Review article

This paper proposes relationships for a mathematical model describing the deformation process of shells and accounting for energy loss in accordance with the Rayleigh dissipation function. Nonlinearity of geometric relationships, transverse shear, rotational inertia, and material orthotropy are also considered. The system of equations is derived in the form of the Euler-Lagrange equations. An example of calculating a shallow shell with double curvature is presented, selecting different coefficients in the Rayleigh dissipation function. The graphs show the behavior of the structure after the dynamic load is removed.