Spectral problem for shells with fluid

Variational eigenvalue equations describing vibrations of orthotropic shells containing an ideal incompressible fluid are obtained. The vibration frequencies are assumed to be small, which makes it possible to use linear equations and to consider the boundary of the wet surface of the shell to be unchanged. The equations of anisotropic shells are based on the linear relations of multifield theory, which allows to obtain a more accurate model of anisotropic shells that satisfies the conditions of the finite-element method. The fluid flow is considered irrotational and is described using the Laplace equation. A finite-element algorithm is designed to determine the natural frequencies and modes of vibrations of an arbitrary multilayer orthotropic shell of revolution which is partially filled with an ideal incompressible fluid.