Resonant phenomena in a cylindrical shell containing a spherical inclusion and immersed in an elastic medium

The effect of radiation force on a drop of liquid in an acoustic field is examined. It is established that the force depends on the ratio of the densities of the liquid and the drop and on their adiabatic elastic moduli Keywords: acoustic wave, plane wave, sound pressure, liquid sphere, radiation force Introduction. Various issues of motion and interaction of liquid drops, gas bubbles, and cavities were addressed in [2, 3, 8, 13, etc.]. The motion of drops in an acoustic field under radiation forces is of certain technological interest. A radiation force acting on an obstacle in an acoustic field comes about from a change, within some volume, in the time-average momentum carried by a wave and is determined by the integral of the time-average sound (radiation) pressure over the surface of the obstacle. Note that the exact values of radiation pressure in Lagrangian and Eulerian coordinate systems are generally different [1]. In the former case, it is defined as the time-average sound pressure on the surface oscillating in an acoustic field. In the latter case, it is defined as a convolution of the momentum flux density tensor and the normal unit vector to the surface.To determine the radiation force (independent of time) acting on an obstacle in an acoustic field, the liquid pressure is calculated up to the second-order terms, which are due to the nonlinearity of the acoustic field and, hence, do not vanish after averaging over time. The obstacle changes the acoustic field by generating a reflected wave. Therefore, it is necessary to solve a diffraction problem. If the obstacle is a gas bubble, the oscillatory processes excited by the incident wave in the bubble may affect the wave scattering significantly: if the frequency of the wave and the natural frequency of the bubble are close, then the effective scattering diameter will be many times that of the bubble [4,7]. As a result, the reflected wave noticeably contributes to the radiation force.The radiation force can be determined in several steps. The first step is to identify the wave scattered by the obstacle. Since the liquid pressure can be determined up to second-order terms in linear approximation [10], the reflected wave can be identified by solving a linear diffraction problem. The solution of this problem is used at the second step to determine the resultant force exerted by the liquid on the obstacle. At the third step, this force is averaged over time to filter out the constant (radiation) force and to study the behavior of the obstacle under the radiation force.Since the wave reflected from the obstacle is determined by solving the linear diffraction problem, the interaction of the incident and reflected waves is neglected. In what follows, we will use the above approach to examine the case where the obstacle in a liquid is a drop of liquid of other kind. The cases of single solid particles and systems of such particles were discussed in [9].1. Diffraction Problem. Let us first identify the wave reflected from a liquid drop. If the drop is a sphere o...

Section: )mentioning

confidence: 99%

Effect of acoustic radiation on a spherical drop of liquid

Жук

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].…”

mentioning

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):

“…Two types of motion are considered: nonlinear normal modes and traveling waves Introduction. The geometrically nonlinear deformation vibrations of cylindrical shells attract the attention of both researchers and engineers [1,2,5,10]. This is because of the wide use of cylindrical shells in aerospace, power, and mechanical engineering.…”

mentioning

confidence: 99%

“…The models used to analyze the nonlinear vibrations of cylindrical shells may be divided into two large groups: (i) low-dimensional models with two or three degrees of freedom [1,2,5,10] and (ii) multidimensional models obtained and studied numerically [8].…”

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confidence: 99%

Multidimensional models of traveling waves and nonlinear modes in cylindrical shells

Аврамов

2011

The nonlinear dynamic deformation of a cylindrical shell is modeled taking into account several conjugate vibration modes. Two types of motion are considered: nonlinear normal modes and traveling waves Introduction. The geometrically nonlinear deformation vibrations of cylindrical shells attract the attention of both researchers and engineers [1,2,5,10]. This is because of the wide use of cylindrical shells in aerospace, power, and mechanical engineering. The available data on the nonlinear vibrations of cylindrical shells are reviewed in [6,8].The models used to analyze the nonlinear vibrations of cylindrical shells may be divided into two large groups: (i) low-dimensional models with two or three degrees of freedom [1, 2, 5, 10] and (ii) multidimensional models obtained and studied numerically [8].There are many cylindrical shells with a crowded spectrum of natural frequencies. In describing their geometrically nonlinear dynamic deformation, it is necessary to account for three to four natural modes. It is such shells that are addressed here.1. Equations of Vibrations. Consider a hinged thin shell with shear and longitudinal inertia neglected. The shell undergoes geometrically nonlinear deformation that causes small strains, moderate displacements, and nonlinear strain-displacement relationship. The stresses and strains are related by Hooke's law. The shell is perfectly cylindrical and its vibrations are described by the Donnell-Mushtari-Vlasov equations