The dynamic behavior of reinforced shells of revolution in an elastic medium is modeled. Pasternak's model is used. A problem of vibration of discretely reinforced shells of revolution is formulated and a numerical algorithm is developed to solve it. Results from an analysis of the dynamic behavior of a reinforced spherical shell on an elastic foundation are presented as an example Keywords: reinforced shells, elastic foundation, nonstationary vibration, numerical method Introduction. The static interaction of shells and rods with an elastic medium is well understood [2,7]. Of interest is the dynamic behavior of shells and elastic elements with media. The properties of an elastic medium with a deformable system inside are best described by the equations of elasticity. However, this problem is very complicated mathematically [3]. The problem of describing the elastic medium can be given a relatively simple mathematical formulation, which would allow us to determine the reaction of the elastic medium to the structure with adequate accuracy. Noteworthy are studies of the deformation of single-layer and multilayer beams and cylindrical shells on an elastic foundation under nonstationary loads [4,5,9,11], where the Winkler model was mainly used. There are very few studies on shells of other shapes (except for cylindrical) interacting with elastic media under dynamic loads. The dynamic behavior of reinforced shells on an elastic foundation is of interest. Dynamic problems for reinforced cylindrical shells on an elastic foundation were solved in [10]. Nonstationary vibrations of reinforced cylindrical and ellipsoidal shells are studied in [12,13]. Free vibration of reinforced open cylindrical shells is addressed in [11].The objective of the present paper is to study the dynamic behavior of reinforced shells of revolution in an elastic medium under a nonstationary distributed load. Use will be made of Pasternak's model [7].1. Problem Formulation. Consider a reinforced isotropic shell of revolution in an elastic medium under an internal impulsive load. The elastic medium is modeled by a Pasternak foundation [7]. This model is characterized by two moduli of subgrade reaction C 1 and C 2 to tension/compression and shear, respectively.The inhomogeneous shell structure consists of a smooth shell (casing) of revolution and ring ribs rigidly attached to it. To describe the forced vibration of this structure, we will use a hyperbolic system of nonlinear differential equations of the Timoshenko theory of shells and curvilinear rods. We assume that the displacements vary as follows throughout the thickness of the casing (in coordinates s z , ):
