Natural vibrations of cylindrical shell partially resting on elastic foundation

The paper presents the results of an investigation of the natural vibrations of circular cylindrical shells resting on an elastic foundation, which is described by the two-parameter Pasternak model. The elastic medium is inhomogeneous along the shell length, and the inhomogeneity is an alternation of areas with the presence or absence of a medium. The behavior of the shell is considered in the framework of the classical shell theory, which is based on the Kirchhoff-Lyav hypotheses. The corresponding geometrical and physical relations together with the equations of motion are reduced to the system of eight ordinary differential equations for new unknowns. The problem is solved by the Godunov orthogonal sweep method, and the differential equations are integrated using the Runge-Kutta method with fourth-order accuracy. The eigenfrequencies are calculated in the stepwise iterative procedure, followed by further refinement by a bisection method. A comparison of the obtained results with the known numerical-analytical solutions confirmed their validity. The numerical calculations made for cylindrical shells under various combinations of boundary conditions revealed the dependence of minimum vibration frequencies on the characteristics of elastic medium exhibiting different types of inhomogeniety. It is shown that a discontinuity in the smoothness of the curves is caused both by a change in the mode with a minimum frequency of oscillations and by the ratio of the size of the elastic foundation to the total length of the shell and its rigidity, as well as by the combination of boundary conditions specified at the ends of the thin-walled structure.