Abstract
A mathematical model, methods and algorithm for estimating the natural vibrations of inhomogeneous axisymmetric systems in a three-dimensional statement are presented in the paper. The problem is solved by the semi-analytical finite element method (FEM). The reliability of the developed methods and algorithms was validated by comparing the results obtained with the exact solution of a number of test problems for three-dimensional bodies, as well as by comparing the results with the results of field experiments. Spatial natural vibrations of inhomogeneous spatial axisymmetric systems, i.e. the models of nuclear power plants (NPPs) shielding shell in a three-dimensional statement were investigated. The results were analyzed to detect mechanical effects and revealed that the presence of multiple (close) eigenfrequencies in real spatial axisymmetric systems is not an exception, but a rule.
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