The equations of linear elasticity for rotationally symmetric deformations are expanded using a small parameter related to the thickness to radius of curvature ratio of the shell to obtain the classical thin shell equations of conical shells as a first approximation. These classical equations with variable coefficients permit further asymptotic expansions in the cases of steep as well as shallow cones, yielding systems of equations with constant coefficients. Solutions of these equations are used to compute the influence coefficients relating edge loads and edge displacements.
The feasibility of two-beam speckle interferometry for the study of time-varying mechanical deformation of diffusely reflecting bodies is demonstrated. A sequence of speckle patterns produced by a vibrating cantilever beam was recorded photographically by means of a high-speed camera. These speckle photographs were subsequently digitized using a CCD camera for input into an image processing computer. By gray-level subtraction of carefully registered pairs of speckle images, fringes corresponding to the relative surface displacements were obtained. A sequence of these fringe patterns was reconstructed to obtain the time-history of deformation. These are compared with time-frozen (strobed) patterns for the same body.
The development of a nondestructive, full-field, quantitative optical technique, and its feasibility to study dynamic deformations of opaque and diffusively reflecting solids under transient loads, are discussed. The technique involves recording a sequence of dynamically changing two-beam speckle interference patterns (also called holographic speckle patterns) of a rapidly deforming body which is doubly illuminated by a laser light source. The time sequence of speckle patterns is recorded by means of a high-speed camera on an ultra-sensitive 35-mm film. The developed negatives are then digitized by a CCD camera into an image processing system. An initial speckle pattern corresponding to the undeformed state of the object is taken as the reference, and subsequent speckle patterns are digitally subtracted (reconstructed) from it to produce time-varying fringe patterns corresponding to the relative deformation of the test object. In order to gain confidence that the technique can be used to record truly transient deformation, it is tested here on a vibrating plate at resonance, thereby obtaining the evolution of the fringe pattern during 1/2 cycle of deformation corresponding to 160 µs.