Moscow University Mechanics Bulletin最新文献

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.

The paper considers the problem of unsteady wave propagation in the cross section of an infinite hollow cylinder made of a viscoelastic functionally graded material with nonmonotonically varying properties along the radius. The cylinder is replaced by a piecewise-homogeneous one with a large number of coaxial homogeneous layers approximating the properties of the source material. Based on the previously constructed solution for a layered cylinder, wave processes in a cylinder made of a viscoelastic functionally graded material with different types of nonmonotonic inhomogeneities are studied.

The problem is considered for the indentation of a functionally graded strip by a rigid punch of finite dimension with a surface microrelief. Boundary variational formulations of the problem are given using the Poincaré–Steklov operator that maps contact stresses to displacements. To approximate this operator, the discrete Fourier transform is applied. A variational formulation of a boundary value problem for transforms of displacements is used to calculate a transfer function. Some regularities of contact interaction are established.

This paper uses the assumption on the smallness of deformations, flexural-torsional characteristics and angles of rotation of the shell elements, as well as the assumption on shell’s shallowness. Based on this assumption, a geometrically nonlinear moment-membrane theory of elastic shells is constructed with the help of the three-dimensional geometrically nonlinear moment theory of elasticity and by preserving only those nonlinear terms that come from normal displacement (deflection) and its derivatives. The constructed theory is interpreted as a continuum theory of the deformation behavior of flexible two-dimensional nanomaterials, in particular, of carbon nanotubes and graphene.

We investigate three-phase flows in porous media caused by carbon dioxide and water injection into an oil reservoir. We construct a numerical model of the flow complicated by the phase transitions between oil and gas and the hysteresis changes in the gas relative permeability. The model is coupled with the economic estimates of the profitability of oil recovery. Using a numerical model, we estimate the effect of the hysteresis on the most profitable strategies of the alternating injection of water and carbon dioxide. We show that the hysteresis behavior requires the injection of larger volumes of gas to maximize the profit.

In the paper we continue the research on the modified Hodgkin–Huxley model in the presence of random noise. It is shown that, adding a certain short-time stimulation current, a random noise of low amplitude does not prevent the system transition from the motion within a neighborhood of the small stable limit cycle (the mode ‘‘None’’ in accordance with the principal neurophysiological ‘‘All or none’’-law) to the motion along the big stable limit cycle called ‘‘duck nose’’ (the mode ‘‘All’’ respectively). At the same time, the high amplitude random noise can yield a series of transitions from one regime to the other and vice versa, even for a short-time stimulation. In the absence of stimulation and in the presence of high amplitude noise, such series of transitions were observed earlier during computer simulation.