Abstract:
The paper investigates the stability of circular vertical layered cylindrical shells completely filled with a quiescent compressible fluid subjected to hydrostatic and external static loads. The behavior of the elastic structure and the fluid medium is described within the framework of classical shell theory and Euler equations. The linearized equations of motion of the shell and the corresponding geometrical and physical relations are reduced to a system of ordinary differential equations with respect to new unknowns. An acoustic wave equation is transformed to a system of differential equations using the method of generalized differential quadrature. The solution of the formulated boundary value problem is reduced to the calculation of natural vibration frequency in terms of Godunov's orthogonal sweep method. For this purpose, a stepwise procedure is applied in combination with a subsequent refinement by the Muller method. The reliability of the obtained results is verified through a comparison with known numerical solutions. The dependence of critical external pressure on the ply angle of simply supported, rigidly fixed and cantilevered two-layer and three-layer cylindrical shells is analyzed in detail. The influence of the combined static pressure on the optimal ply angle providing an increase of the stability boundary is evaluated.
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