The Numerical Investigation of Natural Vibrations of a Truncated Layered Conical Shell Filled with a Fluid

The paper presents the numerical study of natural vibrations of truncated straight layered conical shells of rotations filled with an ideal compressible fluid. The behavior of the elastic structure and the fluid medium is described in the classical shell theory based on the Kirchhoff – Love hypotheses and Euler equations. The equations of motion of the shell together with the corresponding geometrical and physical relations are reduced to a system of ordinary differential equations with respect to new unknown values. The acoustic wave equation is written for the hydrodynamic pressure and transformed to a system of differential equations using the method of generalized differential quadrature. The solution of the formulated boundary value problem is developed using the Godunov orthogonal sweep method with a numerical integration of differential equations using the Runge – Kutta method of the fourth order. The calculation of the natural frequencies of vibrations is carried out using a combination of the stepwise procedure with the subsequent refinement of the values in the obtained range by the Muller method. The validity of the obtained results is confirmed by a comparison with the known numerical solutions. The dependences of the lowest vibration frequencies on the cone angle and ply angle of simply supported, rigidly clamped and cantilevered two-layer and three-layer composite conical shells are analyzed. The study allows us to assess the possibility of changing the lowest frequencies and the corresponding mode shapes of the vibration in relation to the preset combination of the cone angle, boundary conditions on the edges, layup scheme and ply angle of the composite shells. An extensive series of calculations has revealed the existence of configurations, for which the lowest frequencies exceed the values corresponding values of the equivalent layered circular cylindrical shell.