Impact response of laminated shells with orthogonal curvatures

A set of analytic solutions is presented to predict the dynamic response of simply-supported, doubly curved, cross-ply laminated shells impacted by a solid striker. The solutions are based on a higher-order shear deformation theory (HSDT) which accounts for the parabolic distribution of transverse shear strain through the thickness of a shell and tangential stress-free boundary conditions on the surface of the shell. An analytic impact force function recently proposed by the authors is used to predict the contact force between the striker and the shell and this is incorporated into the solutions. Fundamental frequencies of cross-ply laminated spherical and cylindrical shells are calculated using the present solutions and the results are compared with those published by others. In terms of the characterising coefficients, the solutions can be reduced to versions of the first-order shear deformation theory (FSDT) and the classical shell theory (CST). A comparison of the solutions based on the various theories (HSDT, FSDT and CST) is also made.