Propagation of cylindrical blast waves in a multicomponent,viscoplastic medium having variable viscosity

Institute of Fluid Mechanics, Academy of Sciences of the Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 28, No. 10, pp. 29–35, October, 1992.     

Diffraction of stationary cylindrical and plane sound waves by a cylinder in a viscous heat-conducting medium

The diffraction of cylindrical and plane stationary sound waves by a cylinder in a viscous heat-conducting medium is analyzed. A solution of this problem is given in [1] without regard for heat conduction.Tula. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 147–154, May–June, 1972.     

Propagation of cylindrical shock waves in a gravitating medium

We study gas motion behind the front of a cylindrical shock wave created by the motion of a piston in a gravitating medium. The problem is self-similar, but the solution cannot be obtained in closed form. A numerical calculation is made for various Mach numbers. The calculation shows that the central part of the configuration is displaced a definite distance from the axis of symmetry.Cylindrical shock waves through a compressible homogeneous medium in a gravity field have been examined by Sedov [1] and Lin [2], However, these studies contain the essential assumption that the total energy (i. e., the sum of the kinetic and thermal energies) within the region bounded by the expanding shock wave is independent of time.In the following we extend the previous studies to the case of shock waves in nonhomogenous media, which propagate in the fluctuating gravity field created by the disturbed mass itself. The shock wave is created by the motion of a piston whose velocity varies as some power of the time, i. e., v. The total energy of the configuration also depends on the time.The authors wish to thank M. P. Murgai for cooperation and assistance and C. D. Ghildyal for valuable advice, as well as L. I. Sedov and G. I. Petrov for their critical comments.     

Propagation of harmonic waves along a cylindrical cavity in a compressible medium with initial stresses

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 26, No. 2, pp. 31–36, February, 1990.     

短峰波与双层开孔圆筒柱相互作用的数值分析

应用比例边界有限元法（SBFEM）研究了短峰波与双层开孔圆筒柱相互作用。该方法将整个计算域划分成两个有限子域和1个无限子域,利用SBFEM使空间维数降低一阶,并在降维方向保持解析的特点,只需对求解域外圆柱边界进行离散。通过比例坐标与直角坐标之间的转换,并利用变分原理推导了各个子域的SBFEM方程。然后,SBFEM针对有限域和无限域分别采用贝塞尔函数和汉克尔函数作为基函数来求解对应域的解,并将计算结果与解析解进行比较,验证了该方法是一种用很少单元便能得到精确结果的高效方法。进一步研究了诸如相对波数ka、内外柱半径比a/b和内外壁孔隙影响系数G等对双层开孔圆筒柱结构所受波浪荷载、结构内外侧波浪爬升及绕射波轮廓的影响。为双层开孔圆筒柱水动力分析和结构设计提供了有价值的参考。     

Propagation of magnetoelastic stress waves from a cylindrical cavity in a conducting medium

We study the influence of a constant axial magnetic field on the propagation of magnetoelastic compression waves from a cavity containing a magnetoacoustic medium with a jump of the surface force given at the wall. The problem is examined in [1] in the case in which there is a vacuum in the cavity and an ideal conductor outside, without any study of the effect of a magnetic field.Here we examine the problem for both weak and ideal conductivities. The equations are linearized and Laplace transformed. Approximate asymptotic solutions are constructed which are valid in the vicinity of the wave fronts. The solutions are studied analytically and numerically.In conclusion the author wishes to thank Ya. S. Uflyand for discussions of certain questions.     

Higher-order approximations in the analysis of nonlinear cylindrical waves in a hyperelastic medium

The nonlinear wave equation is solved analytically in cylindrical coordinates using the third-order approximation of the Hankel function. The second-order and third-order solutions are compared. The evolution of the initial wave profile is simulated numerically for different initial frequencies __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 4, pp. 36–45, April 2007.     

Spherical wave propagation in a viscoplastic medium

Summary A study is presented of the problem of spherical wave propagation in an infinite viscoplastic medium. The surface of a spherical cavity is subjected to a uniform impact load which is continuously maintained. The material is elastic/viscoplastic, satisfying Mises condition, isotropic hardening, and viscoplastic incompressibility. A generalized form of Malvern's constitutive relation is used with a bilinear static shear stressshear strain curve, the method of characteristics, and an IBM 7040–7094 digital computer. Particular emphasis is placed on the influence of strain hardening and of the viscosity coefficient. It is shown that changes in the strain hardening coefficient and in the viscosity coefficient have considerable influence on the results, which is to some extent unexpected in view of previous work on this subject.

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Übersicht Eine konkave innere Oberfläche wird durch eine konstante gleichmäßig verteilte Kraft belastet. Das Material wird als elastisch-viscoplastisch angenommen mit isotroper Verfestigung und viscoplastischer Inkompressibilität; es genügt der von Mises'schen Fließbedingung. Es werden eine sinngemäße Erweiterung der Malvernschen Materialgleichung und numerische Lösungen für ein Material mit bilinearer Schubspannungs- and Scherungskennlinie angegeben. Dabei zeigt sich überraschenderweise, daß Änderungen des Verfestigungskoeffizienten und der Viscosität die spherische Wellenausbreitung erheblich beeinflussen.

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This investigation was supported by the National Science Foundation under a grant to Yale University.     

Unsteady flows of a viscoplastic medium in channels

We numerically study the nonstationary Poiseuille problem for a Bingham-Il’yushin viscoplastic medium in ducts of various cross-sections. The medium acceleration and deceleration problems are solved by using the Duvaut-Lions variational setting and the finite-difference scheme proposed by the authors. The dependence of the stopping time on internal parameters such as density, viscosity, yield stress, and the cross-section geometry is studied. The obtained results are in good agreement with the well-known theoretical estimates of the stopping time. The numerical solution revealed a peculiar characteristic of the stagnant zone location, which is specific to unsteady flows. In the annulus, disk, and square, the stagnant zones arising shortly before the flow cessation surround the entire boundary contour; but for other domains, the stagnant zones go outside the critical curves surrounding the stagnant zones in the steady flow. The steady and unsteady flows are studied in some domains of complicated shape.     

Nonstationary shear flow of a viscoplastic medium

We consider problems involving nonstationary shear flow of a viscoplastic medium between two parallel plates and also in a cylindrical tube under the action of a time-varying shear stress applied to the walls of the passage.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 133–137, July–August, 1972.     

粘塑性变截面杆中冲击波的演化

讨论了粘塑性变截面杆中的一维应力波传播规律。在粘塑性本构理论框架的基础上,利用特征关系和冲击波阵面上的突跃条件,得出了冲击波在传播过程中的演化规律,包括其微分方程和解析表达式,并对Bodner和Johnson-Cook材料和不同收缩形式的杆中冲击波的演化规律进行了讨论,同时计算和讨论了杆中冲击波后方应力波传播规律的特点。     

Motion of a viscoplastic liquid in a porous inhomogeneous medium

Equations of motion are derived for a viscoplastic liquid in a nonuniform medium of type 2 (piecewise uniform) or type 3 (with a variable filtration coefficient) [1] on the assumption that the motion is of steady-state type. Solutions are presented for a parallel flow and a flow with axial symmetry.