Parametric oscillations of liquid with a free surface in reservoir of conic shape

Abstract

The problem about parametric oscillations of liquid with a free surface in reservoir of conic shape
(the Faraday problem) is under investigation. Liquid is considered as ideal, incompressible,
reservoir is a rigid body of conic shape. Investigation is done on the basis of nonlinear model of
combined motion of liquid with reservoir with representation of liquid motion as decomposition
with respect to normal modes of oscillations. Resolving mathematical model is obtained in the
form of a system of ordinary differential equations relative to parameters of motion of reservoir
and amplitudes of excitation of normal modes of oscillation of liquid with a free surface. It is
shown how tank walls inclination and initial conditions influence development of dynamic processes.