L. N. Sretinskij's problem for a cylindrical vessel with elastic bottom and a liquid with free surface (Q2880003)

A mechanical system consisting of a cylindrical vessel and an ideal liquid is considered. The system performs oscillations under the action of an elastic force applied to the vessel. The elements of the cylinder are assumed to be rigid, and the bottom is represented by an elastic plate. The equations of motion of this mechanical system are given by considering the potential flow of the liquid. For the linearized dynamical equations, a modal analysis is carried out with respect to the basis functions as eigenforms for the boundary value problem in a rigid vessel. Then, the author uses eigenfunctions of the associated fourth-order differential operator to construct the forms of the joint oscillations of liquid and plate. An important feature of this work is that the frequency equation is derived for a plate with initial tension. This paper extends L. N. Sretenskij's results for the case of a vessel with elastic bottom and the liquid with free boundary.