Natural vibration of composite elliptical cylindrical shells filled with fluid

S. V. Lekomtsev ; V. P. Matveenko

Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 24 (2024) no. 1, pp. 71-85

Résumé

The aerospace industry often uses cylindrical shells with elliptical cross-section, which are manufactured from composite material using a filament winding method. During the fabrication process or operation of the structure, there is a probability of shape imperfection in the form of deviation from a circular cross-section. The vibration analysis of such structures containing fluid requires an in-depth study to determine the performance characteristics affecting their life cycle. In this article we develop a mathematical formulation and present the corresponding finite element algorithm for determining the natural frequencies of vibrations of layered composite elliptical cylindrical shells filled with fluid. The problem is solved in a three-dimensional formulation by the finite element method. The curvilinear surface of the shell is represented as a set of flat rectangular segments, in which the relations of the classical laminated plate theory are fulfilled. The membrane displacements are described using bilinear Lagrange shape functions. The deflection in the direction normal to the lateral surface and the rotation angles are approximated by incompatible cubic Hermite polynomials. Small vibrations of an ideal compressible fluid are described in the framework of the acoustic approximation by a wave equation for hydrodynamic pressure, which, together with the boundary conditions and the impermeability condition on the wetted surface, is transformed to a weak form. The verification of the developed numerical algorithm is carried out by comparing the obtained natural frequencies of vibration with the known data presented in the literature for layered composite circular cylindrical shells. A number of examples are considered to evaluate the influence of geometrical dimensions of the structure, boundary conditions at the shell edges and the ratio of ellipse semi-axes. New quantitative and qualitative dependencies have been established, and the possibility of the natural frequency control through the selection of parameters of composite material has been shown.