Abstract
An optical technique based on transparent diffraction gratings is described by which the deflection contours of deformed, nearly flat plates may be obtained to any required sensitivity between 0.00005 in. and 0.010 in. The theory of diffraction gratings in reflection arrangements is given and the optical requirements to eliminate perspective distortion are outlined. Experimental verification using diffraction gratings containing 1000 lines per inch to give a deflection sensitivity of 0.00081 in./fringe shows the method to be reliable.
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Abbreviations
- α:
-
angle of incidence
- β:
-
angle of emergence
- δ:
-
phase change
- δ′:
-
constant depending upon ruling characteristic
- λ:
-
wavelength of light
- v :
-
Poisson's ratio
- μ:
-
refractive index
- θ:
-
absolute phase relation
- a :
-
outside radius of disk
- a u :
-
amplitude of emergence of sequenceP u ,r-P u
- A :
-
amplitude of emergent beam
- C r :
-
phase constant depending upon viewing conditions
- f :
-
fractional position of a point within a ruling pitch
- h :
-
grid pitch
- K,k :
-
constant phase relations
- m,n :
-
integer numbers
- p :
-
spectral order number
- r :
-
resultant order sequence number radius
- t :
-
air-gap thickness at point of emergence
- ω:
-
ruling pitch theoretical defelction
- x,y,z :
-
rectangular Cartesian coordinates
References
Duncan, J. P., “Interferometry Applied to the Study of Elastic Flexure,”Proc. Inst. Mech. Eng. (London) 176 (16),379–389 (1962).
Theocaris, P. S., “Isopachic Patterns by the Moiré Method,”Proc. SESA, XXI, (1),153–159 (June 1954).
Guild, J., “The Interference Systems of Crossed Diffraction Gratings,”Monographs on the Physics and Chemistry of Materials, Clarendon Press, Oxford (1956).
Middleton, E. and Jenkins, C. J., “A Moiré Method of Strain Analysis for Student Use,” Bulletin Mech. Eng. Ed., Manchester College of Science and Technology, Permagon Press, Issue No. 3 (1966).
Timoshenko, S. and Woinowsky-Krieger, S., “Theory of Plates and Shells,” McGraw-Hill Book Co., 60 (1959).
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Middleton, E. A reflection technique for the survey of the deflection of flat plates. Experimental Mechanics 8, 56–62 (1968). https://doi.org/10.1007/BF02326127
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DOI: https://doi.org/10.1007/BF02326127