Stresses and Deformations in a Uniformly Rotating Rectangular Mirror

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Publisher: SMPTE — White Plains, NY, USA
Doc Type: Journal Article
Content Type: Original Research
Abbreviated Title: J SMPTE
Volume: 73, No. 12, pp. 1032–1036
Abstract: Exact expressions for the stresses and displacements in a uniformly rotating mirror of rectangular cross section are presented in dimensionless form. Dimensionless plots of stresses and displacements are given for various ratios of mirror width to thickness, and the distorted shape of the mirror is illustrated for one specific case. It is shown that a mirror can be ground in an initial shape such that it becomes rectangular when operating at the desired speed. The technique for determining this shape is presented and the required shape is illustrated for one specific case. An expression for the curvature of the reflecting surfaces is not given but can readily be obtained using the displacement equations.
Publication Date: 1964-12-01
DOI: 10.5594/J15386
ISSN: Print: 0361-4573
Link: https://doi.org/10.5594/J15386
Author(s): Karl K. StevensDepartment of Theoretical and Applied Mechanics, University of Illinois, Urbana
Robert E. MillerDepartment of Theoretical and Applied Mechanics, University of Illinois, Urbana
Copyright: © 1964 Society of Motion Picture and Television Engineers, Inc.

Bibliographic Reference(s)

A High-Speed Rotating-Mirror Frame Camera [Active]
Bibliography on High-Speed Photography: Including Schlieren and Cathode-Ray Oscillograph Photography [Active]
1. Cladis J. B. Jones C. S. Wickersheim K. A. , “High-speed light pulse shaper using a 5000 rps rotating mirror,” Rev. Sci. Instr. , 27 : 83 – 87 , Feb. 1956 . EXTERNAL
4. Holland T. E. Davis W. C. , “Effects of elastic distortion of rotating mirrors on time resolution in smear cameras,” J. Opt. Soc. Am. , 48 : 365 – 371 , June 1958 . EXTERNAL
5. Johnson H. T. , “Stress distribution in a uniformly rotating equilateral triangular shaft,” J. Appl. Mech. , 77 : 255 – 259 , June 1955 . EXTERNAL
6. Kirkwood W. Markow C. Morton R. , “Photoelastic study of a rotating mirror,” Lawrence Radiation Laboratory Report UCRL-5558, April 1959 . EXTERNAL
7. Timoshenko S. Goodier J. N. , “Theory of elasticity,” McGraw-Hill Book Co., Inc. , New York , 1951 , 2nd ed. , pp. 22 – 27 . EXTERNAL
8. Pickett G. , “Application of the Fourier Method to the solution of certain boundary problems in the theory of elasticity,” Trans. ASME , 11 : A176 – A182 , Sept. 1944 . EXTERNAL
9. Reference 7: 5–7. EXTERNAL

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Karl K. Stevens and Robert E. Miller; Stresses and Deformations in a Uniformly Rotating Rectangular Mirror, Journal of the SMPTE ( Volume: 73, Issue: 12, December 1964); SMPTE, 1964. Available at https://doi.org/10.5594/J15386

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Karl K. Stevens and Robert E. Miller; Stresses and Deformations in a Uniformly Rotating Rectangular Mirror, Journal of the SMPTE ( Volume: 73, Issue: 12, December 1964); SMPTE, 1964. Available at https://doi.org/10.5594/J15386

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<span class="citation">Karl K. Stevens and Robert E. Miller; <cite>Stresses and Deformations in a Uniformly Rotating Rectangular Mirror</cite>, Journal of the SMPTE ( Volume: 73, Issue: 12, December 1964); SMPTE, 1964. Available at <a href="https://doi.org/10.5594/J15386" target="_blank" rel="noopener">https://doi.org/10.5594/J15386</a></span>

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Karl K. Stevens and Robert E. Miller; <cite id="bib-10-5594-j15386">Stresses and Deformations in a Uniformly Rotating Rectangular Mirror</cite>, Journal of the SMPTE ( Volume: 73, Issue: 12, December 1964); SMPTE, 1964
<span class="doi">10.5594/J15386</span>
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Referenced By

Progress Committee Report for 1964 [Active]