Dynamics of a three-layer hemispherical shell under non-stationary loading

Dynamic processes are decisive in calculating the behavior of layered structures. Currently, the problem of studying non-stationary dynamic processes of layered shell structures to assess their performance under dynamic loads is quite relevant.On the example of a three-layer hemispherical shell of a symmetric and asymmetric structure with a discrete-inhomogeneous filler, non-stationary dynamic processes were investigated. In the studies, the shear theory of shells and rods of S.P. Tymoshenko was applied using independent static and kinematic hypotheses for each layer and the finite element method was used to calculate the characteristics of the stress-strain state (SSS) and structural vibrations.To derive the oscillation equations of an asymmetric three-layer structure inhomogeneous in thickness, the Hamilton-Ostrogradsky variational principle of stationarity was used.A finite element model of the structure was created for numerical analysis of the dynamics of a layered hemispherical shell with a discrete rib-reinforced filler under the action of dynamic loading.The influence of the physical, mechanical and geometric parameters of the load-bearing layers on the SSS of a three-layer shell under dynamic loading was revealed. Numerical results of solving specific problems are presented.The general trend of the dynamics of all considered variants of the three-layer hemispherical shell structures was a significant response to a change in the elastic modulus of the polymer filler, the magnitude of which significantly affected the nature of the oscillation.The obtained calculation results indicate: an increase in the elastic modulus of the polymer filler by an order of magnitude significantly reduces the effect of the reinforcement action in the structure.The conducted studies show that by selecting the material of the layered package of the hemispherical structure, the thickness of its bearing layers, and the elasticity of the filler, it is possible to create a hemispherical shell structure with predicted dynamic behavior under unsteady