Concentrated Impact on the Apex of a Hemispherical Sandwich Shell with Asymmetric Thickness Structure

The dynamics of an asymmetric hemispherical sandwich shell with a discretely symmetric light core reinforced with ribs under a concentrated impact on its apex is studied. The model of the Timoshenko theory of shells and rods with independent static and kinematic hypotheses for each layer is used to analyze the elastic structure members. Using the Hamilton–Ostrogradsky variational principle, the equations of motion of the asymmetric structure are obtained. A corresponding finite-element model of the shell that relates the potential strain energy in the shell and the potential of the applied forces is created. The numerical results on the dynamics of an elastic sandwich structure with asymmetric thickness are obtained using the finite element method. The influence of geometric, physical, and mechanical parameters of the asymmetric layers of the shell on its dynamic behavior under a concentrated impact on its apex is studied and new mechanical effects are revealed.