Dynamic behavior of a cylinder with a cutout.

Abstract

The present study presents results of both analytical and experimental investigations of the dynamic behavior of a cylinder with a rectangular cutout. The potential and kinetic energy of a thin shell are approximated by two-dimensional finite difference methods. An algebraic eigenvalue problem is obtained by application of the principle of minimum total energy. The resulting algebraic equation system, which may have as many as 4200 unknowns, is solved efficiently on a high-speed digital computer. The analytical study shows the influence of the cutout on the natural frequencies of the shell, on the mode shape, and on the internal stress distribution. The cutouts range in size from very small holes to openings having an included angle of 120°. Such designs have been encountered in practice and the results for this case are of particular interest for special applications. The experimental verification was performed on a machined aluminum cylinder which had integral end rings and had a radius to thickness ratio of 180 and a length to radius ratio of 1.3. Excellent agreement between experiment and theoretical predictions was obtained, with the maximum discrepancies being on the order of 4%. The cutout had very little influence on the natural frequencies that were experimentally observed.