Mode shape analysis of angle-ply-laminated composite shallow shells

This work represents the first known comprehensive study concerned with the natural mode shapes of angle-ply-laminated composite shallow shells having rectangular planform and various boundary conditions. The Ritz method with algebraic polynomial displacement functions is used. Convergence studies are made which demonstrate that reasonably accurate results are obtainable before ill conditioning starts to cause problems. Shallow shells with spherical, circular cylindrical, and hyperbolic paraboloidal curvatures and completely free, cantilevered, and doubly cantilevered (i.e., two adjacent edges clamped and the others free) boundary conditions are considered. The effects of the fiber orientation, curvature, and boundary conditions upon the mode shapes are studied. Nodal line crossing in the mode shapes, which exists for most of the cross-ply shells, is replaced by curve veering for angle-ply ones. A gradual change in the mode shapes is observed as the lamination angle increases. Lamination, curvature, and boundary condition change the mode shape characteristics drastically. The information presented in this paper should be useful for engineers and researchers who are interested in the acoustical characteristics of these structural elements.