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The problem of forced nonaxisymmetric vibrations of reinforced ellipsoidal shells under nonstationary loads is formulated. A numerical algorithm of solving it is developed and the results obtained are analyzed Keyword: reinforced ellipsoidal shells, geometrically nonlinear theory, numerical method, nonstationary vibrationsThe problem of forced vibrations of reinforced shells is well understood now. According to reviews and monographs on the subject, the axisymmetric and nonaxisymmetric harmonic vibrations of reinforced shells of simple geometry (cylindrical, conical, and spherical) were mainly studied [1-3, 6, 18]. Results on the forced vibrations of reinforced shells under impulsive loads are presented in [7][8][9][10][11][15][16][17]. Studies on the dynamic behavior of reinforced shells of more complex geometry are very few. Among them are the studies [8,9,11], which are concerned with the forced vibrations of shells of revolution, including reinforced ellipsoidal shells. It is of interest to study the nonaxisymmetric vibrations of shells reinforced with discrete ribs and subjected to nonstationary loads.We will present equations describing the nonaxisymmetric vibrations of a discretely reinforced ellipsoidal shell. To describe the casing and ribs, we will use Timoshenko's refined model of shells and rods [9,12]. To derive the vibration equations, the Hamilton-Ostrogradsky variational principle will be used. The dynamic equations will be solved numerically using the integro-interpolation method for differencing equations with discontinuous coefficients. The nonaxisymmetric vibrations of a transversely reinforced ellipsoidal shell under a distributed internal load will be considered as a numerical example.

Problems of forced nonaxisymmetric vibrations of ellipsoidal shells under nonstationary loads are formulated. A numerical algorithm to solve them is developed. The solutions obtained are analyzedKeywords: ellipsoidal shell, nonstationary load, forced nonaxisymmetric vibrations, numerical algorithm Introduction. It is important to study free and forced vibrations of elastic elements in the dynamics of deformable systems; in particular, in the dynamics of shells and shell structures. Such studies are of theoretical interest and are necessary for various modern engineering areas. The traditional approach involves solving linear problems for isotropic and orthotropic shells of canonic configuration (circular cylinder, cone, sphere, etc.). These problems are mainly solved with analytical methods, which can reveal qualitative and quantitative dynamic characteristics of shell elements. Such approaches are used to consider the dynamic behavior of shell structures under nonstationary waves [1] and the interaction of nonstationary waves with deformable bodies immersed into a liquid or gas [3,13].The class of problems extended to include shells of complex shape can be solved using different numerical approaches [11,12]. The free vibrations of complex shell elements are analyzed numerically and analytically in [2] using different theories. The forced vibrations of smooth and reinforced canonic shells under nonstationary loads are numerically studied in [7,8,14].This paper considers the forced nonaxisymmetric vibrations of an ellipsoidal shell under nonstationary distributed load. We will use a geometrically nonlinear version of the Timoshenko shell theory of the second order. The numerical algorithm combines an integro-interpolation method for differencing in spatial coordinates a 1 and a 2 and an explicit finite-difference scheme in time coordinate t [10]. A numerical solution of this problem is given.1. Problem Statement. Consider an ellipsoidal shell whose midsurface is described as follows [5]: