Analysis of the influence of parametric resonance on the motion of a tractor tank when transporting liquid cargoes

Abstract

The process of transportation of a liquid cargo in a tank or cistern is simulated in the presence of an interface between liquid and gas. Oscillations of the walls lead to overflow along the free surface and redistribution of the mass of liquid in the tank. It is shown that, under unfavorable conditions, coupled vertical and horizontal oscillations of the liquid lead to the appearance of parametric resonance. Principles are formulated and stages are assigned for the development of a new mathematical model capable of investigating the process of transporting a liquid cargo, taking into account the main linear and nonlinear relationships between the motion parameters, as well as the possibility of resonances. When describing fluid oscillations, a discrete model of partial oscillators is used, into which a number of permissible simplifications have been introduced. The outlined simplifications are based on the principle of equivalent replacement of the real shape of the container with the shape of a rectangular parallelepiped. The principle of reduction is to preserve the size of the free surface of the liquid and the mass of the liquid in the tank. It is established that for problems with ergonomic criteria, it is enough to use three partial oscillators for each form of oscillations: longitudinal, transverse and torsional. The principles adopted were used to study the longitudinal and lateral vibrations of a tractor that transports a tank with a liquid on a trailer. A computational study of the change in the parameters of the vehicle movement in the vicinity of the parametric resonance is carried out. During the simulation it is shown that the parametric resonance is significantly influenced by the properties of the transported fluid and the characteristics of the external kinematic excitation.