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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 68, Iss. 7 — Jul. 1, 1978
  • pp: 924–931

General theory of time-averaged holography for the study of three-dimensional vibrations at a single frequency

Renzo Tonin and David A. Bies  »View Author Affiliations


JOSA, Vol. 68, Issue 7, pp. 924-931 (1978)
http://dx.doi.org/10.1364/JOSA.68.000924


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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

Citation
Renzo Tonin and David A. Bies, "General theory of time-averaged holography for the study of three-dimensional vibrations at a single frequency," J. Opt. Soc. Am. 68, 924-931 (1978)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-68-7-924


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References

  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).

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