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TECHNICAL PAPERS

Vibrations of Complete Spherical Shells With Imperfections

[+] Author and Article Information
Thomas A. Duffey

P.O. Box 1239, Tijeras, NM 87059tduffey2@aol.com

Jason E. Pepin

 Los Alamos National Laboratory, Los Alamos, NM 87544jpepin@lanl.gov

Amy N. Robertson

2340 Kohler, Boulder, CO 80305amynrobertson@gmail.com

Michael L. Steinzig

 Los Alamos National Laboratory, Los Alamos, NM 87544steinzig@lanl.gov

Kimberly Coleman

 New Mexico Tech, 801 Leroy Place, Socorro, NM 87801harper@nmt.edu

J. Vib. Acoust 129(3), 363-370 (Feb 01, 2007) (8 pages) doi:10.1115/1.2731415 History: Received June 26, 2006; Revised February 01, 2007

Numerous theoretical investigations on the natural frequencies for complete spherical shells have been reported over the past four decades. However, attempts at correlating the theoretical results with either experimental or simulated results (both for axisymmetric and nonaxisymmetric modes of vibration) are almost completely lacking. In this paper, natural frequencies and mode shapes obtained from axisymmetric and nonaxisymmetric theories of vibration of complete spherical shells and from finite element computer simulations of the vibrations, with and without geometrical imperfections, are presented. Modal tests reported elsewhere on commercially available, thin spherical marine floats (with imperfections) are then utilized as a basis for comparison of frequencies to both the theoretical and numerical results. Because of the imperfections present, “splitting” of frequencies of nonaxisymmetric modes is anticipated. The presence of this frequency splitting phenomenon is demonstrated. In addition, results of a “whole field” measurement on one of the imperfect shells using dynamic holography are presented.

Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 4

Finite element simulations using constant average radius and thickness

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Figure 13

Average radius as a function of meridional angle, shell No. 17

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Figure 14

Comparison of extracted modal frequencies from PRISM®, FEM, and Accelerometer 3

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Figure 15

Comparison of extracted modal frequencies from PRISM®, FEM, and Accelerometers 2 and 3 for n=2

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Figure 5

Degenerate nonaxisymmetric modes for n=5

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Figure 6

Finite element simulations including meridional variations in thickness

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Figure 7

Finite element simulations including meridional variations in both thickness and radius

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Figure 8

Frequencies from accelerometer No. 3 data, float No. 17

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Figure 9

Resonant frequencies obtained in shell No. 17 using the PRISM® whole field technique

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Figure 10

Shell No. 17 before excitation

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Figure 11

Shell No. 17, first observed mode (5093Hz)

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Figure 12

Average thickness as a function of meridional angle, shell No. 17

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Figure 1

Complete spherical shell

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Figure 2

Float frequencies using higher order theory

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Figure 3

First three lower branch axisymmetric modes of a complete spherical shell

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