Interaction of differently shaped bodies in a potential flow of perfect compressible fluid: Axisymmetric internal problem

The paper addresses the stability of solutions of ordinary differential equations of particular type for different statements and assumptions. The equations are interpreted as models of motion of a rigid body under the action of the ambient medium Keywords: stability of solutions, ordinary differential equation, rigid body, ambient medium Introduction. In studying the motion of a rigid body with a flat front end through a resisting medium, the main task is to establish conditions for self-oscillations in a finite neighborhood of rectilinear translational deceleration [9, 10]. There is a need for a complete nonlinear analysis. Its initial stage is to neglect the damping effect of the medium. Functionally, this means the assumption that a pair of dynamic functions describing the effect of the medium depends on one parameter: the angle of attack [15,20,22,23].If the additional damping effect of the medium is disregarded, which is the simplest assumption, then it will be impossible to establish conditions for self-excited vibrations in a finite neighborhood of rectilinear translational deceleration.In this paper, we study the motion of a body through a medium. The medium exerts a damping moment on the body, thus introducing additional dissipation which may make the rectilinear translational deceleration stable. Note that the dynamics of bodies and systems in fluid was addressed in [26, 27, 31, etc.]. Formulation of the Problem and the Dynamic Part of the Equations of Motion.Consider a homogeneous rigid body of mass m undergoing plane-parallel motion in a medium with quadratic drag. Some portion of the body's surface is a flat plate AB of length D and is in a jet flow of the medium [6,17]. By this is meant that the effect of the medium on the plate (body) reduces to a force S (applied at a point N) orthogonal to the plate (Fig. 1). The remaining portion of the surface can be placed inside the volume bounded by the jet surface separated from the plate edge. What is more important is that the medium does act upon this portion of the surface. Similar conditions may arise, for example, after a body enters water [7,8,26].Assume that one of the motions of the body is rectilinear translational deceleration. This is possible if (i) the velocities of all points of the body are orthogonal to the plate AB and (ii) the perpendicular drawn from the center of gravity C of the body to the plate coincides with the line of action of the force S.To describe the plate, we choose a coordinate system D xyz

Section: Free Deceleration Of a Body In A Medium Withmentioning

confidence: 99%

Section: Free Deceleration Of a Body In A Medium Withmentioning

confidence: 99%

Some model problems of dynamics for a rigid body interacting with a medium

Шамолин

2007

“…Various models describing the flight of vaporizing droplets in gas with nonlinear drag can be found in [4]. Dynamic problems of the interaction of spherical bodies, including droplets in fluid were solved in [13][14][15][16] and other publications cited in the review [12]. Some peculiar features in the vertical motion of a spherical body with decreasing mass are mentioned in [17].…”

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confidence: 99%

A peculiar feature in the vertical motion of a particle with variable mass in upward flow

Ol'shanskii

Ольшанский

2012

The reversal of the vertical motion of a spherical particle with variable mass and radius in air flow is described using the analytical solutions of the Cauchy problem. It is shown that a particle with decreasing mass falling against an upward flow slows down to a stop and moves upward. If its mass is increasing, the particle moving with upward flow slows down to a stop and then moves downward Introduction. The classical dynamics of bodies of variable mass was intensively developed to follow the development of rocketry. The especial importance of this problem relegated the other applied problems in this area of mechanics to the background. Besides rocket dynamics, however, there are many processes that involve moving particles of variable mass. Among them are vaporization of dispersed fire-extinguishing substances moving in heated gas, vaporization and burning of moving liquid fuel droplets in engines, flight of burning particles of solid fuels in boiler furnaces, etc. While moving, such bodies decrease in size and weight. Therefore, the ballistic properties of particles with variable parameters are still of interest.Many early works on the mechanics of bodies of variable mass are included in the generalizing publications [6,7,11]. Various models describing the flight of vaporizing droplets in gas with nonlinear drag can be found in [4]. Dynamic problems of the interaction of spherical bodies, including droplets in fluid were solved in [13][14][15][16] and other publications cited in the review [12]. Some peculiar features in the vertical motion of a spherical body with decreasing mass are mentioned in [17]. The extremal properties of the velocity of vertical motion of particles with variable parameters, which are absent when the mass of particles is constant, were studied in [8,9]. Further ballistic analysis showed that a particle with decreasing size and mass moving with an upward gas flow may reverse its direction of motion. A falling particle of decreasing mass may start rising, while a rising particle of increasing mass may start falling. Here we study this effect.The goal of the paper is to quantitatively describe the reversal of the vertical motion of a spherical particle with variable parameters in upward gas flow.1. Reversal of the Falling of a Particle with Decreasing Mass in a Counter Flow. Let the variation in the radius r of a falling spherical body follow the Sreznevsky law (the surface area of the particle proportionally increases with time t):

“…Formulating problems of this class, developing methods to solve them, and establishing transient patterns are of current importance for modern acoustics because of the demands of advanced engineering. Note that the nonstationary electroelasticity and vibrations of cylindrical shells with a fluid were studied in [14][15][16][17]. …”

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confidence: 99%

“…For example, to determine the pressure in the fluids filling the ambient and intershell spaces, it is necessary to substitute (16) and (17) into expressions (12) and (14) and to invert them:…”

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confidence: 99%

Electric to acoustic conversion by a spherical piezoceramic shell with shields

Савин

Morgun

2007

A problem of nonstationary hydroelectroelasticity is solved to determine the pressure in the ambient medium when a spherical thin-walled piezoelectric transducer with a shield either inside or outside is excited with an electric pulse Keywords: nonstationary hydroelectroelasticity, electric and acoustic pulses, conversion, piezoceramic spherical shell, inside and outside shields Introduction. Nowadays, the piezoelectric effect is widely used in the industry, which explains the considerable interest in piezoceramic materials and devices made from them.The widespread use of piezoceramics is due to their capability of converting mechanical energy to electric energy, and vice versa. Today, piezoceramic transducers are employed in various areas of modern technology, medicine, biology, and agriculture. They are most popular in sonar systems used in navigation safety, ocean research, marine geology, fishery, monitoring and analysis of the acoustic fields of ships and parameters of sonar equipment.Of the widest use are plate, rod, cylindrical, and spherical piezoelectric transducers. Piezoelectric plates mainly operate to receive acoustic vibrations and convert them into electric signals. Rod, cylindrical, and spherical transducers either generate or receive acoustic vibrations. Applied hydroacoustics is currently interested in the use of electric pulses with a complex law of voltage variation for the nonstationary excitation of piezoelectric transducers. The overwhelming majority of the available publications on the nonstationary hydroelectroelasticity of thin-walled piezoceramic shells studies the nonstationary behavior of cylindrical shells [1][2][3][4][5]. Those few publications that address transient modes in spherical piezoceramic shells [11], spherical piezoceramic shells with inside impedance shield [12], and two concentric spherical piezoceramic shells [1, 6] do not provide methods and a theory for the development of modern sonar systems.The present paper is concerned with the transients induced by a variable voltage in a thin-walled piezoceramic spherical shell (piezoelectric transducer) with a perfectly rigid spherical body inside (internal rigid shield) or an elastic shell inside or outside. This shielded transducer is placed in a fluid. Formulating problems of this class, developing methods to solve them, and establishing transient patterns are of current importance for modern acoustics because of the demands of advanced engineering. Note that the nonstationary electroelasticity and vibrations of cylindrical shells with a fluid were studied in [14][15][16][17].