Abstract
We propose a mathematical model of vibration of elastic systems formed by conjugated shells of revolution with different geometry in the field of combined static axisymmetric loads. The model is based on the concepts of geometrically nonlinear theory of mean bending and realized within the framework of the classical Kirchhoff–Love theory with the use of contemporary methods of applied mathematics and numerical analysis. The spectral picture of a shell structure with elements of positive, zero, and negative Gaussian curvature is constructed. This picture enables us to detect resonance situations under specific dynamic actions and determine dangerous combinations of static loads in the analysis of stability of the equilibrium states of the structure.
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