Masters Theses


"This thesis provides a vibration analysis of an internally damped, tapered, truncated, cantilever beam. Using two formulations of the problem based on: (1) Discrete mass and (2) continuous mass distribution, solutions are given for a beam having square cross section with linear depth and linear width variation. A Kelvin viscoelastic material for the beam is assumed. The vibration of the beam is considered to produce plane stress in the material, and the stress-strain relationship is applied only to the strain in the plane of bending. An exact solution for frequency of oscillation, mode shape, and steady state response is obtained in the continuous analysis of the problem. To compare results of the discrete and continuous analyses, the first two modes of a typical beam are evaluated numerically. The natural frequencies determined by the two methods differ by less than 9% and the mode shapes are in approximate agreement. The steady state response to harmonic excitation of the supported base of the beam is found. The fundamental natural frequency of the beam is selected as the excitation frequency, and response of the discrete model is determined. The response by continuous analysis in not found because of difficulty in evaluating Bessel functions with complex arguments. Instead, the steady state response of an equivalent continuous beam with uniform cross section is found"--Abstract, page ii.


Cunningham, Floyd M.

Committee Member(s)

Barker, Clark R.
Keith, Harold D. (Harold Dean), 1941-


Mechanical and Aerospace Engineering

Degree Name

M.S. in Engineering Mechanics


University of Missouri--Rolla

Publication Date



ix, 85 pages

Note about bibliography

Includes bibliographical references (page 58).


© 1969 Chimanbhai Magandas Patel, All rights reserved.

Document Type

Thesis - Open Access

File Type




Subject Headings

Structural analysis (Engineering)
Structural dynamics -- Mathematical models
Columns -- Testing -- Mathematical models

Thesis Number

T 2197

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