Motion of a gas bubble in fluid under vibration

This paper is concerned with the analysis of motion of a gas bubble in a uniformly oscillating incompressible fluid. A theoretical model explaining the effect of sinking of gas bubbles in the absence of a standing pressure wave is validated experimentally. The conditions under which this effect occurs are determined, and a simple formula is derived for the average velocity of a gas bubble in the fluid.     

A rigid inclusion in an elastic space under the action of a uniform heat flow in the inclusion plane

A solution is presented for the three dimensional static thermoelastic problem of an absolutely rigid inclusion (anticrack) in the case when a uniform heat flow is directed along the inclusion plane. By using the potential method and the Fourier transform technique, the problem is reduced to a system of coupled two-dimensional singular integral equations for the shear stress jumps across the inclusion. As an illustration, a typical application to the circular anticrack is presented. Explicit expressions for the thermal stresses in the inclusion plane are obtained and discussed from the point of view of material failure.     

Relaxation of a liquid layer under the action of capillary forces

The theory of creeping motion is used to study the relaxation of an infinite viscous fluid layer (membrane) of nonuniform thickness. The propagation of boundary perturbations in a semi-infinite layer under the action of surface-tension forces is also considered. The layer has at least one common boundary with a gas. It is found that relaxation processes of an infinite layer or the propagation of boundary perturbations inside a bounded layer are non-monotonic, and that wave-like surface perturbations always arise. Relaxation times are determined. Maximum distances are found over which separate regions of the layer can affect each other.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No. 1, pp. 73–77, January–February, 1970.The author wishes to thank V. G. Levich for discussions.     

Motion of gas bubbles in a liquid under the influence of a temperature gradient

This study deals with the motion of a gas bubble developing under the influence of surface-tension forces in an imponderable viscous liquid with a temperature gradient. A theory of steady-state motion of a bubble in a field with constant temperature gradient is given for the case of small Reynolds numbers. Experimental results that show qualitative agreement with the theory are presented.The authors wish to thank M. A. Lavrent'ev for formulating the problem and giving constant attention to their work.     

Vibrations of a gas in tubes under the action of a periodically varying pressure

The article discusses the vibrations of a gas in a tube under the action of a periodically varying pressure at the frequency of its linear resonance and heating-up of the gas by the shock waves arising. The problem is solved by a linear method, having a third order of exactness with respect to the coordinate and the time. A difference algorithm is proposed for calculation of the parameters at the boundary. Approximate relationships are obtained which make it possible to determine the behavior of the parameters of the system as a function of the time.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 177–180, September–October, 1978.     

弯矩作用下薄板振动的仿真分析

针对工程中广泛存在的弯矩作用下板结构的振动问题,分别建立四边固定、三边固定一边自由、两对边固定两对边自由的3种不同边界条件下板的振动模型;基于有限元法计算振动板的频率响应,计算了各节点振动速度的平方和;运用部分追加法正交试验方案分别对板厚、边界条件、板的损耗因子三因素三水平、激励点位置四水平进行了正交试验。实例结果表明,以速度平方和的大小为目标,影响薄板振动的主次因素顺序为:损耗因子、板厚、边界、激励点位置;当振动板两对边固定另两对边自由支承、板厚为0.014m、在(0.5m,0.4m)点处激励且板的损耗因子为0.0008时,此组合为薄板结构振动最小的最优组合。     

Motion of a vertical wall fixed on springs under the action of surface waves

A two-dimensional unsteady hydroelastic problem of interaction between surface waves and a moving vertical wall fixed on springs is studied. An analytical solution of the problem is constructed using a linear approximation, and a numerical solution within the framework of a nonlinear model of a potential fluid flow is found by a complex boundary element method. By means of analysis of the linear and nonlinear solutions, it is found that the linear solution can be used to predict some important characteristics of the wall motion and the fluid flow in the case of moderate wave amplitudes.     

Motion of a gas shock layer with a free boundary under nonadiabatic conditions

This paper is a study of the effect of heat input (removal) on the characteristics of a shock layer produced by a gas at high supersonic velocity encountering a mobile boundary, which for generality is assumed to be free. We will use the Chernyi method, which was employed previously to solve the problem of a shock layer in an adiabatic flow [1, 2]. The results obtained can be useful for analysis of the effect of radiation (absorption) and processes involving the relaxation of internal degrees of freedom of molecules, condensation, chemical reactions, etc., whose effect on the gasdynamics of the flow in a shock layer may be similar to heat input or removal [3–5].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 152–154, May–June, 1976.The author thanks A. K. Rebrov for discussion of the results.     

Oscillations of a gas bubble in a non-Newtonian liquid under the action of an acoustic field

The evolution of the radius of a spherical cavitation bubble in an incompressible non-Newtonian liquid under the action of an external acoustic field is investigated. Non-Newtonian liquids having relaxation properties and also pseudoplastic and dilatant liquids with powerlaw equation of state are studied. The equations for the oscillation of the gas bubble are derived, the stability of its radial oscillation and its spherical form are investigated, and formulas are given for the characteristic frequency of oscillations of the cavitation hollow in a relaxing liquid. The equations are integrated numerically. It is shown that in a relaxing non-Newtonian liquid the viscosity may lead to the instability of the radial oscillations and the spherical form of the bubble. The results obtained here are compared with the behavior of a gas bubble in a Newtonian liquid.     

基于扫频振动环境的燃气陀螺仪动态漂移控制技术

燃气陀螺仪是一种依靠火药燃气驱动的陀螺本体为机械框架式结构的惯性陀螺仪,它能够准确地测出弹体在飞行过程中随时间变化的姿态角,是弹体控制回路中的关键测量部件,其在不同振动环境中的漂移控制技术对制导武器弹体姿态的准确测量非常重要。本文利用欧拉方法,推导了陀螺仪的测量原理和漂移产生机理,分析了摩擦力矩、不平衡力矩,以及弹体环境施加的外力矩对陀螺漂移度的影响,并设计燃气陀螺仪的扫频振动试验找到陀螺对外加力矩的敏感频率。试验结果表明,在敏感频率400～800Hz范围内,通过改善弹体安装环境,可将陀螺仪漂移从大于3°减少至0.5°范围内。该方案具有较高的工程实用价值。     

Flexural vibrations of a thin circular elastic inclusion in an unbounded body under the action of a plane harmonic wave

The interaction of a plane harmonic longitudinal wave with a thin circular elastic inclusion is considered. The wave front is assumed to be parallel to the inclusion plane. Since the inclusion is thin, the matrix-inclusion interface conditions (perfect bonding) are formulated on the mid-plane of the inclusion. The bending displacements of the inclusion are determined from the bending equation for a thin plate. The problem is solved using discontinuous Lamé solutions for harmonic vibrations. Therefore, the problem can be reduced to the Fredholm equation of the second kind for a function associated with the discontinuity of normal stresses on the inclusion. The equation obtained is solved by the method of mechanical quadratures using Gaussian quadrature formulas. Approximate formulas for the stress intensity factors are derived. Results from a numerical analysis of the dependence of the SIFs on the dimensionless wave number and the stiffness of the inclusion are presented __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 5, pp. 16–21, May 2008.     

Nonstationary motion of drops under the action of capillary and mass forces

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 28–35, July–August, 1991.     

Motion of a piston under the influence of gas pressure in the presence of an initial temperature gradient

A study is made of the motion of a piston without initial velocity under the influence of gas pressure. Under the assumption that the temperature gradient is constant and fairly small, expressions are obtained for the distributions of the gas-dynamic parameters in the disturbed region between the piston and the leading edge of the sound wave propagating through the gas at rest.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 177–180, March–April, 1984.