Masters Theses


"This thesis provides a vibration analysis of a rotating cantilever beam with an independently rotating thin circular disk on the free end. The exact differential equations of the system as defined by classical Bernoulli-Euler beam theory are written using the methods of the calculus of variations. The exact equations are not solved, but two different approximations are found by assuming a cubic polynomial deflection curve and applying the equation of Lagrange. The solutions are restricted to small deflections of the beam and a shaft stiffness which permits a deflection in only a single plane. Nonlinear differential equations result in the second approximation and are solved by a digital analog simulation. The nonlinear equations are then linearized using only the dominant terms. Using the linearized equations, the first two natural frequencies and their respective amplitude ratios are solved for in a general computer program that can be applied to many different free vibration beam problems. The results show that the fundamental mode frequency decreases with increasing tip mass and increasing beam rotational speed which results in instability at high speeds. The relative spin of the disk with respect to the beam has no effect at zero beam rotation, but the effect of the relative spin of the disk increases as the beam rotation increases. The results obtained follow the trend reported in other works for limiting cases of this problem"--Abstract, pages ii-iii.


Barker, Clark R.

Committee Member(s)

Rocke, R. D. (Richard Dale), 1938-
Keith, Harold D. (Harold Dean), 1941-


Mechanical and Aerospace Engineering

Degree Name

M.S. in Mechanical Engineering


University of Missouri--Rolla

Publication Date



viii, 77 pages

Note about bibliography

Includes bibliographical references (page 35).


© 1970 Darrell Blaine Crimmins, All rights reserved.

Document Type

Thesis - Open Access

File Type




Subject Headings

Machinery -- Vibration
Machinery -- Vibration -- Computer simulation
Machinery -- Testing -- Mathematical models
Structural dynamics -- Mathematical models

Thesis Number

T 2485

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