Determination of the Natural Frequencies of Compound Anisotropic Shell Systems Using Various Deformation Models

An approach to determining the natural frequencies and modes of compound systems of shells of revolution of different geometry and relative thickness, continuously and/or discretely inhomogeneous across the thickness is proposed. The shells are made of isotropic, orthotropic, and anisotropic materials with a single plane of elastic symmetry. The approach involves construction of a mathematical model based on the classical Kirchhoff–Love theory, Timoshenko-type refined theory, spatial elasticity theory (particular case), and numerical-analytical technique of solving associated two- and three-dimensional problems by reducing their dimension and using the successive approximation and step-by-step search methods in combination with the orthogonal sweep method. Examples of solving various problems in different fields of engineering are presented.