Abstract

The theory of time-averaged holography for static displacements is extended to include three-dimensional vibrations of the most general kind at a single frequency. The introduction of the theory of generalized least squares to solve the nonlinear characteristic equation allows the determination of component amplitudes and phases. The theory is used to analyze the motion of a cylinder with shear-diaphragm ends vibrating in coupled temporal modes and a distorted cylinder vibrating in superposed spatial modes.

© 1978 Optical Society of America

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  1. K. A. Stetson, "Method of stationary phase for analysis of fringe functions in hologram interferometry," Appl. Opt. 11, 1725–1731 (1972).
  2. C. S. Vikram, "Stroboscopic holographic interferometry of vibration simultaneously in two sinusoidal modes," Opt. Commun. 11, 360–364 (1974).
  3. A. D. Wilson, "Computed time-average holographic interferometric fringes of a circular plate vibrating simultaneously in two rationally or irrationally related modes," J. Opt. Soc. Am. 61, 924–929 (1971).
  4. A. D. Wilson and D. H. Strope, "Time-average holographic interferometry of a circular plate vibrating simultaneously in two rationally related modes," J. Opt. Soc. Am. 60, 1162–1165 (1970).
  5. W. J. Dallas and A. W. Lohmann, "Deciphering vibration holograms," Opt. Commun. 13, 134–137 (1975).
  6. C. S. Vikram and G. Bose, "Holographic interferometry of damped oscillations with two frequencies," Optik 43, 253-258 (1975).
  7. G. R. Reddy, "Holographic interferometry of non-harmonic periodic motions," Indian J. Phys. 50, 445–448 (1975).
  8. A. D. Wilson, "Characteristic functions for time-average holography," J. Opt. Soc. Am 60, 1068–1071 (1970).
  9. C. S. Vikram, "Holographic interferometry of superposition of motions with different time functions," Optik 45, 55–64 (1976).
  10. M. Zambuto and M. Lurie, "Holographic measurement of general forms of motion," Appl. Opt. 9, 2077–2072 (1970).
  11. C. S. Vikram, "Holographic interferometry of superposition of two motions," Optik 43, 65–70 (1975).
  12. T. Matsumoto, K. Iwata, and R. Nagata, "Measuring accuracy of three-dimensional displacements in holographic interferometry," Appl. Opt. 12, 961–967 (1973).
  13. K. A. Haines and B. P. Hildebrand, "Surface-deformation measurement using the wave front reconstruction technique," Appl. Opt. 5, 595–602 (1966).
  14. F. Bellani and A. Sona, "Measurement of three-dimensional displacements by scanning a double-exposure hologram," Appl. Opt. 13, 1337–1341 (1974).
  15. S. K. Dhir and J. P. Sikora, "An improved method for obtaining the general-displacement field from a holographic interferogram," Exp. Mech. 323–327 (July, 1972).
  16. C. A. Sciammarella and J. A. Gilbert, "Strains analysis of a disk subjected to diametral compression by means of holographic interferometry," Appl. Opt. 12, 1951–1956 (1973).
  17. N. E. Molin and K. A. Stetson, "Measuring combination mode vibration patterns by hologram interferometry," J. Phys. E 2, 609–612 (1969).
  18. K. A. Stetson and P. A. Taylor, "The use of normal mode theory in holographic vibration analysis with application to an asymmetrical circular disk," J. Phys. E 4, 1009–1015 (1971).
  19. D. A. Evensen, "Application of holography to panel flutter," AIAA J. 14, 1671–1674 (1976).
  20. R. Tonin and D. A. Bies, "Time-averaged holography for the study of three-dimensional vibrations," J. Sound Vib. 52, 315–323 (1977).
  21. R. Tonin and D. A. Bies, "Analysis of three-dimensional vibrations from time-averaged holograms" (unpublished).
  22. J. A. Levitt and K. A. Stetson, "Mechanical vibrations: mapping their phase with hologram interferometry," Appl. Opt. 15, 195–199 (1976).
  23. D. B. Neumann, C. F. Jacobson, and G. M. Brown, "Holographic technique for determining the phase of vibrating objects," Appl. Opt. 9, 1357–1362 (1970).
  24. N. G. Vlasov and A. E. Shtan'ko, "Determination of order number and sign of interference fringes," Sov. Phys. Tech. Phys. 21, 111–112 (1976).
  25. Optimization, edited byR. Fletcher (Academic, New York, 1969), Chap. 16.
  26. R. Tonin and D. A. Bies, "The vibration of circular cylinders of variable thickness" (unpublished).
  27. R. N. Arnold and G. B. Warburton, "Flexural vibrations of the walls of thin cylindrical shells having freely supported ends," Proc. R. Soc. A 197, 238–256 (1949).

1977

R. Tonin and D. A. Bies, "Time-averaged holography for the study of three-dimensional vibrations," J. Sound Vib. 52, 315–323 (1977).

1976

J. A. Levitt and K. A. Stetson, "Mechanical vibrations: mapping their phase with hologram interferometry," Appl. Opt. 15, 195–199 (1976).

C. S. Vikram, "Holographic interferometry of superposition of motions with different time functions," Optik 45, 55–64 (1976).

N. G. Vlasov and A. E. Shtan'ko, "Determination of order number and sign of interference fringes," Sov. Phys. Tech. Phys. 21, 111–112 (1976).

D. A. Evensen, "Application of holography to panel flutter," AIAA J. 14, 1671–1674 (1976).

1975

W. J. Dallas and A. W. Lohmann, "Deciphering vibration holograms," Opt. Commun. 13, 134–137 (1975).

C. S. Vikram and G. Bose, "Holographic interferometry of damped oscillations with two frequencies," Optik 43, 253-258 (1975).

G. R. Reddy, "Holographic interferometry of non-harmonic periodic motions," Indian J. Phys. 50, 445–448 (1975).

C. S. Vikram, "Holographic interferometry of superposition of two motions," Optik 43, 65–70 (1975).

1974

F. Bellani and A. Sona, "Measurement of three-dimensional displacements by scanning a double-exposure hologram," Appl. Opt. 13, 1337–1341 (1974).

C. S. Vikram, "Stroboscopic holographic interferometry of vibration simultaneously in two sinusoidal modes," Opt. Commun. 11, 360–364 (1974).

1973

1972

1971

K. A. Stetson and P. A. Taylor, "The use of normal mode theory in holographic vibration analysis with application to an asymmetrical circular disk," J. Phys. E 4, 1009–1015 (1971).

A. D. Wilson, "Computed time-average holographic interferometric fringes of a circular plate vibrating simultaneously in two rationally or irrationally related modes," J. Opt. Soc. Am. 61, 924–929 (1971).

1970

1969

N. E. Molin and K. A. Stetson, "Measuring combination mode vibration patterns by hologram interferometry," J. Phys. E 2, 609–612 (1969).

1966

1949

R. N. Arnold and G. B. Warburton, "Flexural vibrations of the walls of thin cylindrical shells having freely supported ends," Proc. R. Soc. A 197, 238–256 (1949).

Arnold, R. N.

R. N. Arnold and G. B. Warburton, "Flexural vibrations of the walls of thin cylindrical shells having freely supported ends," Proc. R. Soc. A 197, 238–256 (1949).

Bellani, F.

Bies, D. A.

R. Tonin and D. A. Bies, "Time-averaged holography for the study of three-dimensional vibrations," J. Sound Vib. 52, 315–323 (1977).

R. Tonin and D. A. Bies, "Analysis of three-dimensional vibrations from time-averaged holograms" (unpublished).

R. Tonin and D. A. Bies, "The vibration of circular cylinders of variable thickness" (unpublished).

Bose, G.

C. S. Vikram and G. Bose, "Holographic interferometry of damped oscillations with two frequencies," Optik 43, 253-258 (1975).

Brown, G. M.

Dallas, W. J.

W. J. Dallas and A. W. Lohmann, "Deciphering vibration holograms," Opt. Commun. 13, 134–137 (1975).

Dhir, S. K.

S. K. Dhir and J. P. Sikora, "An improved method for obtaining the general-displacement field from a holographic interferogram," Exp. Mech. 323–327 (July, 1972).

Evensen, D. A.

D. A. Evensen, "Application of holography to panel flutter," AIAA J. 14, 1671–1674 (1976).

Gilbert, J. A.

Haines, K. A.

Hildebrand, B. P.

Iwata, K.

Jacobson, C. F.

Levitt, J. A.

Lohmann, A. W.

W. J. Dallas and A. W. Lohmann, "Deciphering vibration holograms," Opt. Commun. 13, 134–137 (1975).

Lurie, M.

M. Zambuto and M. Lurie, "Holographic measurement of general forms of motion," Appl. Opt. 9, 2077–2072 (1970).

Matsumoto, T.

Molin, N. E.

N. E. Molin and K. A. Stetson, "Measuring combination mode vibration patterns by hologram interferometry," J. Phys. E 2, 609–612 (1969).

Nagata, R.

Neumann, D. B.

Reddy, G. R.

G. R. Reddy, "Holographic interferometry of non-harmonic periodic motions," Indian J. Phys. 50, 445–448 (1975).

Sciammarella, C. A.

Shtan’ko, A. E.

N. G. Vlasov and A. E. Shtan'ko, "Determination of order number and sign of interference fringes," Sov. Phys. Tech. Phys. 21, 111–112 (1976).

Sikora, J. P.

S. K. Dhir and J. P. Sikora, "An improved method for obtaining the general-displacement field from a holographic interferogram," Exp. Mech. 323–327 (July, 1972).

Sona, A.

Stetson, K. A.

J. A. Levitt and K. A. Stetson, "Mechanical vibrations: mapping their phase with hologram interferometry," Appl. Opt. 15, 195–199 (1976).

K. A. Stetson, "Method of stationary phase for analysis of fringe functions in hologram interferometry," Appl. Opt. 11, 1725–1731 (1972).

K. A. Stetson and P. A. Taylor, "The use of normal mode theory in holographic vibration analysis with application to an asymmetrical circular disk," J. Phys. E 4, 1009–1015 (1971).

N. E. Molin and K. A. Stetson, "Measuring combination mode vibration patterns by hologram interferometry," J. Phys. E 2, 609–612 (1969).

Strope, D. H.

Taylor, P. A.

K. A. Stetson and P. A. Taylor, "The use of normal mode theory in holographic vibration analysis with application to an asymmetrical circular disk," J. Phys. E 4, 1009–1015 (1971).

Tonin, R.

R. Tonin and D. A. Bies, "Time-averaged holography for the study of three-dimensional vibrations," J. Sound Vib. 52, 315–323 (1977).

R. Tonin and D. A. Bies, "Analysis of three-dimensional vibrations from time-averaged holograms" (unpublished).

R. Tonin and D. A. Bies, "The vibration of circular cylinders of variable thickness" (unpublished).

Vikram, C. S.

C. S. Vikram, "Holographic interferometry of superposition of motions with different time functions," Optik 45, 55–64 (1976).

C. S. Vikram, "Holographic interferometry of superposition of two motions," Optik 43, 65–70 (1975).

C. S. Vikram and G. Bose, "Holographic interferometry of damped oscillations with two frequencies," Optik 43, 253-258 (1975).

C. S. Vikram, "Stroboscopic holographic interferometry of vibration simultaneously in two sinusoidal modes," Opt. Commun. 11, 360–364 (1974).

Vlasov, N. G.

N. G. Vlasov and A. E. Shtan'ko, "Determination of order number and sign of interference fringes," Sov. Phys. Tech. Phys. 21, 111–112 (1976).

Warburton, G. B.

R. N. Arnold and G. B. Warburton, "Flexural vibrations of the walls of thin cylindrical shells having freely supported ends," Proc. R. Soc. A 197, 238–256 (1949).

Wilson, A. D.

Zambuto, M.

M. Zambuto and M. Lurie, "Holographic measurement of general forms of motion," Appl. Opt. 9, 2077–2072 (1970).

AIAA J.

D. A. Evensen, "Application of holography to panel flutter," AIAA J. 14, 1671–1674 (1976).

Appl. Opt.

Indian J. Phys.

G. R. Reddy, "Holographic interferometry of non-harmonic periodic motions," Indian J. Phys. 50, 445–448 (1975).

J. Opt. Soc. Am

A. D. Wilson, "Characteristic functions for time-average holography," J. Opt. Soc. Am 60, 1068–1071 (1970).

J. Opt. Soc. Am.

J. Phys. E

N. E. Molin and K. A. Stetson, "Measuring combination mode vibration patterns by hologram interferometry," J. Phys. E 2, 609–612 (1969).

K. A. Stetson and P. A. Taylor, "The use of normal mode theory in holographic vibration analysis with application to an asymmetrical circular disk," J. Phys. E 4, 1009–1015 (1971).

J. Sound Vib.

R. Tonin and D. A. Bies, "Time-averaged holography for the study of three-dimensional vibrations," J. Sound Vib. 52, 315–323 (1977).

Opt. Commun.

W. J. Dallas and A. W. Lohmann, "Deciphering vibration holograms," Opt. Commun. 13, 134–137 (1975).

C. S. Vikram, "Stroboscopic holographic interferometry of vibration simultaneously in two sinusoidal modes," Opt. Commun. 11, 360–364 (1974).

Optik

C. S. Vikram, "Holographic interferometry of superposition of motions with different time functions," Optik 45, 55–64 (1976).

C. S. Vikram and G. Bose, "Holographic interferometry of damped oscillations with two frequencies," Optik 43, 253-258 (1975).

C. S. Vikram, "Holographic interferometry of superposition of two motions," Optik 43, 65–70 (1975).

Proc. R. Soc. A

R. N. Arnold and G. B. Warburton, "Flexural vibrations of the walls of thin cylindrical shells having freely supported ends," Proc. R. Soc. A 197, 238–256 (1949).

Sov. Phys. Tech. Phys.

N. G. Vlasov and A. E. Shtan'ko, "Determination of order number and sign of interference fringes," Sov. Phys. Tech. Phys. 21, 111–112 (1976).

Other

Optimization, edited byR. Fletcher (Academic, New York, 1969), Chap. 16.

R. Tonin and D. A. Bies, "The vibration of circular cylinders of variable thickness" (unpublished).

R. Tonin and D. A. Bies, "Analysis of three-dimensional vibrations from time-averaged holograms" (unpublished).

S. K. Dhir and J. P. Sikora, "An improved method for obtaining the general-displacement field from a holographic interferogram," Exp. Mech. 323–327 (July, 1972).

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