MECHANICAL VIBRATIONS by J. P. DEN HARTOG.Originally published in 1917. PREFACE: This book grew from a course of lectures given to students in the Design School of the Westinghouse Company in Pittsburgh, Pa., in the period from 1926 to 1932, when the subject had not yet been introduced into the curriculum of our technical schools. From 1932 until the beginning of the war, it became a regular course at the Harvard Engineering School, and the book was written for the purpose of facilitating that course, being first published in 1934. In its first edition, it was influenced entirely by the authors industrial experience at Westinghouse the later editions have brought modifications and additions suggested by actual problems published in the literature, by private consulting practice, and by service during the war in the Bureau of Ships of the U. S. Navy. The book aims to be as simple as is compatible with a reason ably complete treatment of the subject. Mathematics has not been avoided, but in all cases the mathematical approach used is the simplest one available. In the third edition the number of problems has again been increased, while the principal changes in the text concern subjects in which recent advances have been made, such as airplane wing flutter, helicopter ground vibration, torsional pendulum dampers, singing ships propellers, and electronic instruments. The author expresses his gratitude to the many readers who have written him calling attention to errors and making sugges tions for improvements and hopes that readers of this third edition will also offer suggestions. J P. DEN HAIITOG. CAMBRIDGE, MASS., January, 1947. Contents include: PREFACE. . . LIST OF SYMBOLS CHAPTER I KINEMATICS OF VIBRATION 1. Definitions . 2. The Vector Method of Representing Vibrations 3. Beats 4. A Case of Hydraulic-turbine Penstock Vibration tS 5. Representation by Complex Numbers 11 6. Work Done on Harmonic Motions. . . . . . 14 7. Non-harmonic Periodic Motions. . . . . . 19 CHAPTER II THE SINGLE DEGREE OF FREEDOM SYSTEM 8. Degrees of Freedom 34 9. Derivation of the Differential Equation , 36 10. Other Cases 38 11. Free Vibrations without Damping 43 12. Examples 47 13. Free Vibrations with Viscous Damping . ... 51 14. Forced Vibrations without Damping ... .57 15. Forced Vibrations with Viscous Damping. .... 63 16. Frequency Measuring Instruments. ... ... 72 17. Seismic Instruments .75 18. Electrical Measuring Instruments ... . SO 19. Theory of Vibration Isolation .... ... S9 20. Application to Single-phase Electrical Machinery 92 21. Application to Automobiles Floating Power 96 CHAPTER III Two DEGREES OF FREEDOM 22. Free Vibrations Natural Modes 103 23. The Undamped Dynamic Vibration Absorber 112 24. The Damped Vibration Absorber .119 viii CONTENTS 25. Ship Stabilization by Means of Frahms Tanks 133 26. Gyroscopic Ship Stabilizers 139 26a. Activated Ship Stabilizers 142 27. Automobile Shock Absorbers 145 CHAPTER IV MANY DEGREES OF FREEDOM 28. Free Vibrations without Damping 155 29. Forced Vibrations without Damping 160 30. Free and Forced Vibration with Damping 165 31. Strings and Organ Pipes Longitudinal and Torsional Vibra tions of Uniform Bars 170 32. Rayleighs Method 178 33. Bending Vibrations of Uniform Beams 185 34. Beams of Variable Cross Section 194 35. Normal Functions and Their Applications 198 35a. Stodolas Method for Higher Modes 202 36. Rings, Membranes, and Plates 205 CHAPTER V MULTICYLINDER ENGINES 37. Troubles Peculiar to Reciprocating Engines 213 38. Dynamics of the Crank Mechanism 217 39...

Mechanical Vibrations

Science & Math

Hartog, J. P. Den

Den Hartog, Jacob P.

Physics

McGraw-Hill Companies

First published over 40 years ago, this work has achieved the status of a classic among introductory texts on mechanics. Den Hartog is known for his lively, discursive and often witty presentations of all the fundamental material of both statics and dynamics (and considerable more advanced material) in new, original ways that provide students with insights into mechanical relationships that other books do not always succeed in conveying. On the other hand, the work is so replete with engineering applications and actual design problems that it is as valuable as a reference to the practicing engineer as it is as a text or refresher for the general engineering student. Mechanics is not a "heavy" book, despite the amount of material it covers and the clarity and exactness with which it treats this material. It is undoubtedly one of the most readable texts in the field. More than 550 drawings and diagrams in the regular text and in the highly praised 112-page section of problems and answers further contribute to its lucidity and value. The emphasis is consistently on illuminating fundamental principles and in showing how they are embodied in a high number of real engineering and design problems concerning trusses, loaded cables, beams, jacks, hoists, brakes, cantilevers, springs, balances, pendulums, projectiles, cranks, linkages, propellers, turbines, fly ball engine governors, hydraulic couplings, anti-roll devices, gyroscopes, and hundreds of other mechanical systems and devices. Chapters cover Discrete Coplanar Forces, Conditions of Equilibrium, Distributed Forces, Trusses and Cables, Beams, Friction, Space Forces, The Method of Work, Kinematics of a Point, Dynamics of a Particle, Kinematics of Plane Motion, Moments of Inertia, Dynamics of Plane Motion, Work and Energy, Impulse and Momentum, Relative Motion, and Gyroscopes. Particularly in the last two chapters, Den Hartog provides advanced material not usual in introductory texts. "Very thoroughly recommended to all those anxious to improve their real understanding of the principles of mechanics." — Mechanical World. Index. List of equations. 334 problems, all with answers. Over 550 diagrams and drawings.

Mechanics (Dover Books on Physics)

Dover Publications

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