Masters Theses


"It is well known that the unbalanced inertia forces present in rotating shafts set up violent vibrations in a transverse direction at certain speeds known as critical speeds, whirling speeds or whipping speeds. Therefore one who deals with the design of rotating machine parts, such as turbine rotors, multi-cylinder engine crankshafts etc., must consider transverse vibrations of rotating parts.

Practical solutions for finding the critical speeds of simple rotating systems, such as a single disk on a shaft with a single span, were derived by many authors. But as the number of loads and spans increases the problem becomes complex and hence difficult. Mr. M. A.Prohl published a paper introducing a method for finding critical speeds of Multi-Mass, Multi- Span systems.

In this investigation the author has tried to find critical speeds and modes of transverse vibrations of the rotating system symmetrically loaded and supported on three bearings. Each span carries three concentrated loads. Therefore the whole system will have six critical frequencies. The weight of the shaft was considered by dividing it into small segments and finding the concentrated equivalent weight. The bearings were considered to be self aligning and the system to be simply supported. If the system is allowed to operate at or near the critical speed the stress and deflection become quite large. In the analysis of the problem, the system was considered in transverse vibration and gyroscopic effects were neglected.

While solving this problem the author has made use of the IBM- 1620 digital computer to locate the critical frequencies and modes. Until the advent of the digital computer no practical solution to the problem was available for more than two modes of vibration. The method used here is adaptable to many loads and spans.

This problem was chosen by the author because of his interest in the field of vibrations"--Introduction, pages 1-2.


Edwards, Charles L., 1934-

Committee Member(s)

Miles, Aaron J.
Schowalter, Ralph E., 1923-2001
Oeffner, Richard Eugene


Mechanical and Aerospace Engineering

Degree Name

M.S. in Mechanical Engineering


Missouri School of Mines and Metallurgy

Publication Date



v, 44 pages

Note about bibliography

Includes bibliographical references (page 37).


© 1963 Pravinchandra M. Upadhyay, All rights reserved.

Document Type

Thesis - Open Access

File Type




Thesis Number

T 1536

Print OCLC #