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.

PREFACELIST OF SYMBOLSCHAPTER 1. KINEMATICS OF VIBRATION1.1. Definitions1.2. The Vector Method of Representing Vibrations1.3. Beats1.4. A Case of Hydraulic-turbine Penstock Vibration1.5. Representation by Complex Numbers1.6. Work Done on Harmonic Motions1.7. Non-harmonic Periodic MotionsCHAPTER 2. THE SINGLE-DEGREE-OF-FREEDOM SYSTEM2.1. Degrees of Freedom2.2. Derivation of the Differential Equation2.3. Other Cases2.4. Free Vibrations without Damping2.5. Examples2.6. Free Vibrations with Viscous Damping2.7. Forced Vibrations without Damping2.8. Forced Vibrations with Viscous Damping2.9. Frequency-measuring Instruments2.10. Seismic Instruments2.11. Electrical Measuring Instruments2.12. Theory of Vibration Isolation2.13. Application to Single-phase Electrical Machinery2.14. Application to Automobiles; Floating PowerCHAPTER 3. TWO DEGREES OF FREEDOM3.1. Free Vibrations; Natural Modes3.2. The Undamped Dynamic Vibration Absorber3.3. The Damped Vibration Absorber3.4. Ship Stabilization3.5. Automobile Shock Absorbers3.6. Isolation of Non-rigid FoundationsCHAPTER 4. MANY DEGREES OF FREEDOM4.1. Free Vibrations without Damping4.2. Forced Vibrations without Damping4.3. Free and Forced Vibrations with Damping4.4. Strings and Organ Pipes; Longitudinal and Torsional Vibrations of Uniform Bars4.5. Rayleigh's Method4.6. Bending Vibrations of Uniform Beams4.7. Beams of Variable Cross Section4.8. Normal Functions and Their Applications4.9. Stodola's Method for Higher Modes4.10. "Rings, Membrances, and Plates"CHAPTER 5. MULTICYLINDER ENGINES5.1. Troubles Peculiar to Reciprocating Engines5.2. Dynamics of the Crank Mechanism5.3. Inertia Balance of Multicylinder Engines5.4. Natural Frequencies of Torsional Vibration5.5. Numerical Example5.6. Torque Analysis5.7. Work Done by Torque on Crank-shaft Oscillation5.8. Damping of Torsional Vibration; Propeller Damping5.9. Dampers and Other Means of Mitigating Torsional VibrationCHAPTER 6. ROTATING MACHINERY6.1. Critical Speeds6.2. Holzer's Method for Flexural Critical Speeds6.3. Balancing of Solid Rotors6.4. Simultaneous Balancing in Two Planes6.5. Balancing of Flexible Rotors; Field Balancing6.6. Secondary Critical Speeds6.7. Critical Speeds of Helicopter Rotors6.8. Gyroscopic Effects6.9. Frame Vibration in Electrical Machines6.10. Vibration of Propellers6.11. Vibration of Steam-turbine Wheels and BladesCHAPTER 7. SELF-EXCITED VIBRATIONS7.1. General7.2. Mathematical Criterion of Stability7.3. Instability Caused by Friction7.4. Internal Hysteresis of Shafts and Oil-film Lubrication in Bearings as Causes of Instability7.5. Galloping of Electric Transmission Lines7.6. Kármán Vortices7.7. Hunting of Steam-engine Governors7.8. Diesel-engine Fuel-injection Valves7.9. Vibrations of Turbines Caused by Leakage of Steam or Water7.10. Airplane-wing Flutter7.11. Wheel ShimmyCHAPTER 8. SYSTEMS WITH VARIABLE OR NON-LINEAR CHARACTERISTICS8.1. The Principle of Superposition8.2. Examples of Systems with Variable Elasticity8.3. Solution of the Equation8.4. Interpretation of the Result8.5. Examples of Non-linear Systems8.6. Free Vibrations with Non-linear Characteristics8.7. Relaxation Oscillations8.8. Forced Vibrations with Non-linear Springs8.9. Forced Vibrations with Non-linear Damping8.10. Subharmonic ResonancePROBLEMSANSWERS TO PROBLEMSAPPENDIX: A COLLECTION OF FORMULASINDEX