Averaging the Parameters of an Elastic Shell with a Non-Uniform Poisson’s Ratio Across Its Thickness Using the Example of Shell Modes of a Cylindrical Shell

The problems of design and operation of various pipelines, supports, tanks, elements of offshore structures, which are modeled by heterogeneous cylindrical shells, remain relevant for modern industry. The study analyzes a shell whose inhomogeneous elastic parameters depend on the radial coordinate and can be described by piecewise continuous functions. The application of various methods for averaging the elastic parameters of shells of the Kirchhoff–Love and Timoshenko type with inhomogeneity of the Poisson’s ratio over its thickness is considered. Calculations are carried out using the example of harmonic vibrations of a two-layer circular cylindrical shell of the Kirchhoff–Love type. Its shell modes are considered. The potential energy of the shell element is analyzed and the dependence of the shell’s natural frequencies and its reduced stiffness values as functions of the Poisson’s ratio are examined. The study is a continuation of testing these averaging methods in the case of inhomogeneity of the Young’s modulus over the shell thickness. The results obtained are compared with calculations using the ANSYS finite element package. The range of applicability of various models for averaging inhomogeneous shell parameters is analyzed. A method is proposed that makes it possible to increase the accuracy of calculations and reduce their complexity when considering various profiles of Poisson’s ratio. Together with previously obtained results, the methods considered make it possible to study the effects due to the inhomogeneity of shells; for example, to assess the change in shell frequencies due to its hydrogen embrittlement.