Abstract
This paper describes a non-contacting optical technique for vibration measurement, which can be used to determine the magnitude and phase of every point of a continuous surface under steady-state conditions. In this method, the vibrating surface to be studied is illuminated by a white-light, sinusoidal grating projected from an oblique angle. A series of precisely timed digital images of the vibrating object is recorded as the grid is moved across the surface. An automated analysis then extracts magnitude and phase data at each pixel in the recorded images. The use of white light makes it possible to study the motion of larger surfaces than might be conveniently possible with more conventional Moiré or holographic techniques, and the optical arrangement used seems relatively insensitive to external disturbances. The method seems particularly well suited to the study of structures undergoing relatively low-frequency, large-amplitude vibrations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- ϕ:
-
optical phase-shift at a given pixel
- θ:
-
angle between the projector centerline and the viewing direction
- Δ:
-
pitch of the projected grid at the point of contact with the object
- L :
-
distance from the central point of the object to the projector
- x, y :
-
position coordinates for an analysis point
- z :
-
displacement from the zero phase reference line
- M :
-
fringe sensitivity
- A :
-
vibration amplitude
- H :
-
magnitude transfer function
- ϕ:
-
phase angle between the force input and the vibration response
- ω:
-
vibration frequency
- t :
-
time
References
Ewins, D.J., Modal Testing: Theory, Practice and Application, 2nd edition.Research Studies Press, Hertfordshire, UK (2000).
Sciammarella, C.A., “Overview of Optical Techniques That Measure Displacements: Murray Lecture,”EXPERIMENTAL MECHANICS,43 (1),1–19 (2003).
Soucy, Y., Graham, W.B., and Mitchell, A.K., “A Multichannel Laser System for Modal Testing of Large Space Structures,” Proceedings of 12th International Modal Analysis Conference, Honolulu, HI (1994).
Lehmann, M., Jacquot, P., andFacchini, M., “Shape Measurements on Large Surfaces by Fringe Projection,”Experimental Techniques,23 (2),31–35 (1999).
Robinson, D.W. andReid, G.T., editors, Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, Institute of Physics Publishing, Bristol (1993).
Hopstone, P., Katz, A., andPolitch, J., “Infrastructure of Time-averaged Projection Moiré Fringes in Vibration Analysis,”Applied Optics,28 (24),5305–5311 (1989).
Glasvik, K.J., “Moiré Technique by Means of Digital Image Processing,”Applied Optics,22, (23),3543–3548 (1983).
Rosvold, G.O., “`,”Applied Optics,33 (5),775–786 (1994).
Sutton, M.A., Zhao, W., McNeill, S.R., Schreier, H.W., andChao, Y.J., “Development and Assessment of a Single-image Fringe Projection Method for Dynamics Applications,”EXPERIMENTAL MECHANICS,41 (3),205–217 (2001).
Gasvik, K.J., andRobbersmyr, G.K., “Autocalibration of the Setup for the Projected Moiré Fringe Method,”Experimental Techniques,17 (2),41–44 (1993).
Mitchell, A.K., “Deflection Shape Visualization Using White-light Projected Fringes,” Proceedings of 22nd International Modal Analysis Conference, Dearborn, MI (2004).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mitchell, A.K. Optical modal analysis using white-light projected fringes. Experimental Mechanics 45, 250–258 (2005). https://doi.org/10.1007/BF02427949
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02427949