"In this report the flexural vibrations of the walls of free, thin, circular cylinders are considered. Theoretical expressions are developed for the natural frequencies by extending the approximate energy method of Arnold and Warburton to the free-free case. Furthermore, the developed expressions are shown to apply, as special cases, to the fixed-fixed and simply-supported cylinders analyzed by Arnold and Warburton. The energy solution for free-free cylinders is checked both experimentally using a 3500 pound-force, 5 to 2000 hertz, vibration exciter and numerically using the well documented SABOR IV-DYNAL finite element program. While the derived energy method accounts for any prescribed number of circumferential waves, only the two and three wave cases were selected for experimental and numerical checking. Cylinder geometric parameters investigated are length/radius = 1, 3, 5, 10, 15, and 20; and radius/wall thickness = 30. The experimental natural frequencies deviate by less than eight percent from the corresponding energy method frequencies. Finite element frequency deviations increase with increasing element length and axial half-wave number, m. They are less than nine percent for element-length/radius ≤ 0.625 and m ≤ 5. The mode shapes obtained with the finite element program are also in agreement with the assumed displacement forms of the energy method"--Abstract, page ii.
Cunningham, Floyd M.
Oglesby, David B.
Rocke, R. D. (Richard Dale), 1938-
Mechanical and Aerospace Engineering
M.S. in Engineering Mechanics
National Science Foundation (U.S.)
University of Missouri--Rolla
ix, 44 pages
© 1971 Dale Elmer Leanhardt, All rights reserved.
Thesis - Open Access
Cylinders -- Vibration
Frequencies of oscillating systems
Thin-walled structures -- Mathematical models
Print OCLC #
Electronic OCLC #
Link to Catalog Record
Leanhardt, Dale Elmer, "An energy solution for vibration characteristics of free thin cylinders" (1971). Masters Theses. 5093.