Motion of a solidcontaininga spherical damper

For the purpose of modeling the motion of a solid with a cavity filled with a viscous fluid, M. A. Lavrent'ev [1] has proposed a model in the form of a solid with a spherical cavity in which another solid, spherical in shape, is enclosed. The sphere is separated from the cavity walls by a small, clearance in which viscous forces act (a lubricating film). This simple model with a finite number of degrees of freedom possesses certain mechanical properties of a solid with a cavity containing a viscous fluid. Study of this model is therefore of interest.The present paper examines certain properties of the model, which will be termed a solid with a damper. It is shown that for a highviscosity lubricant the motion of a solid with a damper can be described by the same equations which pertain to the motion of a solid with a spherical cavity filled with a high-viscosity fluid. Expressions relating the parameters of the systems are obtained. If these relations are fulfilled, the systems become mechanically equivalent.The steady motions of a free solid with a damper and their stability conditions are determined.These motions and stability conditions hold for a body with a cavity filled with a viscous fluid [2].     

New solutions of classical problems in rigid body dynamics

The equations of motion of a rigid body acted upon by general conservative potential and gyroscopic forces were reduced by Yehia to a single second-order differential equation. The reduced equation was used successfully in the study of stability of certain simple motions of the body. In the present work we use the reduced equation to construct a new particular solution of the dynamics of a rigid body about a fixed point in the approximate field of a far Newtonian centre of attraction. Using a transformation to a rotating frame we also construct a new solution of the problem of motion of a multiconnected rigid body in an ideal incompressible fluid. It turns out that the solutions obtained generalize a known solution of the simplest problem of motion of a heavy rigid body about a fixed point due to Dokshevich.     

Numerical Simulation of Coherent Structures over Plant Canopy

This paper reports large eddy simulations of the interaction between an atmospheric boundary layer and a canopy (representing a forest cover). The problem is studied for a homogeneous configuration representing the situation encountered above a continuous forest cover, as well as for a heterogeneous configuration representing the situation similar to an edge or a clearing in a forest. The numerical results reproduces correctly all the main characteristics of this flow as reported in the literature: the formation of a first generation of coherent structures aligned transversally with the wind flow direction, the reorganization and the deformation of these vortex tubes into horse-shoe structures. The results obtained when introducing a discontinuity in the canopy (reproducing a clearing or a fuel break in a forest), are compared with the experimental data collected in a wind tunnel; here, the results confirm the existence of a strong turbulence activity inside the canopy at a distance equal to 8 times the height of the canopy, referenced in the literature as the Enhance Gust Zone (EGZ) characterized by a local peak of the skewness factor.     

Penetration of a cumulative jet into a barrier

A solution is given to the problem of the penetration of a cumulative jet with an arbitrary distribution of the velocity along it, taking account of the strength properties of the barrier. Using the example of a jet with a linear distribution of the velocity, the article demonstrates the possibility of obtaining a large puncturing capacity due to a change in the gradient along the jet as a function of the physicomechanical properties of the barrier and the jet. In addition, a distribution of the velocity along the jet is obtained which assures a maximal penetration in a barrier, arranged at a distance where a limiting elongation is not attained either partially or completely over the whole jet.     

A Lagrangian finite element method for the simulation of flow of non-newtonian liquids

A Lagrangian method for the simulation of flow of non-Newtonian liquids is implemented. The fluid mechanical equations are formulated in the form of a variational principle, and a discretization is performed by finite elements.The method is applied to the slow of a contravariant convected Maxwell liquid around a sphere moving axially in a cylinder. The simulations show that the friction factor for a sphere in a narrow cylinder is a rapidly decreasing function of the Deborah number, while the friction factor for a sphere in a very wide cylinder is not significantly affected by fluid elasticity. It is demostrated that the simulated wall effect on the motion of the sphere may be utilized in an experimental identification of a time constant for a given liquid.     

Weak–Strong Uniqueness of Dissipative Measure-Valued Solutions for Polyconvex Elastodynamics

For the equations of elastodynamics with polyconvex stored energy, and some related simpler systems, we define a notion of a dissipative measure-valued solution and show that such a solution agrees with a classical solution with the same initial data, when such a classical solution exists. As an application of the method we give a short proof of strong convergence in the continuum limit of a lattice approximation of one dimensional elastodynamics in the presence of a classical solution. Also, for a system of conservation laws endowed with a positive and convex entropy, we show that dissipative measure-valued solutions attain their initial data in a strong sense after time averaging.     

Scenarios of the onset of unsteady regimes in the problem of plane convective flow through a porous medium

The problem of plane convective flow through a porous medium in a rectangular vessel with a linear temperature profile steadily maintained on the boundary is considered. The onset of unsteady regimes is investigated numerically. It is shown that their onset scenarios depend on the vessel dimensions and the seepage Rayleigh number and may be as follows: the generation of stable and unstable periodic regimes as a result of a one-sided bifurcation, the generation of a stable periodic regime as a result of an Andronov-Hopf cosymmetric bifurcation, the formation of a chaotic attractor, the branching-out of a stable quasi-periodic regime from a point of a single-parameter family of steady-state regimes, and the generation of unstable periodic regimes as a result of disintegration of homoclinic trajectories. The specifics of most of the bifurcations mentioned above are attributable to the cosymmetry of the problem considered.     

Ideal gas flow behind a finite-amplitude shock wave

The equations of one-dimensional (with a plane of symmetry) adiabatic motion of an ideal gas are transformed to a form convenient for studying flows between a moving piston and a shock wave of variable intensity. The solution is found for the equations of a motion containing a shock wave which propagates through a quiescent gas with variable initial density and constant pressure. This solution contains four arbitrary constants and, in a particular case, gives an example of adiabatic shockless compression by a piston of a gas initially at rest.     

Reduction of dimensions in random,elastic soil medium

The paper deals with an application of the plane strain analysis in a stochastic three-dimensional soil medium. In a framework of random elasticity theory, the geostatical state of stresses and the problem of a unit force acting in a statistically homogeneous half-space are considered. Only the modulus of elasticity is considered to be random and is modelled as a three-dimensional (3-D) homogeneous random field. As the result of imposed constrains due to the plane strain assumption the additional body and surface forces are induced. In order to determine them, additional equations must be introduced. The equations in a form of constrain relations are proposed in this paper. These equations are also valid for a case of uniformly distributed external loading.First, the two-dimensional (2-D) problem and its reduction to the uni-axial strain state, for the gravity forces and uniform, unlimited surface loading is considered. Then, it is generalised into a 2-D schematization of the 3-D state. Next, the problem of a unit force acting in a statistically homogeneous half-space is considered. For a 3-D state of stress and strain the resulting stresses are compared with those for a 2-D state. These stresses for the multidimensional state of strain and stress are presented as a sum of two components. The first one reflects plane strain state stresses and is given in a form of a 3-D random field. This term allows for incorporating a spatial, 3-D soil variability into a two-dimensional analysis. The second component can be treated as a correction term and it represents the longitudinal influence of a 3-D analysis.Some numerical results are presented in this paper. The proposed method can be regarded as a framework for further research aiming at application to a variety of geotechnical problems, for which the plane strain state is assumed.     

Dynamical regimes of fiber spinning

An analytical solution is obtained that describes fiber spinning with a given force on the receiving bobbin. As an example, a calculation is made of the response of the final fiber section to a periodically varying draw force; a solution is constructed that describes the propagation along the fiber of a finite perturbation associated with a change in the conditions at the spinneret for a fixed draw force. The problem of the small perturbations of a fiber spun at a given rate onto a bobbin is reduced to a linear integrodifferential equation with retardation whose characteristic equation determines the region of the “draw resonance” instability. The reasons for the occurrence for the instability are elucidated.     

A Eulerian/Lagrangian model to calculate the evolution of a water droplet spray

We introduce a Eulerian/Lagrangian model to compute the evolution of a spray of water droplets inside a complex geometry. To take into account the complex geometry we define a rectangular mesh and we relate each mesh node to a node function which depends on the location of the node. The time-dependent incompressible and turbulent Navier-Stokes equations are solved using a projection method. The droplets are regarded as individual entities and we use a Lagrangian approach to compute the evolution of the spray. We establish the exchange laws related to mass and heat transfer for a droplet by introducing a mass transfer coefficient and a heat transfer coefficient. The numerical results from our model are compared with those from the literature in the case of a falling droplet in the atmosphere and from experimental investigation in a wind tunnel in the case of a polydisperse spray. The comparison is fairly good. We present the computation of a water droplet spray inside a complex and realistic geometry and determine the characteristics of the spray in the vicinity of obstacles.     

Nonlinear statics and dynamics of a simply supported nonuniform tube conveying an incompressible inviscid fluid

Nonlinear static and dynamic behaviour of a simply supported fluid-conveying tube, which has a constant inner diameter and a variable thickness is analysed analytically and numerically. Nonlinear static bending is considered in two loading cases: (i) a tube subjected to supercritical axial compressive forces acting at its edges or (ii) a tube loaded by concentrated bending moments, which provide a symmetrical (with respect to the mid-span) shape of a tube. The nonlinear governing equations of motions are derived by using Hamilton's principle. The elementary plug flow theory of an incompressible inviscid fluid is adopted for modelling a fluid–structure interaction. The flow velocity is taken as the sum of a principal constant ‘mean’ velocity component and a fairly small pulsating component. Firstly, eigenfrequencies and eigenmodes of a deformed tube are found from linearised equations of motions. Then resonant nonlinear oscillations of a tube about its deformed static equilibrium position in a plane of static bending are considered. A multiple scales method is used and a weak resonant excitation by the flow pulsation is considered in a single-mode regime and in a bi-modal regime (in the case of an internal parametric resonance) and the stability of each of them is examined. The brief parametric study of these regimes of motions is carried out.     

Transient responses of beams and plates subject to travelling load. Miscellaneous results

The steady-state response of a free and infinite Timoshenko beam is specified analytically in terms of non-dimensional displacements and stresses. The beam is supposed loaded by a travelling concentrated force or a moving step load. By a validated explicit numerical calculation, it is shown how a load travelling on a beam at constant velocity, from defined time and abscissa, generates a response which evolves towards the steady-state solution for a part, and towards a quantified transient solution for another part. Asymptotic values are given for the transient displacements and stresses according to the time and the speed of the loading. The solution is also found for a plate subject to a pressure, which spreads respecting the cylindrical symmetry. It is possible to identify in the response a part which follows the pressure front, and which is comparable with the steady-state response of a beam, and another transient part, which generates displacements and stresses with a much less oscillating character. An asymptotic solution is also presented for the plate.The whole series of the results makes it possible to better understand qualitatively the beginning of the transient response of a beam or of a plate to a moving load, and also makes it possible to estimate the stresses and displacements without needing specialised numerical codes.     

Single-strand strainwire technique: Comparison with existing methods and a proposed photostrain technique

This paper is the third of three papers evaluating a refined internal strainwire technique. This final paper evaluates the technique by comparing it with two elastic solutions, with a photoelastic solution, and with a new proposed photostrain technique. The problem chosen as the basis of comparison was a plane-stress problem of a plate with a circular hole under uniform tension. The proposed technique is experimental in nature and combines parts of the results of a photoelastic solution with those yielded by a three-wire internal strain-gage-rosette analysis to completely fix the state of stress in the model. The scientific techniques used to compare the three-wire strain technique and photostrain technique are as follows: two elastic solutions, one evaluated at a point and one arrived at by integrating the stress functions over a finite length; a finite-element solution; a photoelastic analysis using the shear-difference technique to separate the principal stresses; and a three-wire-rosette analysis. A comparison is made of the values of principal stresses yielded by these methods.     

Effect of boundaries of various shapes on vortex dynamics

The motion of a vortex near a boundary of arbitrary shape is considered within the framework of a two-dimensional problem. Integrable differential equations of motion are obtained. Two forms of the algebraic equation of the vortex trajectories are derived. Examples of vortex motion near a straight-line boundary, in a channel, in an angular domain, in the neighborhood of a flat edge, in a round basin, and near a parabolic boundary.     

Asymptotic solutions by the successive disordering method

We develop the periodic componentmethod [1] and represent the solution of a stochastic boundary value elasticity problem for a random quasiperiodic structure with a given disordering degree of inclusions in the matrix via the deviations from the corresponding solution for a random structure with a smaller disordering degree. An example in which the tensor of elastic properties of a composite is calculated is used to illustrate the asymptotic and differential approaches of the successive disordering method. The asymptotic approach permits representing the quasiperiodic structure with a given chaos coefficient and the desired tensor of effective elastic properties as a result of small successive disordering of an originally ideally periodic structure of a composite with known tensor of elastic properties. In the differential approach, a differential equation is obtained for the tensor of effective elastic properties as a function of the chaos coefficient. Its solution coincides with the solution provided by the asymptotic approach. The solution is generalized to the case of piezoactive composites, and a numerical analysis of the effective properties is performed for a PVF (polyvinylidene fluoride) piezoelectric with various quasiperiodic structures on the basis of the cubic structure with spherical inclusions of a high-module elastic material.     

等差线和等倾线的计算机识别及绘制

在普通光弹仪上配置光电耦合二极管信号采集装置和专用程序计算机,就构成了能实时地处理光弹图象的系统。CCPD-1024成线阵排列,能同时采集模型中一个截面上的光强信号。等色线或等倾线条纹的位置由计算机从光强分布图上读出。CCPD-1024对模型扫描时,计算机记录了各个截面上的等色线和等倾线位置的信息,并据此绘制出反映全场性分布的光弹性条纹图案。     

The extension and oscillation of a non-Hooke's law spring

We derive a wave equation for small-amplitude, undamped, extensional oscillation of a spring-mass system consisting of a mass suspended on a spring governed by a quadratic force-extension relationship. We justify this quadratic model using a Taylor series expansion of the general elasticity equations for a helical spring. Transformation of the equation of motion of the spring leads to a separable wave equation with the spacial component being a transformation of Bessel's equation. The model is successful in predicting static extension and period of oscillation of a helical wire spring for which the wave equation based on Hooke's law is inadequate.     

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.     

New methods in photoelasticity

The principle of polarization of scattered light is applied to determine the principal stresses in the interior of a model. On the basis of the theorem which states that “a series of birefringents is equivalent to a unique birefringent, followed by a medium endowed with rotational power,” it can be assumed that, if the characteristics of a series of birefringents are known, it is possible to find the characteristics of an interior section. The measurement of the characteristics of a birefringent (eventually following a medium endowed with rotational power) can be accomplished by means of the new methods, making use of a photomultiplier, a constant-speed rotating analyzer and a servomechanism These new methods of measurement are applicable to two-dimensional photoelasticity.