Mechanical Vibrations
eBook - ePub

Mechanical Vibrations

J. P. Den Hartog

  1. 464 Seiten
  2. English
  3. ePUB (handyfreundlich)
  4. Über iOS und Android verfügbar
eBook - ePub

Mechanical Vibrations

J. P. Den Hartog

Angaben zum Buch

Über dieses Buch

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.

Häufig gestellte Fragen

Wie kann ich mein Abo kündigen?
Gehe einfach zum Kontobereich in den Einstellungen und klicke auf „Abo kündigen“ – ganz einfach. Nachdem du gekündigt hast, bleibt deine Mitgliedschaft für den verbleibenden Abozeitraum, den du bereits bezahlt hast, aktiv. Mehr Informationen hier.
(Wie) Kann ich Bücher herunterladen?
Derzeit stehen all unsere auf Mobilgeräte reagierenden ePub-Bücher zum Download über die App zur Verfügung. Die meisten unserer PDFs stehen ebenfalls zum Download bereit; wir arbeiten daran, auch die übrigen PDFs zum Download anzubieten, bei denen dies aktuell noch nicht möglich ist. Weitere Informationen hier.
Welcher Unterschied besteht bei den Preisen zwischen den Aboplänen?
Mit beiden Aboplänen erhältst du vollen Zugang zur Bibliothek und allen Funktionen von Perlego. Die einzigen Unterschiede bestehen im Preis und dem Abozeitraum: Mit dem Jahresabo sparst du auf 12 Monate gerechnet im Vergleich zum Monatsabo rund 30 %.
Was ist Perlego?
Wir sind ein Online-Abodienst für Lehrbücher, bei dem du für weniger als den Preis eines einzelnen Buches pro Monat Zugang zu einer ganzen Online-Bibliothek erhältst. Mit über 1 Million Büchern zu über 1.000 verschiedenen Themen haben wir bestimmt alles, was du brauchst! Weitere Informationen hier.
Unterstützt Perlego Text-zu-Sprache?
Achte auf das Symbol zum Vorlesen in deinem nächsten Buch, um zu sehen, ob du es dir auch anhören kannst. Bei diesem Tool wird dir Text laut vorgelesen, wobei der Text beim Vorlesen auch grafisch hervorgehoben wird. Du kannst das Vorlesen jederzeit anhalten, beschleunigen und verlangsamen. Weitere Informationen hier.
Ist Mechanical Vibrations als Online-PDF/ePub verfügbar?
Ja, du hast Zugang zu Mechanical Vibrations von J. P. Den Hartog im PDF- und/oder ePub-Format sowie zu anderen beliebten Büchern aus Technology & Engineering & Civil Engineering. Aus unserem Katalog stehen dir über 1 Million Bücher zur Verfügung.


1.1 Definitions. A vibration in its general sense is a periodic motion, i.e., a motion which repeats itself in all its particulars after a certain interval of time, called the period of the vibration and usually designated by the symbol T. A plot of the displacement x against the time t may be a curve of considerable complication. As an example, Fig. 1.1a shows the motion curve observed on the bearing pedestal of a steam turbine.
The simplest kind of periodic motion is a harmonic motion; in it the relation between x and t may be expressed by
as shown in Fig. 1.1b, representing the small oscillations of a simple pendulum. The maximum value of the displacement is x0, called the amplitude of the vibration.
FIG. 1.1. A periodic and a harmonic function, showing the period T and the amplitude x0.
The period T usually is measured in seconds; its reciprocal f = 1/T is the frequency of the vibration, measured in cycles per second. In some publications this is abbreviated as cyps and pronounced as it is written. In the German literature cycles per second are generally called Hertz in honor of the first experimenter with radio waves (which are electric vibrations).
In Eq. (1.1) there appears the symbol ω, which is known as the circular frequency and is measured in radians per second. This rather unfortunate name has become familiar on account of the properties of the vector representation, which will be discussed in the next section. The relations between ω, f, and T are as follows. From Eq. (1.1) and Fig. 1.1b it is clear that a full cycle of the vibration takes place when ωt has passed through 360 deg. or 2π radians. Then the sine function resumes its previous values. Thus, when ωt = 2π, the time interval t is equal to the period T or
Since f is the reciprocal of T,
For rotating machinery the frequency is often expressed in vibrations per minute, denoted as v.p.m. = 30ω/π.
FIG. 1.2. Two harmonic motions including the phase angle φ.
In a harmonic motion for which the displacement is given by x = x0 sin ωt, the velocity is found by differentiating the displacement with respect to time,
so that the velocity is also harmonic and has a maximum value ωx0.
The acceleration is
also harmonic and with the maximum value ω2x0.
Consider two vibrations given by the expressions x1 = a sin ωt and x2 = b sin (ωt + φ) which are shown in Fig. 1.2, plotted against ωt as abscissa. Owing to the presence of the quantity φ, the two vibrations do not attain their maximum displacements at the same time, but the one is φ/ω sec. behind the other. The quantity φ is known as the phase angle or phase difference between the two vibrations. It is seen that the two motions have the same ω and consequently the same frequency f. A phase angle has meaning only for two motions of the same frequency: if the frequencies are different, phase angle is meaningless.
Example: A body, suspended from a spring, vibrates vertically up and down between two positions 1 and 1½ in. above the ground. During each second it reaches the top position (1½ in. above ground) twenty times. What are T, f, ω, and x0?
Solution: x0 = 1/4 in., T = 1⁄20 sec, f = 20 cycles per second, and ω = 2πf = 126 radians per second.
1.2. The Vector Method of Representing Vibrations. The motion of a vibrating particle can be conveniently represented by means of a rotating vector. Let the vector
(Fig. 1.3) rotate with uniform angular velocity ω in a counterclockwise direction. When time is reckoned from the horizontal position of the vector as a starting point, the horizontal projection of the vector can be written as
a cos ωt
and the vertical projection as
a sin ωt
FIG. 1.3. A harmonic vibration represented by the horizontal projection of a rotating vector.
Either projection can be taken to represent a reciprocating motion; in the following discussion, however, we shall consider only the horizontal projection.
This representation has given rise to the name circular frequency for ω. The quantity ω, being the angular speed of the vector, is measured in radians per second; the frequency f in this case is measured in revolutio...


  1. Cover
  2. Title Page
  3. Copyright Page
  4. Preface
  5. Content
  6. List of Symbols
  7. Chapter 1. Kinematics Of Vibration
  8. Chapter 2. The Single-Degree-Of-Freedom System
  9. Chapter 3. Two Degrees Of Freedom
  10. Chapter 4. Many Degrees Of Freedom
  11. Chapter 5. Multicylinder Engines
  12. Chapter 6. Rotating Machinery
  13. Chapter 7. Self-Excited Vibrations
  14. Chapter 8. Systems With Variable Or Non-Linear Characteristics
  15. Problems
  16. Answers To Problems
  17. Appendix: A Collection Of Formulas
  18. Index