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Experimental Mechanics

, Volume 13, Issue 3, pp 120–125 | Cite as

Vibrations of segmented shells

Paper discusses the results of an experimental and analytical program on the vibrations of segmented shells
  • M. Lashkari
  • V. I. Weingarten
Article

Abstract

An analytical and experimental investigation was performed to determine the natural frequencies and mode shapes of a cone-cylinder segmented shell. The finite-element technique was used to predict the natural frequencies and mode shapes of a clamped segmented shell. In the experimental phase of the program, the shell was excited by an electromagnet and the natural frequencies were determined with the aid of a microphone. Holographic interferometry was used to identify the mode shapes for each resonant frequency. The analytical and experimental results were in good agreement with one another.

Keywords

Mechanical Engineer Fluid Dynamics Experimental Investigation Resonant Frequency Mode Shape 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

ai

coefficient of thei-th term in the assumed displacement field

n

number of circumferential waves

m

number of meridional half-waves

qi

i-th generalized coordinate

\(\dot q_i\)

velocity ofq i

s

shell meridional coordinate

t

time, sec

T

kinetic energy of the shell, in.-lb

u

meridional displacement of the shell, in.

U

strain energy of the shell, in.-lb

v

circumferential displacement of the shell, in.

w

normal displacement of the shell, in.

W

work of the conservative, external loading, in.-lb

θ

shell circumferential coordinate

ϕ

angle between axis of revolution and normal to shell, rad

ω

natural frequency, rad/sec

ψ

rotation of the middle surface

[K]

shell-stiffness matrix

[M]

shell-inertia matrix

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References

  1. 1.
    Weingarten, V. I. and Gelman, A. P., “Free Vibrations of Cantilevered Conical Shells,” ASCE, J. of the Eng. Mech. Div. EMG, 127–138 (Dec. 1967).Google Scholar
  2. 2.
    Margolias, D. S. and Weingarten, V. I., “Free Vibrations of Pressure Loaded Paraboloidal Shells,” to be published in AIAA J.Google Scholar
  3. 3.
    Lashkari, M., “Elastic Stability and Dynamic Analysis of Hyperboloidal Shells of Revolution,” PhD Dissertation, Univ. of Southern California (June 1971).Google Scholar
  4. 4.
    Margolias, D. S., “The Effect of External Loading on the Natural Frequencies of Paraboloidal Shells,” PhD Dissertation, Univ. of Southern California (June 1970).Google Scholar
  5. 5.
    Sanders, J. L., Jr., “Non-Linear Theories for Thin Shells,”Quarterly of App. Math.,21 (1),21–36 (1963).Google Scholar
  6. 6.
    Stroke, G. W., An Introduction to Coherent Optics and Holography, Academic Press, NY (1966).Google Scholar
  7. 7.
    DeVelis, J. B. andReynolds, G. O., Theory and Application of Holography, Addison-Wesley Publishing Co., Reading, MA (1967).Google Scholar
  8. 8.
    Smith, H. M., Principles of Holography, Wiley-Interscience, a division of John Wiley & Sons, Inc., NY (1969).Google Scholar
  9. 9.
    Gabor, D., “A New Microscopic Principle,”Nature,161,777–778 (1948).Google Scholar
  10. 10.
    Gabor, D., “Microscopy by Reconstructed Wave Fronts,”Proc. Royal Soc., Series A, London,197,457–464 (1949).Google Scholar
  11. 11.
    Leith, E. N. and Upatneiks, J., “Wavefront Reconstruction with Continuous-Tone Objects,” J. Opt. Soc. Am.,53 (1963).Google Scholar
  12. 12.
    Leith, E. N. and Upatnieks, J., “Wavefront Reconstruction with Diffused Illumination and Three Dimensional Objects,” J. Opt. Soc. Am.,54 (1964).Google Scholar
  13. 13.
    Powell, R. L. andStetson, K. A., “Interferometric Vibration Analysis by Wavefront Reconstruction,”J. Opt. Soc. Am.,55 (12),1593–1598 (Dec. 1965).Google Scholar
  14. 14.
    Haines, K. A. andHildebrand, B. P., “Surface Deformation Measurement Using the Wavefront Reconstruction Technique,”App. Op.,5 (4),595–602 (April 1966).Google Scholar
  15. 15.
    Lashkari, M., “Elastic Stability and Dynamic Analysis of Hyperboloidal Shells of Revolution,” PhD Thesis, The University of Southern California (1971).Google Scholar

Copyright information

© Society for Experimental Mechanics, Inc. 1973

Authors and Affiliations

  • M. Lashkari
    • 1
  • V. I. Weingarten
    • 2
  1. 1.Department of Mechanical EngineeringAryamehr University of TechnologyTehranIran
  2. 2.Department of Civil EngineeringUniversity of Southern CaliforniaLos Angeles

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