Study of dynamic processes in a rigid cylindrical vessel with elastic bottom partially filled with a liquid

Abstract

The paper reports on the results from an experimental study of the nonlinear deformation of the elastic bottom of and the free liquid surface in a rigid shell. The shell and liquid interact with each other and with a cluster of gas bubbles produced by vibrational excitation Keywords: gas-liquid medium, cylindrical shell, elastic bottom, cluster of bubbles, vibrations Introduction. The deformation modes of elastic shells with rigid bottom filled with a liquid were experimentally and theoretically investigated in [4, 5, 10-12, etc.]. These are conjugate flexural modes excited by a vibrational load and involved in nonlinear interaction. The same publications studied the dynamic interaction between a liquid-filled elastic cylinder and an oscillating sphere. It is indicated in [2,8] that the nonlinear interaction of vibration modes of the shell and liquid is especially complicated when the amplitude of vibration of the shell wall is of the order (and more) of its thickness. When one of several cylindrical shells filled with a liquid and placed on a common elastic foundation is subjected to a vibrational load, vibrations of the other shells are parametrically excited because of their interaction [15]. The nonlinear deformation of elastic shells and free liquid surface and the chaotic motion of the gas-liquid medium, which are because of the interaction between gas bubble clusters (i.e., a liquid-gas nonlinear vibrating system) and the excited vibration modes and the source of excitation, were experimentally investigated in [5,6,8,13,14]. It is established that these processes occur at resonance.The present paper reports on results from an experimental investigation into specific nonlinear deformation of the elastic bottom of and the free liquid surface in a rigid shell that interact with each other and with clusters of gas bubbles in the vibrating liquid. We will discuss the main mechanisms of formation and the dynamic behavior of gas bubbles and their clusters and the chaotic motion of the gas-liquid medium due to the intensive vibrations of the elastic bottom.1. Model, Experimental Equipment, and Technique. The shell was modeled by an organic-glass cylindrical vessel with height H sh = 500 mm, diameter D sh = 150 mm, and wall thickness d sh = 5 mm. Precisely this thickness was chosen to prevent the parametric vibrations of the lateral surface in the frequency range involved. According to [3,5,8], such high-frequency vibrations may cause various kinds of low-frequency large-amplitude motions of the free liquid surface and motions of the gas-liquid medium. The bottom of the shell is an elastic circular plate of thickness d bt = 0.5 mm made of steel. It is rigidly fastened to the shell along the boundary with fit rings and bolts. A VÉDS-100 electrodynamic shaker was used as a source of mechanical vibrations. The vibration accelerations of the shaker table and the end and elastic bottom of the shell were measured with an IS-318 accelerometer and a D-14 vibration transducer (which are coupled with the measuring unit of th...

Dynamics of a cylindrical shell with elastic bottom filled with a gas–liquid mixture and subject to two-frequency excitation

“…Experimental data on the nonlinear deformation of the elastic bottom of a rigid shell and the free surface of the fluid in it because of the interaction between them and with bubble clusters under one-frequency excitation are reported in [16].…”

“…Based on the information on the deformation of the elastic bottom and free liquid surface under one-frequency excitation [16], we examined several cases of two-frequency excitation:…”

“…As shown in [16], the presence of bubble clusters in the vibrating fluid in the shell subjected to one-frequency vibrational excitation significantly intensifies the nonlinear deformation of the elastic bottom and the chaotic motion of the gas-liquid medium. The occurrence of bubble clusters in the vibrating fluid, which gives rise to a nonlinear vibrating fluid-gas system [1,4,8], changes the type of motion of the body [4,7] at a certain ratio between the parameters of external vibrational excitation ( f v and g v ).…”

“…In this connection, the dynamic behavior of gas-liquid mixture in cylindrical, spherical, and ellipsoidal rigid shells under two-frequency excitation was studied in [2,4,6]. The nonlinear dynamic deformation of the elastic wall of a cylindrical shell, the formation of gas bubbles and their clusters, the motion of a gas-liquid mixture because of their interaction under two-frequency vibratory excitation were studied in [17].Experimental data on the nonlinear deformation of the elastic bottom of a rigid shell and the free surface of the fluid in it because of the interaction between them and with bubble clusters under one-frequency excitation are reported in [16].The present paper discusses experimental data of the nonlinear dynamic deformation of the elastic bottom and the free surface of the fluid without bubble clusters and the deformation of the bottom, the behavior of the gas-liquid mixture and bubble clusters. We will find and analyze the resonant ratio between the two excitation frequencies and the natural frequencies of the shell-gas-liquid system that causes the most intensive deformation of the elastic bottom of the cylindrical tank and the free liquid surface and intensifies the motion of the gas-liquid mixture, especially when a nonlinear vibrating liquid-bottom-gas system forms.…”

“…The major effect of bubble formation and clustering is the excitation of intensive vibrations of the elastic bottom at the first fundamental resonant frequency of the fluid-bottom system [4,16].…”