LONGITUDINAL-RADIAL VIBRATIONS OF THE ELASTIC CYLINDRICAL SHELL FILLED WITH A VISCOUS COMPRESSIBLE FLUID

In this paper, the longitudinal-radial vibrations of the elastic cylindrical shell filled with a viscous compressible fluid are studied using the mathematical model proposed. The general equations for the longitudinal-radial vibrations of the shell made of the homogeneous and isotropic material are derived. These equations can be used to obtain refined equations of vibrations. The proposed algorithm allows one to uniquely determine the stress-strain state of points in any section of the considered hydroelastic system using the field of the required functions in coordinates and time. The benchmark problem of harmonic oscillations in a cylindrical shell with a viscous fluid is solved. The dependences of the frequency on the wave number are obtained for various shell- fluid interaction cases.

Ultrasonic Intensification of Mass Transfer in Organic Acid Extraction

The mechanism of ultrasonic extraction was discovered and analyzed in detail for the liquid membrane technique from the consideration of the specific features of the radial vibrations of a droplet of the dispersed phase placed into an immiscible continuous phase subjected to ultrasonic irradiation. Analytical formulas were derived for the rate of mass transfer as a function of the amplitude of acoustic pressure oscillations and the time of ultrasonic treatment of an extraction system. Conditions for achieving the maximum efficiency of the extraction of a substance under the stimulating effect of ultrasound were analyzed. A nonlinear equation was derived for the radial vibrations of a spherical droplet of the dispersed phase in an immiscible continuous phase under forcing in the form of acoustic pressure periodically changing with time. Experimental study of the dependence of sulfosalicylic acid distribution on time in an aqueous two-phase system with ultrasound shows good agreement of experimental results with the calculations performed.

Transient responses in Piezoceramic Multilayer Actuators Taking into Account External Viscoelastic Layer

The work develops a generalized approach to the study of thickness (radial) vibrations arising in the piezoceramic plates, cylinders, spheres under electrical loads. The state of the problem and the main approaches, used in the problems of studying the oscillations of electroelastic bodies, are described. The use of multilayer elements with electroded interface surfaces and variable direction of polarization of the layers increases the conversion efficiency of electrical energy into mechanical energy, so multilayer piezoceramic plates, cylinders, spheres with changing polarization directions with electroded interfaces are considered. Because of piezoelectric elements are often embedded in the housing and supplemented with matching layers to protect against mechanical damage, it is necessary to study their effect on the oscillations of the element. The proposed approach makes it possible to study the vibrations of plane, cylindrical and spherical bodies with layers made of various electroelastic and elastic materials. Numerical implementation is carried out using finite differences. Nonstationary oscillations of PZT-4 ceramic elements at zero initial conditions are investigated. Oscillations of multilayer plates, cylinders and spheres with and without an external elastic or viscoelastic reinforcing layer under impulse and harmonic unsteady loads are investigated and compared. There are found own frequencies for 5-layer bodies of different geometry with and without an external layer. The first natural frequency for cylinder and sphere corresponds to the radial mode of oscillations, while the second natural frequency for cylinders and spheres and the first for flat bodies are almost equal and correspond to thickness mode. The transient processes in the elements under impulse loads and the influence of the outer elastic layer (housing or matching layer) are studied, taking into account the Rayleigh attenuation. It is established that for a flat layer the outer layer increases the amplitude and the period of free vibrations after removing the load, and for cylinders and spheres it decreases. The presence of an elastic layer enhances the third and dampens the fourth natural frequency of the transducer, thereby expanding the frequency range of its operation.

Monitoring of a Cross-Sectional Vibrational Mode in the Trunk of a Palm Tree

Palm trees, like all other tree species, are living entities that may be subject to the attack of several natural agents which affect the strength of the trunk. The most serious of these damaging agents are parasites and rot fungi, which proliferate in the substance of the stem, destroying its cells and fibers and weakening it. Consequently, this decay affects the physical characteristics of the modes of vibration in the tree trunk regarding resonance frequency, shape, and damping. Advanced stages of rot infection in a tree trunk may reach such an extreme level that substantial amounts of its solid mass are removed, ultimately leading to a hollow trunk rather than one of substance. In cases like these, the trunk presents less resistance to forced vibrations, and the active modes affecting the cross section of the trunk exhibit decreased resonance frequency values. This paper aims to present a method based on vibrations which might be employed for tracking a specific mode of radial vibrations known as the ovalling mode. To achieve this goal, the trunk of a palm tree was set into vibration via mechanical excitation in the radial direction and its response at some specific point on the trunk was examined. This method uses a single concentrated source of excitation and two vibration sensors, which are diametrically positioned and fastened to the surface of the tree trunk. The ovalling mode might be extracted from the frequency response by adding the signals recorded by the two sensors, which are in phase for a test specimen with a perfectly circular, cylindrical shape made of homogeneous, isotropic material. This study provides a preliminary investigation into the feasibility and reliability of this nondestructive method when applied for the identification of rot hosting by the trunks of standing trees, wooden poles, and logs, as well as the level of severity of rot attack.

Lateral Vibrations in Deep Hole Drilling Due to Land Width Variation

In drilling processes, self-excited vibrations have a negative influence on the achievable drilling qualities and tool life. Low-frequency radial vibrations are characterised by oscillating movements of the tool tip and the generation of lobed holes in drilling. This study focuses on the participation and influence of the land widths of twisted drilling tools on these vibrations. Therefore, drilling tools with different land widths and a length-to-diameter ratio of 12 are used, and different parameters, such as feed rate, cutting speed, coolant pressure, pre-hole diameter, and chuck selection, are varied in a drill-out process. The results show that the land widths have a statistically significant influence on the formation of lateral vibrations and the generation of lobed holes.