liquid oscillations

The article deals with an investigation of the system of "reservoir -- liquid with a free surface", when the reservoir is fixed on pendulum suspension, which suspension point performs a given motion. The system behavior is studied for the below-resonant, near-resonant and above-resonant modes. The description of the system behavior is done based on a nonlinear model of motion, which takes into account the combined character of motion of the system components. The numerical modeling shows that general regularities of the system behavior coincide qualitatively with known experiments.

Problem of dynamics of a reservoir of cylindrical shape, partially filled with liquid, on pendulum suspension with movable suspension point is under investigation. The problem is considered in nonlinear statement with the purpose of clarification of the effect of pendulum suspension on both frequency characteristics and the system behavior in the near-resonance zone. Analytical and numerical study shows that normal frequencies of oscillations have considerable changes for both quasi-rigid pendulum mode of motion and especially for frequency of liquid sloshing modes.

A problem about normal oscillations of ideal homogeneous liquid, which partially fills a reservoir with vertical walls, but with variable (inclined) bottom, is under consideration. A numerical implementation of the Ritz method was developed, and by partial example, which corresponds to a plane inclined bottom, the results of numerical realization are shown. We determined frequencies and normal modes of liquid oscillations as well as errors of satisfaction of the non-flowing boundary condition at the bottom. The results showed that the wave profiles for different directions of liquid oscilla