Stability of spatial motion of a body of revolution in an elastoplastic medium

A previously constructed model that describes the spatial motion of a body of revolution in an elastoplastic medium (without flow separation and with nonsymmetric separation of the medium flow taken into account) is used to study the Lyapunov stability of rectilinear motion of a body in the case of frozen axial velocity on a half-infinite time interval. Some stability criteria are obtained and the influence of tangential stresses is analyzed.     

Formation of separation zones in an asymmetric motion of a body in an elastic medium

We obtain an analytical solution of the problem on the motion of a body with wedge-shaped nose in an elastic medium for the case in which a medium separation zone may occur near the nose owing to asymmetry. The character of the dependence of the separation region length on the body velocity, the nose opening angle, the motion asymmetry degree, and the friction coefficient is found. It is shown that if the body moves at a velocity greater than the transverse wave velocity, then there is a limit velocity at which the separation region near the nose of the body disappears.     

Linear theory of unsteady gas flow under the influence of nonpotential external forces

We determine in the linear formulation the velocity and pressure fields excited in a compressible medium by a lifting filament that displaces and deforms arbitrarily. For general unsteady motion of such a filament we give explicit formulas that express the velocity at a given point in terms of the intensity of the free vortices entering the audio signal audibility zone constructed for this point. We examine gas flow caused by an arbitrary external body force field.Studies devoted to the determination of gas velocity fields for flow past slender bodies relate primarily to translational motion of a body with a dominant constant velocity [1–3]. Gas velocities for helical motion of a rectilinear lifting filament within the gas have been examined in [4].     

Motion of a slender body in a fluid under a floating plate

This paper studies the three-dimensional unsteady problem of the hydroelastic behavior of a floating infinite plate under the impact of waves generated by horizontal rectilinear motion of a slender solid in a fluid of infinite depth. An analytic solution of the problem is found based on the known solutions for the unsteady motion of a point source of mass in a fluid of infinite depth under a floating plate. Asymptotic formulas are obtained which model the motion of a solid slender body in a fluid by replacing the body with a source-sink system. These formulas are used to numerically analyze the effect of plate thickness, depth of the body, its dimensions and the velocity of rectilinear motion on the amplitude of deflection of the floating plate. The motion of a submarine under a nonbreakable plate was modeled experimentally. Theoretical and experimental data are in good agreement.     

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.     

On the instability of a car in the vertical plane under rectilinear motion with friction forces taken into account

We consider the problem on the stability and instability of the equilibrium in the vertical plane for a wheeled vehicle performing a uniform rectilinear motion in the presence of rolling friction forces. We assume that the dependence of the rolling friction coefficients on the motion velocity is known and derive necessary and sufficient conditions on the system parameters under which such equilibria are stable.     

Wedging of an elastic medium with the formation of separation zones

The problem of motion of a rigid body in an elastic medium is solved analytically for the case when a separation zone caused by asymmetry is formed in front of the body. A scheme of flow around wedge-shaped and ogive bodies is given for the entire range of the velocities under consideration. It is shown that there exists a limit velocity such that the separation zone disappears when the body moves at a velocity greater than the velocity of transverse waves. The forces exerted on a wedge-shaped body and on an ogive body are the same in the case of the limit velocity.     

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.     

Penetration of a body of revolution into an elastoplastic medium

We consider a model of spatial motion of a body of revolution in a weak soil-type medium with nonsymmetric flow separation taken into account. We obtain a system of equations describing the entry and penetration of a thin body into a half-space. We calibrate the model by comparing it with experiments on penetration of thin cones into plasticine. Test computations show that the model describes complex body motion trajectories for various angles of entry into the target with adequate accuracy.     

Modeling of large elastoviscoplastic deformations with thermophysical effects taken into account

We propose a mathematical model of large elastoviscoplastic deformations where intensive deformation results in temperature increasing and heat transfer processes. As an example of applying the model relations, we present a solution of the boundary-value problem on rectilinear motion and heating of a medium located in the gap between coaxial rigid cylindrical surfaces.     

Stability of periodic motion of fluid in a planar channel

The stability of periodic motion of a fluid in a planar channel was investigated experimentally. Two mechanisms of departure from stability of rectilinear motion — at high and low frequencies, respectively — were observed. The critical Reynolds number was found as a function of the pulsation frequency. The results of the quasistationary theoretical approach to the stability of periodic flows [1] agree with the experiment.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 114–118, November–December, 1979.I thank G. F. Shaidurov, under whose guidance this work was carried out.     

Dynamic properties of a body with discontinual mass variation

In this paper the procedure for the dynamic analysis of body separation is introduced. Based on the general laws of classical dynamics, the method for obtaining the velocity and the angular velocity of the remainder body during separation is developed. Due to the discontinual mass variation, the jump-like change of the velocity and the angular velocity of the body is evident. Various types of motion of the separated body are considered. Depending on the type of motion of the separated body the dynamic properties of the remainder body are obtained. As a special case the in-plane motion of the body before and after separation is considered. The theoretical considerations are applied for the separation analysis of a rotor (a shaft-disc system). The transient motion of the body after separation is investigated. To prove the correctness of the procedure suggested in the paper, the case when the mass and the moment of inertia of the separated body are infinitesimal is analyzed. The obtained differential equations are the same as those previously obtained.     

Controlled motion of a two-module vibration-driven system induced by internal acceleration-controlled masses

The rectilinear motion of a vibration-driven mechanical system composed of two identical modules connected by an elastic element is considered in this paper. Each module consists of a main body and an internal mass that can move inside the main body. Anisotropic linear resistance is assumed to act between each module and the resistant medium. The motion of the system is excited by two acceleration-controlled masses inside the respective main bodies. The primary resonance situation that the excitation frequency is close to the natural frequency of the system is considered, and the steady-state motion of the system as a whole is mainly investigated. Both the internal excitation force and the external resistance force contain non-smooth factors and are assumed to be small quantities of the same order when compared with the maximum value of the force developed in the elastic element during the motion. With this assumption, method of averaging can be employed and an approximate value of the average steady-state velocity of the entire system is derived through a set of algebraic equations. The analytical results show that the magnitude of the average steady-state velocity can be controlled by varying the time shift between the excitations in the modules. The optimal value of the time shift that corresponds to the maximal average steady-state velocity exists and is unchanging with the external coefficients of resistance. For a system with specific parameters, numerical simulations are carried out to verify the correctness of the analytical results. The optimal value of the time shift is numerically obtained, and the optimal situation is studied to show the advantages of the control.     

Controlled synchronization at the existence limit for an excited unbalanced rotor

The synchronization of a controlled unbalanced rotor with a viscoelastically mounted supporting body and force-excitation is studied. The existence and stability conditions for the synchronous regime of motion are derived for a general control law by the method of direct separation of motion. Then a control law is developed using speed gradient method in order to transfer maximum energy from the excitation to the rotor. The free parameters of the control law are derived in such a way that the controlled synchronization is stable at the existence limit.     

The transient motion of a dislocation in a solid of general anisotropy

The transient motion of a dislocation starting from rest and moving in an arbitrary rectilinear motion in an anisotropic solid is analyzed by transform techniques and inversion according to the Cagniard-de Hoop technique.     

Oblique entry of a slender body in an incompressible fluid

The plane problem of oblique penetration of a slender semiinfinite body in an ideal, weightless, and incompressible fluid is examined. Detailed numerical computations are performed for a wedge with rectilinear sides. The formulas obtained are applicable also for the calculation of the hydrodynamic reactions during emergence of a body from a fluid or during transverse motion of a half-blunt body with a low relative velocity. Moreover, the results of the present paper can be used to evaluate the hydrodynamic forces acting on underwater wings or propeller blades during intersection with a free surface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 16–24, September–October, 1977.     

Theory of spall damage accumulation in ductile metals

Spall damage is a type of fracture produced when large tensile stresses are developed in material bodies as a result of the interaction of stress waves. The damage develops independently at various points in the body because of the short duration of stress application, but interacts in a complicated way with the stress wave. A theory of these phenomena is presented for the case where the basic response of the material is viscoplastic, and where the damage takes the form of a distribution of small rounded voids. This theory is specialized to the case of rectilinear motion and an example problem solved numerically.     

A multiparameter family of phase portraits in the dynamics of a rigid body interacting with a medium

The problem of plane-parallel motion of a uniform symmetric rigid body interacting with a medium only through a flat region of its outer surface is studied. The force field is constructed on the basis of information on the properties of jet flow under quasistationarity conditions. The motion of the medium is not studied. The problem of rigid body dynamics is considered for the case when the characteristic time of motion of the body relative to its center of mass is comparable with the characteristic time of motion of this mass center.     

On the problem of free deceleration of a rigid body in a resisting medium

A mathematical model of the influence of a medium on a rigid body with some part of its external surface being flat is considered with due allowance for an additional dependence of the moment of the medium action force on the angular velocity of the body. A full system of equations of motion is given under quasi-steady conditions; the dynamic part of this system forms an independent third-order system, and an independent second-order subsystem is split from the full system. A new family of phase portraits on a phase cylinder of quasi-velocities is obtained. It is demonstrated that the results obtained allow one to design hollow circular cylinders (“shell cases”), which can ensure necessary stability in conducting additional full-scale experiments.