Deformation of Three-Layer Ellipsoidal Shells Reinforced with Longitudinal Ribs Under Non-Stationary Loading

Dynamic problems of the forced vibrations of tree-layer ellipsoidal shells reinforced with longitudinal ribs under non-stationary surface loading are stated. The basic equations for reinforced three-layer ellipsoidal shell are derived using the Timoshenko model and allowing for geometrical nonlinearity. The vibration equations for these shells are derived from the Hamilton–Ostrogradsky variational principle. A numerical technique for solving these problems is developed. It is based on the integro-interpolation method of construction of difference schemes with respect to the spatial coordinates and explicit finite-difference scheme with respect to the time coordinate. The dynamic processes in reinforced and smooth open clamped three-layer ellipsoidal shells acted upon by uniformly distributed impulsive pressure are studied.