Features of a generalized parametric resonance for a hyperboloidal reservoir

Abstract

The problem of the development of parametric fluctuations of liquid with a free surface in a tank in the form of a two-cavity hyperboloid is considered in this paper in the case when the reservoir moves vertically under the action of a force that varies according to a given harmonic law with the possibility of horizontal translational motion. The behavior of the system is considered within the framework of a nonlinear multimode model of a joint reservoir and liquid movement.An important class of problems is the generalization of the classical Faraday problem for a reservoir with a liquid that carries a given motion in the vertical direction. Such a generalization is carried out in three directions: the movement of the system "reservoir - liquid" is carried out with the provision of additional degrees of freedom, for example, the permissible movement of the system in the horizontal direction, or the angular movement of the reservoir; unlike the classical Faraday problem, the problem is considered in a joint statement; cases are considered not only cylindrical shape of the reservoir, but also other forms. Such generalizations correspond to the problems of longitudinal motion of aircraft, vessels, when there is no fixing of the structure of the reservoir with a liquid, and the joint movement takes place.The task is to investigate the behavior of the system "reservoir - a liquid with a free surface" when harmonious excitement of motion by force applied to the reservoir. The behavior of the system is considered for the parametric resonance frequencies determined both on the base of the classical parametric resonance of Faraday and on the base of a generalized parametric resonance problem.The results of numerical simulation indicate that significant demonstration of parametric resonance is observed on the fundamental frequency of joint oscillations. It is shown that the change of the frequency range of the parametric resonance is due to the compatibility of the system components motion, the oscillations are significantly increasing, which requires modeling based on nonlinear algorithms.