Abstract

In a previous paper [ R. Tonin D. A. Bies , J. Sound Vib.52 (3), 315 (1977)] the theory of time-averaged holographic interferometry was extended to include simple harmonic motion in three orthogonal directions at a single frequency. The amended characteristic function formula was used to calculate the radial and tangential components of a vibrating cylinder by first determining the radial component and from this the tangential component of vibration. In this paper the analysis of the previous paper is improved by making use of a technique originally introduced for the investigation of static deflection using time-averaged holography [ S. K. Dhir J. P. Sikora , Exp. Mech.12 (7), 323 (1972)]. The improved procedure allows simultaneous determination of all vibration amplitude components. The procedure is used for the investigation of the low order resonant vibration modes of four cylinders of various sizes and materials with shear-diaphragm end conditions with good results. The procedure is quite general in its application and not restricted to the study of cylinders. It lends itself easily to the study of coupled-mode vibration problems and in fact many complex resonance phenomena.

© 1978 Optical Society of America

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  1. G. M. Brown, M. Grant, G. W. Stroke, J. Acoust. Soc. Am. 45, 1166 (1969).
    [CrossRef]
  2. P. C. Gupta, K. Singh, Indian J. Pure Appl. Phys. 14, 367 (1976).
  3. K. A. Stetson, J. Opt. Soc. Am. 62, 297 (1972).
    [CrossRef]
  4. P. C. Gupta, K. Singh, Appl. Opt. 14, 129 (1975).
    [PubMed]
  5. C. S. Vikram, R. S. Sirohi, Phys. Lett. A 35, 460 (1971).
    [CrossRef]
  6. C. S. Vikram, Opt. Commun. 8, 355 (1973).
    [CrossRef]
  7. C. S. Vikram, Phys. Lett. A 45, 426 (1973).
    [CrossRef]
  8. C. S. Vikram, Opt. Commun. 10, 290 (1974).
    [CrossRef]
  9. C. S. Vikram, Gouranga Bose, Optik 43, 253 (1975).
  10. A. D. Wilson, D. H. Strope, J. Opt. Soc. Am. 60, 1162 (1970).
    [CrossRef]
  11. A. D. Wilson, J. Opt. Soc. Am. 61, 924 (1971).
    [CrossRef]
  12. C. S. Vikram, Optik 43, 65 (1975).
  13. C. S. Vikram, Opt. Commun. 11, 360 (1974).
    [CrossRef]
  14. N. E. Molin, K. A. Stetson, J. Phys. E. 2, 609 (1969).
    [CrossRef]
  15. M. Zambuto, M. Lurie, Appl. Opt. 9, 2066 (1970).
    [CrossRef] [PubMed]
  16. W. J. Dallas, A. W. Lohmann, Opt. Commun. 13, 134 (1975).
    [CrossRef]
  17. K. A. Stetson, J. Opt. Soc. Am. 61, 1359 (1971).
    [CrossRef]
  18. C. S. Vikram, Optik 45, 55 (1976).
  19. R. Tonin, D. A. Bies, J. Sound Vib. 52 (3), 315 (1977).
    [CrossRef]
  20. S. K. Dhir, J. P. Sikora, Exp. Mech. 12(7), 323 (1972).
    [CrossRef]
  21. P. A. Tuschak, R. A. Allaire, Exp. Mech. 15, 81 (March1975).
    [CrossRef]
  22. R. A. Buckingham, Numerical Methods (Pitman Press, New York, 1962), p. 301.
  23. D. P. Bartlett, The Method of Least Squares (Rumford Press, Concord, N.H., 1915), p. 63.
  24. A. W. Leissa, “Vibration of Shells,” NASA-SP288 (U.S. Govt. Printing Office, Washington, D.C., 1973), Chap. 2.
  25. R. K. Erf, Ed., Holographic Nondestructive Testing (Academic, New York, 1974), p. 202.
  26. This method was suggested to one of the authors (D.A.B.) by I. Rudnick at U. California at Los Angeles.
  27. R. Pryputniewicz, K. A. Stetson, Appl. Opt. 15(3), 725 (1976).
    [CrossRef] [PubMed]

1977 (1)

R. Tonin, D. A. Bies, J. Sound Vib. 52 (3), 315 (1977).
[CrossRef]

1976 (3)

P. C. Gupta, K. Singh, Indian J. Pure Appl. Phys. 14, 367 (1976).

C. S. Vikram, Optik 45, 55 (1976).

R. Pryputniewicz, K. A. Stetson, Appl. Opt. 15(3), 725 (1976).
[CrossRef] [PubMed]

1975 (5)

P. C. Gupta, K. Singh, Appl. Opt. 14, 129 (1975).
[PubMed]

P. A. Tuschak, R. A. Allaire, Exp. Mech. 15, 81 (March1975).
[CrossRef]

W. J. Dallas, A. W. Lohmann, Opt. Commun. 13, 134 (1975).
[CrossRef]

C. S. Vikram, Gouranga Bose, Optik 43, 253 (1975).

C. S. Vikram, Optik 43, 65 (1975).

1974 (2)

C. S. Vikram, Opt. Commun. 11, 360 (1974).
[CrossRef]

C. S. Vikram, Opt. Commun. 10, 290 (1974).
[CrossRef]

1973 (2)

C. S. Vikram, Opt. Commun. 8, 355 (1973).
[CrossRef]

C. S. Vikram, Phys. Lett. A 45, 426 (1973).
[CrossRef]

1972 (2)

S. K. Dhir, J. P. Sikora, Exp. Mech. 12(7), 323 (1972).
[CrossRef]

K. A. Stetson, J. Opt. Soc. Am. 62, 297 (1972).
[CrossRef]

1971 (3)

1970 (2)

1969 (2)

N. E. Molin, K. A. Stetson, J. Phys. E. 2, 609 (1969).
[CrossRef]

G. M. Brown, M. Grant, G. W. Stroke, J. Acoust. Soc. Am. 45, 1166 (1969).
[CrossRef]

Allaire, R. A.

P. A. Tuschak, R. A. Allaire, Exp. Mech. 15, 81 (March1975).
[CrossRef]

Bartlett, D. P.

D. P. Bartlett, The Method of Least Squares (Rumford Press, Concord, N.H., 1915), p. 63.

Bies, D. A.

R. Tonin, D. A. Bies, J. Sound Vib. 52 (3), 315 (1977).
[CrossRef]

Bose, Gouranga

C. S. Vikram, Gouranga Bose, Optik 43, 253 (1975).

Brown, G. M.

G. M. Brown, M. Grant, G. W. Stroke, J. Acoust. Soc. Am. 45, 1166 (1969).
[CrossRef]

Buckingham, R. A.

R. A. Buckingham, Numerical Methods (Pitman Press, New York, 1962), p. 301.

Dallas, W. J.

W. J. Dallas, A. W. Lohmann, Opt. Commun. 13, 134 (1975).
[CrossRef]

Dhir, S. K.

S. K. Dhir, J. P. Sikora, Exp. Mech. 12(7), 323 (1972).
[CrossRef]

Grant, M.

G. M. Brown, M. Grant, G. W. Stroke, J. Acoust. Soc. Am. 45, 1166 (1969).
[CrossRef]

Gupta, P. C.

P. C. Gupta, K. Singh, Indian J. Pure Appl. Phys. 14, 367 (1976).

P. C. Gupta, K. Singh, Appl. Opt. 14, 129 (1975).
[PubMed]

Leissa, A. W.

A. W. Leissa, “Vibration of Shells,” NASA-SP288 (U.S. Govt. Printing Office, Washington, D.C., 1973), Chap. 2.

Lohmann, A. W.

W. J. Dallas, A. W. Lohmann, Opt. Commun. 13, 134 (1975).
[CrossRef]

Lurie, M.

Molin, N. E.

N. E. Molin, K. A. Stetson, J. Phys. E. 2, 609 (1969).
[CrossRef]

Pryputniewicz, R.

Sikora, J. P.

S. K. Dhir, J. P. Sikora, Exp. Mech. 12(7), 323 (1972).
[CrossRef]

Singh, K.

P. C. Gupta, K. Singh, Indian J. Pure Appl. Phys. 14, 367 (1976).

P. C. Gupta, K. Singh, Appl. Opt. 14, 129 (1975).
[PubMed]

Sirohi, R. S.

C. S. Vikram, R. S. Sirohi, Phys. Lett. A 35, 460 (1971).
[CrossRef]

Stetson, K. A.

Stroke, G. W.

G. M. Brown, M. Grant, G. W. Stroke, J. Acoust. Soc. Am. 45, 1166 (1969).
[CrossRef]

Strope, D. H.

Tonin, R.

R. Tonin, D. A. Bies, J. Sound Vib. 52 (3), 315 (1977).
[CrossRef]

Tuschak, P. A.

P. A. Tuschak, R. A. Allaire, Exp. Mech. 15, 81 (March1975).
[CrossRef]

Vikram, C. S.

C. S. Vikram, Optik 45, 55 (1976).

C. S. Vikram, Optik 43, 65 (1975).

C. S. Vikram, Gouranga Bose, Optik 43, 253 (1975).

C. S. Vikram, Opt. Commun. 10, 290 (1974).
[CrossRef]

C. S. Vikram, Opt. Commun. 11, 360 (1974).
[CrossRef]

C. S. Vikram, Opt. Commun. 8, 355 (1973).
[CrossRef]

C. S. Vikram, Phys. Lett. A 45, 426 (1973).
[CrossRef]

C. S. Vikram, R. S. Sirohi, Phys. Lett. A 35, 460 (1971).
[CrossRef]

Wilson, A. D.

Zambuto, M.

Appl. Opt. (3)

Exp. Mech. (2)

S. K. Dhir, J. P. Sikora, Exp. Mech. 12(7), 323 (1972).
[CrossRef]

P. A. Tuschak, R. A. Allaire, Exp. Mech. 15, 81 (March1975).
[CrossRef]

Indian J. Pure Appl. Phys. (1)

P. C. Gupta, K. Singh, Indian J. Pure Appl. Phys. 14, 367 (1976).

J. Acoust. Soc. Am. (1)

G. M. Brown, M. Grant, G. W. Stroke, J. Acoust. Soc. Am. 45, 1166 (1969).
[CrossRef]

J. Opt. Soc. Am. (4)

J. Phys. E. (1)

N. E. Molin, K. A. Stetson, J. Phys. E. 2, 609 (1969).
[CrossRef]

J. Sound Vib. (1)

R. Tonin, D. A. Bies, J. Sound Vib. 52 (3), 315 (1977).
[CrossRef]

Opt. Commun. (4)

W. J. Dallas, A. W. Lohmann, Opt. Commun. 13, 134 (1975).
[CrossRef]

C. S. Vikram, Opt. Commun. 11, 360 (1974).
[CrossRef]

C. S. Vikram, Opt. Commun. 8, 355 (1973).
[CrossRef]

C. S. Vikram, Opt. Commun. 10, 290 (1974).
[CrossRef]

Optik (3)

C. S. Vikram, Gouranga Bose, Optik 43, 253 (1975).

C. S. Vikram, Optik 43, 65 (1975).

C. S. Vikram, Optik 45, 55 (1976).

Phys. Lett. A (2)

C. S. Vikram, R. S. Sirohi, Phys. Lett. A 35, 460 (1971).
[CrossRef]

C. S. Vikram, Phys. Lett. A 45, 426 (1973).
[CrossRef]

Other (5)

R. A. Buckingham, Numerical Methods (Pitman Press, New York, 1962), p. 301.

D. P. Bartlett, The Method of Least Squares (Rumford Press, Concord, N.H., 1915), p. 63.

A. W. Leissa, “Vibration of Shells,” NASA-SP288 (U.S. Govt. Printing Office, Washington, D.C., 1973), Chap. 2.

R. K. Erf, Ed., Holographic Nondestructive Testing (Academic, New York, 1974), p. 202.

This method was suggested to one of the authors (D.A.B.) by I. Rudnick at U. California at Los Angeles.

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