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Experiments of free vibration of shells of revolution

Research program is aimed at investigating, analytically and experimentally, the dynamic large-deformation behavior of shells subjected to shock waves

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Abstract

This paper presents experimental techniques used in and results obtained during a series of experiments performed to investigate the free-vibration behavior of 15-in. base-diameter spherical and paraboloidal shell models of various geometric parameters and boundary conditions. The models were manufactured from polyvinyl-chloride (P.V.C.) sheets by a thermo-vacuum process using special molds and templates. To provide the necessary excitation power, a variable control amplitude/frequency audio oscillator was used to drive a loudspeaker which was mounted underneath the models.

A recently developed noncontact fiber-optics instrument, referred to as the “Fotonic Sensor”, was employed in determining the motion of the models. Thirty-two models of different configurations and boundary conditions were tested in the series. The natural frequencies were observed for all models, while the mode shapes associated with the first four-to-six resonant frequencies were mapped only for some of the models, using special scanning devices.

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Abbreviations

E :

Young's modulus of elasticity

f :

natural frequency of free vibration

h :

thickness of shell model

H :

rise of shell model

m :

mass density of material

r 0 :

base radius of shell model

R :

radius of curvature of shell model

w :

normal displacement

ε:

strain

θ:

circumferential angle

ν:

Poisson's ratio

ρ:

specific gravity of material

σ:

stress

ϕ:

meridional angle

References

  1. Kraus, H., Thin Elastic Shells, John Wiley and Sons, New York (1967).

    Google Scholar 

  2. Budiansky, B. and Roth, R. S., “Axisymmetric Dynamic Buckling of Clamped Shallow Spherical Shells”, Collected Papers on Instability of Shell Structures, NASA TN D-1510, 597 (1962).

  3. Nowacki, W., Dynamics of Elastic Systems, trans. from 1962 Polish edition, Chapman and Hall Ltd., London, (1963).

    Google Scholar 

  4. Witmer, E. A., Pian, T. H. H., and Balmer, H. H., “Dynamic Deformation and Buckling of Spherical Shells under Blast and Impact Loading”, Collected Papers on Instability of Shell Structures, NASA TN D-1510, 607 (1962).

  5. Babcok, C. D. and Sechler, E. E., “The Effect of Initial Imperfections on the Buckling Stress of Cylindrical Shells”, Ibid, Collected Papers on Instability of Shell Structures, NASA TN D-1510, 135.

  6. Thompson, J. M. T., “Making of Thin Shells for Model Stress Analysis,”J. Mech. Engg. Sci.,2 (2),165 (1960).

    Google Scholar 

  7. Adam, H. P. andKing, P. A., “Experimental Investigation of the Stability of Monocoque Domes Subjected to External Pressure,”Experimental Mechanics,5 (10),313–320 (1965).

    Google Scholar 

  8. Lin, M. S. andPopov, E. P., “Buckling of Spherical Sandwich Shells,”Experimental Mechanics,9 (10),433–440 (1969).

    Google Scholar 

  9. Kruger, D. S. andGlockner, P. G., “Experiments on the Stability of Spherical and Paraboloidal Shells,”Experimental Mechanics,11 (6),254–262 (1971).

    Google Scholar 

  10. Hwang, C., “Some Experiments on the Vibration of a Hemispherical Shell,”J. Appl. Mech.,33 (4),817 (1966).

    Google Scholar 

  11. Hu, W. C. L. andRaney, J. P.Experimental and Analytical Study of Vibration of Joined Shells,”AIAA J.,5 (5),976 (1967).

    Google Scholar 

  12. Evensen, H. A. andEwan-Iwanowski, R. M., “Dynamic Response and Stability of Shallow Spherical Shells Subject to Time-Dependent Loading,”AIAA J.,5 (5),969–975 (1967).

    Google Scholar 

  13. Lincoln, J. W. andVolterra, E., “Experimental and Theoretical Determination of Frequencies of Elastic Toroids,”Experimental Mechanics,7 (3),211–217 (1967).

    Google Scholar 

  14. Beckwith, T. G., andBuck, N. L., Mechanical Measurements, 2nd ed., Addison-Wesley Publishing Co., Inc., Reading, MA (1969).

    Google Scholar 

  15. Tawadros, K. Z. and Glockner, P. G., “Experiments on Shell Stability in Air-Driven Shock Tubes”, Research Report No. CE 72-9, Dept. of Civil Engn., The Univ. of Calgary (Feb. 1972); Int. J. for Sound and Vibration,25 (2) (Nov. 1972).

  16. Tawadros, K. Z. andGlockner, P. G., “Experiments on Free Vibration and Stability of Shells of Revolution,”Proc. Rilem Symp. on Exp. Ana. of Instability Problems of Reduced and Full-Scale Models, Buenos-Aires, Argentina,II,431 (1971).

    Google Scholar 

  17. Menadier, C., Kissinger, C. and Adkins, H., “The Fotonic Sensor”, Bulletin No. 02-100, Instruments and Control Systems, Mechanical Technology Inc., Latham, NY.

  18. “Application Assistance Guide for Non-Contact Displacement/Vibration Equipment”, Bull. No. 01-101, Mechanical Technology Inc., Instruments Division, Latham, NY.

  19. Tawadros, K. Z. and Glockner, P. G., “Non-Contact Instrumentation in Free Vibration of Shells”, Research Report No. CE 72-20. Dept. of Civil Engn., The Univ. of Calgary (May 1972); Proc. Int. Symp. on Exp. Mech., The Univ. of Waterloo, Waterloo, Ontario, Canada (May 1972).

  20. Evensen, D. A. andAprahamian, R., “Application of Holography to High-Frequency Vibrations and Transient Response”,NASA Report, TRW Systems Group, Redondo Beach, CA (1969).

    Google Scholar 

  21. Smith, G. A., Laura, P. A. andMatis, M., “Experimental and Analytical Study of Vibrating Stiffened Plates Subjected to Inplane Loading”,J. of ASA,48 (3),part 2,707–713 (Sept. 1970).

    Google Scholar 

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The results presented in this paper were obtained in the course of research sponsored by the National Research Council of Canada, Grant No. A-2736, and the Defence Research Board of Canada, Grant No. 6301-11.

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Glockner, P.G., Tawadros, K.Z. Experiments of free vibration of shells of revolution. Experimental Mechanics 13, 411–421 (1973). https://doi.org/10.1007/BF02324885

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