Response of oscillatory system “liquid layer-rod” to driving disturbances

¹ Institute of Geotechnical Mechanics named by N. Poljakov of National Academy of Sciences of Ukraine, 49005, Dnipro, Simferopolska Str., 2a, Ukraine
² Z.I. Nekrasov Iron & Steel Institute of National Academy of Sciences of Ukraine, 49000, Dnipro, Academician Starodubov Sq., 1g, Ukraine.
³ Oles Honchar Dnipro National University, 49010, Dnipro, Haharina Ave., 72, Ukraine.

^* Corresponding author: lvi151156@gmail.com

Abstract

This article deals with main characteristics of the oscillating system “central body – liquid” by means of its well-known representation in the form of a pendulum mathematical model. It makes possible to evaluate spread of specified disturbances at the general physical level and to determine the most dangerous frequencies that lead to increased amplitudes of fluid oscillations. We propose equations for single-frequency pendulums, which influence each other by means of resistance forces and added mass. Several examples with different natural frequencies of the body are considered. The calculation results showed that besides natural frequencies of the components, system has two more natural frequencies. So, system actually responds only to disturbances which frequencies are close to the natural frequency of the liquid layer. In this case, amplitudes of liquid and the body sharply increase. This fact indicates that in real technological processes frequency of dominant disturbance should be as far from the first resonant frequency of the liquid as possible. The further experimental and theoretical studies that take into account the influence of the following modes on the dynamic picture of the process are also of interest.