Family Of Grating Techniques Of Slope And Curvature Measurements For Static And Dynamic Flexure Of Plates

Abstract

A family of optical methods are developed for the measurement of slope and curvature of flexed plate surfaces. Slope and curvature contour fringes are generated by using gratings as filters in the light path emerging from the flexed surface. General field equations are derived for gratings placed anywhere in the field. Depending upon the pitch and the position and the number of gratings used, a variety of techniques are obtained for the contouring of slopes or curvatures. When a low density grating is used, the resulting shadowgram yields slope contour fringes if it is placed at the real focal plane of the field lens. Otherwise, the shadow gram fringes are not slope contours. However, slope contours can be obtained if a double-exposure technique or a double grating is used to generate the moire fringes. If a grating of sufficiently high frequency is used, the resulting pattern is a curvature pattern, for which a monochromatic light source is needed. A successive plotting method is also proposed for curvature contouring whereby white light and a grating of arbi-trary pitch can be used. The methods are verified by a series of experiments using cantilever beams and clamped circular plates. Applications to a variety of other problems, including flexure wave propagation, are also demonstrated.