http://doi.org/1058225/sw.2023.2-197-202 FREE OSCILLATIONS OF A RING-REINFORCED, SHEAR-DAMAGED CYLINDRICAL SHELL IN CONTACT WITH VISCOELASTIC SOIL AND FLUID Latifov Fuad Seyfaddin- doctor of phy. and math.sc., professor, department of Higher Mathematics, AzUAC, flatifov@mail.ru Mardanov Ilham Jumail- doctor of phy. and math. sc., prof., department of Higher Mathematics, AzUAC, Sadikov Polad Mammed- doctor of phy. and math. scie., ass.prof., department of Higher Mathematics, AzUAC, sadikov-54@yandex.com The system we studied consists of a cylindrical shell reinforced with discretely distributed ribs made of viscoelastic, orthotropic material in contact with viscoelastic soil. The incisions are rectangular in shape and located in a section divided by rings, as shown in Figure 1. To study the oscillations of this system, we will use the full energy of the viscoelastic, orthotropic perforated cylindrical shell reinforced with ribs, as well as the work done in the displacements of the points of the cylindrical shell and the contact conditions added to them. However, the total energy of the system is carried not over the entire surface, but over the , surface, where is the cross-sectional area. It should be noted that the liquid is located inside the cylindrical shell, while the soil is located outside. The liquid is considered ideal, while the soil is considered viscoelastic.