nonlinear dynamics of liquid

The problem of motion of the cylindrical reservoir, partially filled with liquid, on pendulum suspension is considered in combined statement.  The system motion occurs under the presence of uniform outflowing of liquid with the neglect of outflowing local effects.  It was shown that the constructed mathematical model of the system describes the main mechanical effects and does not violate the conservation laws.  Peculiarities the system dynamics under the presence of liquid outflowing are shown by the numerical examples of the system behavior for initial kinematic perturbation and under the

Variation of resonant properties of the system liquid – structure caused by changes of distribution of normal frequencies is under consideration. It was shown that different types of mobility of carrying body (translational or rotational motion with different types of constraints) causes growth of normal frequencies, which correspond to antisymmetric oscillations of a liquid free surface, while the rest of frequencies do not change.  General arrangement of normal frequencies, which corresponds to the case of immovable reservoir, is considerably violated.

Structure of geometrical nonlinearities in mathematical model of liquid sloshing in tanks of non-cylindrical shape is under consideration. In contrast to the case of cylindrical reservoir, some new types of nonlinearities occur in mathematical statement of the problem. They are connected with four main reasons. First, they are determined by new normal modes, which correspond to non-cylindrical shape of the tank and take into account some nonlinear properties of the problem (for example, they follow tank walls above level of a free surface).

Two generalizations of the classical Faraday problem on development of parametric resonance in mechanical system "reservoir – liquid with  free surface", namely, the effect of supplementary degree of freedom, i.e., possibility of horizontal motion of reservoir due to transversal motion of free surface of liquid, and effect of supplementary degree of freedom, i.e., possibility of angular oscillations of reservoir, which is suspended as pendulum, due to transversal oscillations of a free surface of liquid.