Dynamics of a truncated elastic cone

The problem of determining the nonstationary wave field of an elastic truncated cone with nonzero dead weight is formulated in terms of wave functions. The Laplace transform with respect to time and an integral transform with respect to time polar angle are used to reduce the problem to a one-dimensional vector problem in the transform domain. The transforms of the wave functions are expanded into series in inverse powers of the Laplace transform parameter, which makes it possible to study the wave process at the initial instants of interaction. A method is proposed to solve the problem for an elastic cone doubly truncated by spherical surfaces     

Torsional deformation of a thin inhomogeneous truncated cone

Baku University, Azerbaidzhan. Translated from Prikladnaya Mekhanika, Vol. 30, No. 3, pp. 62–66, March, 1994.     

锥台嵌挤预应力约束混凝土的抗侵彻性能

在侧限约束条件下,混凝土材料的抗侵彻性能可得到较大提高,在此基础上施加预应力围压,其抗侵彻性能可进一步提高,但现有预应力方法对约束混凝土施加预应力较为困难。基于此,提出了一种相对简便的锥台嵌挤预应力约束方法,采用楔形块楔紧的原理,将锥面倾角为3°和直径微大于约束环的锥台形混凝土靶体挤入与之匹配的约束钢环内,通过锥面配合契紧的方式对混凝土靶体沿径向施加预应力,以锥台靶体的下压深度、盈差以及压入力的大小等指标控制预应力大小。采用LS-DYNA软件验证了该方法施加预应力的可行性,并通过重启动算法开展了预应力约束混凝土靶的抗侵彻性能研究。数值计算结果表明,靶体预应力随着其下压深度或盈差的增大近似线性增加,且混凝土靶体的抗侵彻性能随预应力增大而提高,但预应力过大时靶体内部发生损伤,导致其抗侵彻性能反而快速下降。对钢环强度、混凝土强度、含钢率和弹体速度等参数进行敏感性分析,结果表明,合理匹配钢环强度和混凝土强度,并选择合适的靶体含钢率,可有效提高靶体的预应力、抗侵彻性能以及钢材利用率;且弹体初速度越高,预应力对提高靶体抗侵彻性能的作用越明显。提出的锥台嵌挤预应力约束方法可为提高混凝土等脆性材料的抗侵彻性能提供一种新思路和方法。

     

Free convection from a truncated cone subject to constant wall heat flux in a micropolar fluid

The paper studies the problem of free convection about a vertical frustum of a cone in a micropolar fluid. It is assumed that the flow is laminar, steady and the wall is subjected to a constant heat flux and the angle of the frustum of the cone is large enough so that the transverse curvature effects are negligible. Under these assumptions, the governing boundary layer equations subject to appropriate boundary conditions are transformed into a set of equations of parabolic type, that are solved using the local non-similarity method. The space of parameters contains the Prandtl number Pr, the micropolar parameter Δ and the microrotation parameter n. Numerical solutions are obtained by varying Pr from 6.7 to 100, Δ from 0 (Newtonian fluid) to 2 and considering two values of n with physical significance (0 and 0.5). Flow and heat transfer characteristics are determined and are shown in graphs. The results are discussed and compared at some extent with those reported by the present author in a previous study (Postelnicu in Int. J. Eng. Sci. 44:672–682, 2006) on the isothermal case.     

The effect of end conditions on the dynamic loading of plastic shells

A circular cylindrical shell of a rigid plastic material is uniformly loaded by a radial step pressure pulse. Explicit formulas are obtained for the maximum deformation in the shell as a function of the shell geometry and pressure magnitude. It is found that for moderately long shells the deformation is essentially independent of the support conditions at the end of the shell.     

Analysis of functionally graded thick truncated cone with finite length under hydrostatic internal pressure

Finite Element Method based on Rayleigh–Ritz energy formulation is applied to obtain the elastic behavior of functionally graded thick truncated cone. The cone has finite length, and it is subjected to axisymmetric hydrostatic internal pressure. The inner surface of the cone is pure ceramic and the outer surface is pure metal, and the material composition varying continuously along its thickness. Using this method, the effects of semi-vertex angle of the cone and the power law exponent on distribution of different types of displacements and stresses are considered.     

Three-dimensional isothermal lava flows over a non-axisymmetric conical surface

Within the thin-layer approximation for a highly-viscous heavy incompressible fluid, a hydrodynamicmodel of a 3D isothermal lava flow over a non-axisymmetric conical surface is constructed. Using analytical methods, a self-similar solution for the law of leading-edge propagation is obtained in the case of a flow from a non-axisymmetric source located at the apex of a conical surface with smoothly varying properties. In the case of a flow over a substantially non-axisymmetric surface, it is shown that there exists a self-similar solution for the free-surface shape and the law of leading-edge motion. This solution is studied numerically for particular examples of the substrate surface and the source. In the general case of a non-self-similar flow over a substantially non-axisymmetric conical surface, a local analytical solution is obtained for the free-surface shape and the velocity field near the leading flow front.     

Free convection flow over a truncated cone embedded in a porous medium saturated with pure or saline water at low temperatures

Steady free convection boundary layer about a truncated cone embedded in a porous medium saturated with pure or saline water at low temperatures has been studied in this paper. The governing coupled partial differential equations are solved numerically using a very efficient finite-difference method. Several new parameters arise and the results are given for some specific values of these parameters. The obtained results for a Boussinesq fluid are compared with known results from the open literature and it is shown that the agreement between these results is very good.     

The reflection of a shock wave over a cone

An investigation was made of the reflection of planar shock waves from cones. 86 cones, the half apex angle of which varied from 10° to 52° at every 0.5°, were installed in a 60 mm×150 mm diaphragmless shock tube equipped with holographic interferometry. The diaphragmless shock tube had a high degree of reproducibility with which the scatter of shock wave Mach number was within ±0.25% for shock wave Mach number ranging from 1.16 to approximately 2.0. The reflection of shock waves over cones was visualized using double exposure holographic interferometry. Whitham's geometrical shock wave dynamics was used to analyse the motion of Mach stems over cones. It is found that for relatively smaller apex angles of cones trajectory angles of resulting irregular reflections coincide with the so-called glancing incidence angles and their Mach stems appear to be continuously curved from its intersection point with the incident shock wave, which shows the chractericstic of von Neumann reflection. The domain of the existence of the von Neumann reflection was analytically obtained and was found to be broadened much more widely than that of two-dimensional reflections of shock waves over wedges.     

Gas pressure equalization in a porous medium filling a pipe with a closed end under shock loading

The problem of gas pressure equalization in a porous medium filling a pipe with a closed end under shock loading is solved. In this case, the initial filtration velocity behind the shock wave should be specified as initial data, in addition to the shock pressure. It is shown that the shock decays at a finite distance and pressure equalization occurs in a finite time. Approximate submodels of discontinuous and smooth solutions are obtained.     

Solution of the problem of flow of a non-axisymmetric swirling submerged jets

This paper considers the problem of a non-axisymmetric swirling jet of an incompressible viscous fluid flowing in a space flooded with the same fluid. The far field of the jet is studied under the assumption that the angular momentum vector corresponding to the swirling of the jet is not collinear to the momentum vector of the jet. It is shown that the main terms of the asymptotic expansion of the full solution for the velocity field are determined by the exact integrals of conservation of momentum, mass, and angular momentum. An analytical solution of the problem describing the axisymmetric swirling jet is obtained.     

Instability of Hagen-Poiseuille flow for non-axisymmetric mode

An investigation is described for instability problem of flow through a pipe of circular cross-section. As a disturbance motion, we consider a general non-axisymmetric mode. An associated amplitude or modulation equation has been derived for this disturbance motion. This equation belongs to a diffusion type. The coefficient of it can be negative while Reynolds number increases, because of the complex interaction between molecular diffusion and convection. The negative diffusivity, when it occurs, causes a concentration and focussing of energy within decaying slugs, acting as a role of reversing natural decays.     

The boundary layer flow of a Reiner-Rivlin fluid near a spinning cone

Summary The steady motion of an incompressible inelastic Reiner-Rivlin fluid near a spinning cone has been studied and a similarity solution has been presented. It has been shown that the flow patterns can be obtained from Srivastava-Jain's work. But the pressure distribution is not the same and we have given the numerical values of the pressure in two tables and have also shown their variation in two figures.Sponsored by the Mathematics Research Center, United States Army, Madison Wisconsin under Contract No.: DA-11-022-ORD-2059.     

Three-dimensional measurements in non-axisymmetric flow experiment using a one-or two-component laser-Doppler anemometer

 A method to determine the velocity components in the third direction for steady-non-axisymmetric nozzle flow experiments has been developed in addition to the two components that could be directly measured by a one-or two-component laser-Doppler anemometer. With the aid of this method, rotation for either the test rig or the anemometer become unnecessary. Results obtained by this approach were used to compare with those directly measured in the downstream wake of a co-axial nozzle with a central five-lobe forced mixer where the flow is non-axisymmetric. Good agreement could be obtained with maximum discrepancy at about 5%. The present approach can be readily applied to many other non-axisymmetric nozzle flow situations with only some minor modifications. Received: 13 May 1996 / Accepted: 10 October 1996