Masters Theses


"This report investigates the application of transmission Matrices to determine natural frequencies of non-uniform Bernoulli-Euler beams. The classes of non-uniform beams considered includes: truncated wedges, truncated cones, and truncated rectangular pyramids. Two transmission matrices were derived from solutions to the Bernoulli-Euler equation. One was an exact closed form solution which was applicable for the above classes of beams excluding uniform and nearly uniform beams. The second solution was an approximate one limited to the use for nearly uniform beams, but which does give the correct solution to the uniform beam in the limiting case. The transmission matrix has two advantages: (a) It allows for the consideration of multi-segmented beams where the cross-sectional parameters are discontinuous at each segment boundary. (b) Once the 16 transmission matrix elements are calculated, natural frequencies for any set of boundary conditions can be directly obtained. The formulated transmission matrices were verified by comparing calculated natural frequencies for one and two segment beams to those previously reported in the literature. In concluding this work the first three natural frequencies were calculated for three segment beams. The two set of boundary conditions considered were fixed-fixed and pinned-pinned. The beam geometry was composed of non-uniform first and third segments which were symmetric about a uniform mid-segment"--Abstract, page ii.


Rocke, R. D. (Richard Dale), 1938-

Committee Member(s)

Faucett, T. R.
Keith, Harold D. (Harold Dean), 1941-


Mechanical and Aerospace Engineering

Degree Name

M.S. in Mechanical Engineering


National Defense and Education Act Title IV Fellowship


University of Missouri--Rolla

Publication Date



xi, 87 pages


© 1972 Dean Irle Parker, All rights reserved.

Document Type

Thesis - Open Access

File Type




Library of Congress Subject Headings

Vibration -- Measurement
Boundary value problems
Structural dynamics -- Mathematics

Thesis Number

T 2714

Print OCLC #


Electronic OCLC #