Moscow University Mechanics Bulletin最新文献

In this paper, a variational principle of Lagrange and the Ritz method with generalized reduced and selective integration for mixed piecewise polynomial functions are used to obtain a stiffness matrix and a system of linear algebraic equations for micropolar theory of elasticity. This approach is implemented for anisotropic, isotropic, and centrally symmetric material in case of nonisothermal process. The cube problem is considered. The performance for finite element with mixed piecewise polynomial functions is exposed.

We continue the systematic analytical study of the nonlinear Maxwell-type constitutive equation for shear flow of tixotropic viscoelastoplastic media formulated in the previous article. It accounts for interaction of deformation process and structure evolution, namely, the influence of the kinetics of formation and breakage of chain cross-links, agglomerations of molecules, and crystallites on viscosity and shear modulus and deformation influence on the kinetics. The constitutive equation is governed by an increasing material function and six positive parameters. Assuming that the stress is constant (in order to simulate creep conditions), we formulate the set of two nonlinear differential equations for two unknown functions (namely, strain and cross-links density) and obtain its exact general solution in explicit form. We examine the properties of creep curves generated by the model for arbitrary material function and material parameters and analyze dependence of creep curves and cross-links density on time, stress level, initial cross-links density, and material parameters governing the model. Thus, we prove that the model not only describes basic phenomena observed for simple shear flow of shear thinning fluids, but can simulate creep, relaxation, and other phenomena observed for solid bodies.

Capturing human movements and determining their features are often necessary in the development of devices worn by persons or used by them in daily work. In this regard, the problem of detecting the beginning of rotation seems to be relevant and has many applications in bionavigation and biomechanics. One of the main difficulties in these tasks is minimizing the delay in detecting the motion. In this paper the problem of detecting the head turn beginning by inertial sensors data fixed on it—three-axis accelerometer and CRS—is considered. The requirement to determine the head turn beginning appears when trying to solve the problem of supplementing vestibular information under special conditions, for example, to solve the problem of the vestibulo-sensory conflict that occurs in a state of weightlessness.

The problem of deceleration of a finned body in a homogeneous resistive medium is studied. The body is affected only by the medium. The plumage of the body consists of a single blade. It is shown that a circular kind trajectory of deceleration with somersaults is possible for blade profiles with both low and high aerodynamic quality. For airfoils with high aerodynamic quality, additional circular regimes of deceleration are possible that are in the style of a parachute.

The problem of the motion of a ball between two uniformly rotating horizontal planes with linear viscous friction is considered. Steady motions of the ball are found and the parameters of the system under which these motions are stable or unstable are indicated. It is shown that the equations of motion of a low-inertia ball have the form of Tikhonov’s equations with a small parameter as a coefficient at some derivatives. The dynamics of this ball on an arbitrary finite time interval in the limit as the central moment of inertia of the ball tends to zero is studied.

Using the bicycle model, the dynamics of a biaxial four-wheeled vehicle is studied at the initial stage of skidding, which develops as a result of slipping of the driving axis wheels. To describe the interaction of wheels with the reference plane, the Coulomb friction model, the lateral slip model, and the nonholonomic model are used. A model of the variable structure describing the stages of movement of the vehicle is constructed. Asymptotic methods and the phase plane method are used for the study.

In this paper, the motion of a spherical body with anisotropic magnetizable elastomer in a viscous liquid under the action of a magnetic field of the coil with current is investigated. A mathematical model of the movement of such a body is proposed taking into account various limiters of its movement. The case when the body is rigidly fixed at the end of the rod, which is pivotally fixed on the axis of the coil with current, is considered. And also the case when the movement of the body is limited from below by a horizontal surface and the body can roll or slide on this surface is presented. The trajectories of the body movement from the position on the axis of the coil when the magnetic field is turned on are constructed in the case when the anisotropy vector at the initial instance is not parallel to the vector of the magnetic field. In this case, an anisotropic body (unlike an isotropic one) can deviate from the axis of the coil. The deviation of the body from the axis of the coil is calculated for various parameters of the problem.

An analytical method for solving the wave equation describing the oscillations of systems with moving boundaries is considered. By changing the variables that stop the boundaries and leave the equation invariant, we reduce the original boundary value problem to a system of functional-difference equations, which can be solved using direct and inverse methods. An inverse method is described that allows approximating quite diverse laws of boundary motion by laws obtained from solving the inverse problem. New particular solutions are obtained for a fairly wide range of laws of boundary motion. A direct asymptotic method for the approximate solution of a functional equation is considered. The errors of the approximate method are estimated depending on the velocity of the boundary movement.

An approach to obtaining approximations and constructing a three-dimensional shell model of a filler layer based on the use of effective approximating functions used in two-dimensional models of bearing layers in the general case of irregular three-layer cylindrical shells, including those weakened by rectangular cutouts, is presented. The effective approximating functions of the displacements of the bearing layers are based on the initial approximation of deformations. As an example, studies of the influence of the angular dimension of rectangular cutouts on the stress and strain state of sandwich cylindrical shells are carried out for the first time.

This paper presents the results of three-dimensional computational modeling of processes in the combustion chamber of a hybrid solid-fuel engine. Polymethylmethacrylate was used as a solid fuel, and air was used as an oxidizer. In the model used, the heated oxidizer in gaseous form was fed into the combustion chamber at supersonic speed. As a result of the interaction of the oxidizer with the surface of the solid fuel, it begins to warm up and decompose with the release of flammable gases. The geometry of the combustion chamber and solid fuel was based on experimental work. The results of a series of calculations for various geometries of the combustion chamber were presented. The distribution of physical parameters corresponding to the diffusion mode of combustion was obtained.