion for Uniform Strings, Rods, and Circular Shafts
389(6)
A-1 String
389(1)
A-2 Rod
390(2)
A-3 Circular Shaft
392(3)
Appendix B Shear Beams
395(8)
B-1 Introduction
395(1)
B-2 Model
396(1)
B-3 Equation of Motion via Momentum Principle
397(2)
B-4 An Alternative Route to Equation of Motion
399(1)
B-5 The Shear Coefficient, k0
400(1)
B-6 Conclusion
401(1)
B-7 References
401(2)
Appendix C Electric Transmission Lines
403(6)
C-1 Introduction
403(1)
C-2 Introducing a Transmission Line into a Circuit
403(3)
C-3 Distributive Properties of Transmission Lines
406(1)
C-4 Equations of Motion of Lossless Transmission Line
407(1)
C-5 Reference
408(1)
Answers to End-of-Chapter Problems 409(8)
List of Vignettes 417(2)
List of Tables 419(2)
Index 421
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