The forced vibrations of a longitudinally reinforced elliptic cylindrical shell under nonstationary loading are analyzed numerically. The problem is formulated and a numerical algorithm to solve it is developed. The system of differential equations is based on the Timoshenko-type theory of orthotropic shells and rods. The dynamic behavior of the shell is studied Keywords: longitudinally reinforced elliptic cylindrical shell, forced vibrations, Timoshenko-type theory, numerical solutionIntroduction. The forced vibrations of reinforced shells under various loads are addressed in many publications. The classical problem formulation for rib-reinforced shells (Kirchhoff-Love shell model, Kirchhoff-Clebsch rod model) is given in [1]. A refined form (Timoshenko-type model of shells and rods) of vibration equations is given in [3] where the dynamic behavior of reinforced shells of canonical shape (cylindrical, conical, and spherical) was studied.Formulating and solving problems of the dynamic behavior of reinforced elliptic cylindrical shells involve substantial difficulties. The stress-strain state of a rib-reinforced elliptic cylindrical shell is determined in three stages: (i) description of forced vibrations, (ii) description of the geometry of a noncanonical structure (elliptic cylindrical shell), and (iii) description of the effect of stiffening ribs [4]. This procedure has been used very rarely. The free and forced vibrations of smooth elliptic cylindrical shells or the vibrations of reinforced circular cylindrical shells were mainly studied in [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. There are very few studies on the dynamic behavior of reinforced elliptic cylindrical shells under nonstationary loads.We will use the Timoshenko-type theory of orthotropic shells and rods to formulate the problem of the forced vibrations of orthotropic reinforced elliptic cylindrical shells, develop a numerical algorithm to solve it, and analyze the numerical results.1. Problem Formulation. Basic Equations. Consider a reinforced elliptic cylindrical shell under a distributed internal load P s s t
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