Dynamics of Asymmetric Three-Layer Spherical Shells with a Discretely Inhomogeneous Core Under Nonstationary Loading*

The dynamics of asymmetric three-layer spherical shells with a ribbed discrete-symmetric lightweight core under nonstationary loading is studied. The elements of the elastic structure are analyzed using the Timoshenko model of the theory of shells and rods and independent static and kinematic hypotheses for each layer. The equations of motion of the shells under axisymmetric impulsive loading are derived using the Hamilton–Ostrogradsky variational principle. A finite-element shell model that relates the potential strain energy in the body and the potential of the applied forces is developed. The numerical results on the dynamics of the asymmetric three-layer elastic structure with face layers made of dissimilar materials are obtained using the finite-element method. The effect of the geometrical and mechanical parameters of the asymmetric layers of the shell on its dynamic behavior under axisymmetric internal nonstationary loading is studied. New mechanical effects are revealed.