基于机械振动理论的垂直侵彻弹靶作用模型

为了给侵彻引信抗高过载优化设计提供准确的力学输入,将机械振动理论引入侵彻过程建模领域,提出了一种侵彻战斗部刚体运动与一阶轴向振动相结合的垂直侵彻弹靶作用模型。在垂直侵彻过程受力分析的基础上,基于牛顿第二定律建立了战斗部刚体运动模型,基于单自由度弹簧-质量-阻尼系统建立了战斗部一阶轴向振动模型,并采用数值积分的方法获得了垂直侵彻过程中各物理量的变化规律。和火炮试验实测加速度信号的对比分析结果表明:考虑战斗部一阶轴向振动后的垂直侵彻弹靶作用模型能更准确地描述侵彻过程,能更有效地指导侵彻引信的抗高过载优化设计。     

Stability, Paths, and Dynamic bending of a Blunt Body of Revolution Penetrating into an Elastoplastic Medium

The deep penetration of a thin body with a blunt nose and rear into a lowstrength medium is explored. The motion of the body is described by a system of autonomous integrodifferential equations using the physical model of a separated asymmetric flow over the body and the localinteraction method. An analytical calculation of the Lyapunov stability boundary for straightline motion is performed for bodies with a parabolic meridian. The dependences of the dynamic stability of the body on various parameters are studied numerically. Curved motion paths are constructed in the region of instability, and the classification of paths proposed in previous studies of the motion of pointed bodies is confirmed. It is shown that an reverse ejection is possible when a blunt impactor enters a semiinfinite target. It is established that there is a fundamental possibility of attaining a path close to a specified one and that there is a weak dependence of motion characteristics with a developed separation on the separation angle. Examples are given of calculations of the evolution of the lateral load, the transverse force and moment, and the strength margin of the body using the theory of dynamic bending of a nonuniform rod.     

A quasi-static approach to the stability of the path of heavy bodies falling within a viscous fluid

We consider the gravity-driven motion of a heavy two-dimensional rigid body freely falling in a viscous fluid. We introduce a quasi-static linear model of the forces and torques induced by the possible changes in the body velocity, or by the occurrence of a nonzero incidence angle or a spanwise rotation of the body. The coefficients involved in this model are accurately computed over a full range of Reynolds number by numerically resolving the Navier–Stokes equations, considering three elementary situations where the motion of the body is prescribed. The falling body is found to exhibit three distinct eigenmodes which are always damped in the case of a thin plate with uniform mass loading or a circular cylinder, but may be amplified for other geometries, such as in the case of a square cylinder.     

On the penetration of nonaxisymmetric bodies into a deformable solid medium and their shape optimization

We consider the problem of penetration of rigid pyramidal bodies (impactors) into a strained medium in the case of large speeds of penetration and estimate the depth of the impactor penetration. To this end, we use the two-stage penetration model proposed by Forrestall. We state the shape optimization problem for the penetrating body, which is based on the consideration of a set of bodies of pyramidal external shape with given fixed mass. We study both solid and hollow (shell-shaped) bodies. For the optimization functional we take the penetration depth of the penetrating body, and for the projection variable we take the number of faces of the pyramidal body. We present the results of computations of the penetration depth for different shapes of the impactor and show that, both for shells and solid impactors, the bodies of the shape of a circular cone are optimal. The problems of high-speed penetration of rigid bodies into a deformable medium are nowadays very topical problems [1] which have been studied by Russian and foreign authors [2–8].     

On the penetration of a rotating impactor into an elastic-plastic medium

This research is devoted to the modeling of high-speed rectilinear penetration of a rigid axisymmetric body (impactor with a flat bluntness) into an elastic–plastic media with account for its rotation about the axis of symmetry. The body has an arbitrary shape of the meridian. The resistance to the motion is represented as the sum of the body drag and the contribution of friction. The dynamic system governing the body motion is derived and the qualitative and numerical analysis of the projectile movement and perforation of a slab are performed. The problem of shape optimization of impactor with a flat bluntness is studied using evolutionary algorithm.     

Localized interaction models with non-constant friction for rigid penetrating impactors

We suggest approximate penetration models for rigid body penetration that take into account sliding velocity (SV) and pressure dependence of the friction coefficient (FC). It is showed that introducing variable FC in a localized interaction model (LIM) yields a model that belongs to the class of LIM. We developed a general method for determining the depth of penetration (DOP) using the piecewise linear approximation of the impactor’s generatrix. For some classes of SV dependent friction models we obtained analytical formulas for calculating the DOP. Using the experimental data available in the literature, we determined the dependencies of FC vs. pressure and SV. We conducted numerical modeling of penetration of a metal striker into metal and concrete shields employing models with variable and constant FC. Numerical simulations showed that taking into account variable FC strongly effects the DOP when FC changes appreciably for large velocities that are characteristic for the high-speed penetration.     

Penetration of rigid bodies into loose and layered media

Penetration and motion of rigid bodies in ground media attracts the researchers’ attention because of various problems arising as the technology evolves. In fact, there are two independent directions of studies in this field: (1) the problem of earth excavation when a rigid body of a definite shape slowly moves along a given trajectory in the ground; (2) an impact of a rapidly flying free rigid or deformable body against the ground. In the latter case, to which the proposed studies pertain, it is sometimes of interest to study the medium behavior and the motion of the free body, which moves in the medium after the impact owing to the kinetic energy of itself. In this field, a majority of studies deal with collision and penetration of bodies of various shapes into clay media. An extensive survey of these studies is given in [1]. After this survey appeared, numerous paper dealing with complicated collision conditions have been published [2]. Penetration in loose media has been studied much more rarely. The direct collision with fractured rock was studied in connection with the expected landing of spacecraft on other planets [3, 4]. In this case, the influence of grain dimensions and the density of the filling and vacuum on the penetration was studied for the initial velocities in the range of 1.7–10 m/s. On the other hand, in [5], the results of investigating the penetration of conic bodies in sand at entry velocities of 700–900 m/s are given; these velocities significantly exceed the speed of sound in this medium, which lies in the range of 100–200 m/s for dry sand. Analyzing the experimental results, the author came to the conclusion that it is necessary to use different representations of the drag force in the supersonic and subsonic modes. In the present paper, we do not consider the influence of the grain distribution, sand density, and filling methods on the penetration. But, as follows from the experiments whose results are described in [6] and [7], to represent the results of penetration of rigid bodies at velocities up to several hundreds of meters per second, in addition to the characteristics listed above, it is also required to describe the technology of the experiment preparation, because such media have the property of shape “memory.”     

Calculating the effect of gusts on an arbitrary thin wing

A numerical method of calculating the unsteady flow about a thin wing moving in an ideal incompressible medium is developed on the basis of the lifiting surface scheme. The variation of the boundary conditions on the wing surface with time and coordinates may be arbitrary. Therefore, the method makes it possible to examine the aperiodic motion of a wing as a rigid body, consider any wing deformations, analyze the wing entry into a gust, study the effect of a weak shock wave on the wing, etc. In addition, practically no limitation is imposed on the shape of the thin lifting surface: the method is applicable to monoplane wings of any planform, to annular wings, to systems of similar wings, etc.Studies in which the effect of a gust on a wing is analyzed have been reviewed in [1, 2]. Without dwelling on this review, we note that at subsonic speeds an effective solution of the problem has been obtained only for a profile.The author wishes to thank E. P. Kapustina for working the examples.     

舰船舷侧防护液舱舱壁对爆炸破片的防御作用

针对破片撞击液舱外板,建立分析模型探讨背水靶板的穿甲过程。以能量分析为基础,根据破片 穿甲的运动方程和德玛尔模型,推导破片穿透背水靶板后的剩余速度公式。根据给出的剩余速度公式,计 算不同初始速度(1.0~1.6km/s)的破片穿透背水靶板后的剩余速度,根据已有剩余速度公式计算破片以同 样的初始速度穿透背空靶板后的剩余速度,并用非线性动力学分析软件AUTODYN 对相应的破片穿甲过程 进行数值模拟。模拟结果能较好地与理论计算结果相吻合。与破片穿透空背靶板的情况相比,破片穿透背水 靶板后剩余速度降低更明显。破片初始速度越高,板后的液体对破片阻碍作用越明显,破片速度降越大。     

Prediction of sinkage and motion resistance of a tracked vehicle using plate penetration test

The relationship between contact pressure and sinkage must be represented by a mathematical model to estimate the sinkage and the motion resistance due to a vehicle. In this study an approximate and simple pressure-sinkage model is proposed. This model takes into account the effect of the size of the penetration plate on soil response, and includes two soil values that can be obtained by a single plate penetration test. It is submitted that the sinkage and the motion resistance of a tracked vehicle can be estimated by means of the proposed model.     

Ventilated entry of a slender profile into a compressible liquid at subsonic velocity

The problem of vertical entry at subsonic velocity into an ideal compressible fluid is solved in the linear formulation for a slender profile with open attached cavity. An integral equation is obtained for the potential of the accelerations. Expressions are given for the calculation of the drag of a thin wedge and also some results of calculations which show that in the limiting case of infinite depth of penetration, which corresponds to stationary flow past the thin wedge with separation of a jet, an analog of the Prandtl—Glauert theorem holds.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 9–17, July–August, 1980.     

Soil Behavior at the Interface with a Rigid Projectile During Penetration

The motion and state of soil at the interface with a penetrating rigid projectile is studied by numerical solution of the problem of a cylindrical projectile which expands and at the same time moves translationally along its axis in soil. The soil behavior is described using the model of a compressible elastoplastic medium with transition to a plastic state depending on the pressure in it. It is shown that a thin layer of soil at the interface with the projectile nose should be set in motion and move together with the projectile without sliding. An analysis is performed of the validity of using the dry friction law to determine the shear stresses on the projectile surface during penetration. The heat release in the soil layer at the interface due to internal friction and its possible effect on the penetration are estimated. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 6, pp. 116–127, November–December, 2005.     

An approximate solution of the problem of the penetration of a body into soil

The qualitative features of the problem of the penetration of a solid body into a soil medium are analyzed and its approximate solution is constructed as explicit finite formulas which make it possible to calculate all the parameters of the body motion as functions of time.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 18–24, May–June, 1993.     

Droplet Imbibition into Paper Coating Layer: Pore-Network Modeling Simulation

Liquid penetration into thin porous media such as paper is often simulated using continuum-scale single-phase Darcy’s law. The underlying assumption was that a sharp invasion front percolates through the layer. To explore this ambiguous assumption and to understand the controlling pore-scale mechanisms, we have developed a dynamic pore-network model to simulate imbibition of a wetting phase from a droplet into a paper coating layer. The realistic pore structures are obtained using the FIB-SEM imaging of the coating material with a minimum resolution of 3.5 nm. Pore network was extracted from FIB-SEM images using Avizo software. Data of extracted pore network are used for statistically generating pore network. Droplet sizes are chosen in the range of those applicable in inkjet printing. Our simulations show no sharp invasion front exists and there is the presence of residual non-wetting phase. In addition, penetration of different sizes of droplets of different material properties into the pore network with different pore body and pore throat sizes are performed. We have found an approximately linear decrease in droplet volume with time. This contradicts the expected \(\sqrt{t}\)-behavior in vertical imbibition that is obtained using macroscopic single-phase Darcy’s law. With increase in flow rate, transition of imbibition invasion front from percolation-like pattern to a more sharper one with less trapping of non-wetting phase is also reported. Our simulations suggest that the single-phase Darcy’s law does not adequately describe liquid penetration into materials such as paper coating layer. Instead Richards equation would be a better choice.     

弹丸入水特性的SPH计算模拟

应用SPH方法研究弹丸入水过程中的动力学特征。利用拉格朗日形式的N-S方程自编SPH程序,建立弹丸入水的计算模型,赋予相应的材料参数及状态方程,研究弹丸外形、入水速度和角度等因素对入水过程的影响。模拟结果表明:空化泡的形态及发展规律主要由弹丸的运动姿态决定;弹道越稳定,阻力因数就越小,弹丸的存速就越大。SPH方法具有较强的自适应性,适用于研究弹丸入水的流固耦合问题。     

On the motion of thin plates and shells subject to Stokes damping

The motion of a homogeneous, thin rigid plate or shell subject to Stokes damping over its entire surface and to any additional system of workless forces, including those that are equipollent to zero, is studied. It is shown that the equation for the single-degree of freedom motion of every thin body having the same mass density per unit area is universal; the result, except for sufficient mathematical smoothness essential to integration over the body, is independent of any other physical features or dimensions of the body. A few examples illustrate the general problem and the universal nature of the equation of motion for thin plates and shells.     

Inclined entry of a blunt profile into an ideal fluid

A study is made of the two-dimensional unsteady motion of an ideal incompressible fluid due to the entry into it of a blunt profile at a given angle of attack. In the initial stage of the process, when the penetration depth is relatively small, the problem can be investigated by the methods of asymptotic analysis. The dimensionless time t plays the part of the small parameter. It is shown that to 0(t²) as t 0 the displacement field of the fluid particles does not depend on the angle of attack and is determined by the solution to the problem of vertical entry. The asymptotic behaviors of the principal vector and principal moment of the forces exerted on the profile by the fluid at short times are found. The asymptotic behavior of the principal moment of the forces is proportional to the distance traversed by the body along the surface of the fluid.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 145–150, May–June, 1988.     

Vertical entry of solids into water

The vertical inertial entry of spheres and disks of various masses into water has been investigated experimentally. The values of the virtual mass and the drag coefficients are estimated with the aid of high-speed photography of the penetration process. An expression is obtained for the nonstationary cavity near the body.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 3–9, November–December, 1985.     

On the stress state of shells penetrating into a deformable solid

The motion of an axisymmetric shell in a deformable solid medium is considered. It is assumed that the medium resistance is described by a two-term expression containing a constant term (the rigidity characteristic) and an inertial term quadratic with respect to the penetration velocity. A model of the impactor penetration with the normal interactions with the resisting medium taken into account is proposed. The membrane forces and the arising stresses are determined for decelerated motions of the impactor.