Mechanical Vibrations

This classic textbook by J. P. Den Hartog, retired professor of mechanical engineering at MIT, reflects the author's unique ability to combine the scholarly insight of a distinguished scientist with the practical, problem-solving orientation of an experienced industrial engineer. Although mathematics plays a role in the subject, Den Hartog employs the simplest possible mathematical approaches. His lucid explanations of complex problems are presented in a direct style and supported by illustrative models. Numerous figures in the text enhance its value as a basic foundation in a field which Den Hartog calls "a necessary tool for almost every mechanical engineer." The author examines such topics as the kinematics of vibration (including harmonic motions and non-harmonic periodic motions), degrees of freedom, gyroscopic effects, relaxation oscillations, Rayleigh's method, natural frequencies of torsional vibration, Karman vortices, and systems with variable elasticity. Drawing on his experience as an engineer in private industry and in the U.S. Navy's Bureau of Ships, Den Hartog applies theory to practice, discussing the effects of vibrations on turbines, electrical machines, helicopter rotors and airplane wings, diesel engines and electrical transmission lines.
As a special aid to classroom work or self-study, this practical text includes an extensive selection of 233 problems and answers that test the student's mastery of every section of the book. In addition, a highly useful Appendix contains "A Collection of Formulas" for determining the load per inch deflection of linear springs, the load per radian rotation of rotational springs, the natural frequencies of simple systems, the longitudinal and torsional vibration of uniform beams, the transverse or bending vibrations of uniform beams, and the vibrations of rings, membranes, and plates.
When Mechanical Vibrations was first published in 1934, it was a pioneering work in a field which had just been introduced in America's technical schools. In fact, the author wrote it to assist him in teaching the subject at Harvard. "During the life of the book," he says, "from 1934 on, the art and science of engineering has grown at an astonishing rate and the subject of vibration has expanded with it." Professor Den Hartog's constant revisions have kept his book at the forefront of this vital subject, as useful today as its earlier versions were to students of the past.

Book Contents

PREFACE
LIST OF SYMBOLS
CHAPTER 1. KINEMATICS OF VIBRATION
1.1. Definitions
1.2. The Vector Method of Representing Vibrations
1.3. Beats
1.4. A Case of Hydraulic-turbine Penstock Vibration
1.5. Representation by Complex Numbers
1.6. Work Done on Harmonic Motions
1.7. Non-harmonic Periodic Motions
CHAPTER 2. THE SINGLE-DEGREE-OF-FREEDOM SYSTEM
2.1. Degrees of Freedom
2.2. Derivation of the Differential Equation
2.3. Other Cases
2.4. Free Vibrations without Damping
2.5. Examples
2.6. Free Vibrations with Viscous Damping
2.7. Forced Vibrations without Damping
2.8. Forced Vibrations with Viscous Damping
2.9. Frequency-measuring Instruments
2.10. Seismic Instruments
2.11. Electrical Measuring Instruments
2.12. Theory of Vibration Isolation
2.13. Application to Single-phase Electrical Machinery
2.14. Application to Automobiles; Floating Power
CHAPTER 3. TWO DEGREES OF FREEDOM
3.1. Free Vibrations; Natural Modes
3.2. The Undamped Dynamic Vibration Absorber
3.3. The Damped Vibration Absorber
3.4. Ship Stabilization
3.5. Automobile Shock Absorbers
3.6. Isolation of Non-rigid Foundations
CHAPTER 4. MANY DEGREES OF FREEDOM
4.1. Free Vibrations without Damping
4.2. Forced Vibrations without Damping
4.3. Free and Forced Vibrations with Damping
4.4. Strings and Organ Pipes; Longitudinal and Torsional Vibrations of Uniform Bars
4.5. Rayleigh's Method
4.6. Bending Vibrations of Uniform Beams
4.7. Beams of Variable Cross Section
4.8. Normal Functions and Their Applications
4.9. Stodola's Method for Higher Modes
4.10. "Rings, Membrances, and Plates"
CHAPTER 5. MULTICYLINDER ENGINES
5.1. Troubles Peculiar to Reciprocating Engines
5.2. Dynamics of the Crank Mechanism
5.3. Inertia Balance of Multicylinder Engines
5.4. Natural Frequencies of Torsional Vibration
5.5. Numerical Example
5.6. Torque Analysis
5.7. Work Done by Torque on Crank-shaft Oscillation
5.8. Damping of Torsional Vibration; Propeller Damping
5.9. Dampers and Other Means of Mitigating Torsional Vibration
CHAPTER 6. ROTATING MACHINERY
6.1. Critical Speeds
6.2. Holzer's Method for Flexural Critical Speeds
6.3. Balancing of Solid Rotors
6.4. Simultaneous Balancing in Two Planes
6.5. Balancing of Flexible Rotors; Field Balancing
6.6. Secondary Critical Speeds
6.7. Critical Speeds of Helicopter Rotors
6.8. Gyroscopic Effects
6.9. Frame Vibration in Electrical Machines
6.10. Vibration of Propellers
6.11. Vibration of Steam-turbine Wheels and Blades
CHAPTER 7. SELF-EXCITED VIBRATIONS
7.1. General
7.2. Mathematical Criterion of Stability
7.3. Instability Caused by Friction
7.4. Internal Hysteresis of Shafts and Oil-film Lubrication in Bearings as Causes of Instability
7.5. Galloping of Electric Transmission Lines
7.6. Kármán Vortices
7.7. Hunting of Steam-engine Governors
7.8. Diesel-engine Fuel-injection Valves
7.9. Vibrations of Turbines Caused by Leakage of Steam or Water
7.10. Airplane-wing Flutter
7.11. Wheel Shimmy
CHAPTER 8. SYSTEMS WITH VARIABLE OR NON-LINEAR CHARACTERISTICS
8.1. The Principle of Superposition
8.2. Examples of Systems with Variable Elasticity
8.3. Solution of the Equation
8.4. Interpretation of the Result
8.5. Examples of Non-linear Systems
8.6. Free Vibrations with Non-linear Characteristics
8.7. Relaxation Oscillations
8.8. Forced Vibrations with Non-linear Springs
8.9. Forced Vibrations with Non-linear Damping
8.10. Subharmonic Resonance
PROBLEMS
ANSWERS TO PROBLEMS
APPENDIX: A COLLECTION OF FORMULAS
INDEX