Moscow University Mechanics Bulletin最新文献

Using the previously obtained equations of motion of thin couple stress elastic shells of constant thickness with an arbitrary smooth median surface, the corresponding equations for an isotropic couple stress circular cylindrical shell in the forces and displacements (kinematic parameters) are constructed, while natural kinematic and static boundary conditions are given at the end sections. As a result, twelve equations of motion and corresponding physical relations are obtained.

The paper presents a method for in-flight calibration of a strapdown airborne gravimeter. it is assumed that the aircraft trajectory includes repeated flight lines and the gravity disturbance at each repeated line is the same. Therefore, it can be excluded as an unknown variable from the error equations of gravimeter’s inertial measurement unit by considering the differences between the measurements at two repeated lines. The remaining unknown values in the equations are the gravimeter’s inertial measurement unit instrumental errors (calibration parameters), which are considered constant during the flight. In the work, these parameters are estimated using the least squares method.

A model of the afferent primary neuron in the form of the Hodgkin–Huxley equations modified by Aleksandrov–Soto is under consideration. It is shown that one of the model parameters (temperature) variation allows for a transition between the attraction areas of stationary and periodic solutions. It is concluded that the model under consideration can be used to describe the process of caloric vestibular stimulation.

Taking gravity force into account, the article researches the problem of dynamic drop levitation with a surface double electric layer charge in a vertical electric field. Basing on this problem generalization, the authors consider a new electrocapillary model variant of ball lightning in the kind of spherical Hicks vortex being in a state of quasi-zero gravity at the certain levitation height level and moving under the action of a tangent electric field under the thundercloud.

A mathematical model of the stress-strain state before the onset of high-temperature hydrogen corrosion of a steel hollow cylinder is proposed. Plane deformation of a cross section with cylindrical micropores around which local stresses arise is considered. A criterion is proposed in which the initiation of corrosion cracks is possible when the sum of the circumferential stress under the effect of hydrogen pressure inside the cylinder cavity and the circumferential local stress under the effect of methane pressure inside the micropore reaches the break creep strength.

A method of swinging of the six-legged robot to ensure its overturn from the upside-down position is proposed. As a support, we consider an inclined plane with a slight slope towards the flip, with a pit and optionally with a bump next to it. The support can be rotated sequentially around two different axes. It is shown that the overturn is possible with the help of cyclic movement of the group of legs if the body has an upper shell in the form of a truncated cylinder. The swinging is performed by the legs on the edge of the body opposite to the one through which the flip is to occur. An analytical study of the model problem was performed, along with a simulation of the full dynamics of the robot in contact with the support using the Universal Mechanism software package. Specifics of swinging due to the slope, the pit, and the bump are shown.

The durability for a trapezoidal axial loading cycle can be estimated using a model of scale-structural fatigue for a sinusoidal shape. For materials with frequency-dependent fatigue properties, the evaluation of the rectangular cycle (except for the instantaneous impulses) by the sinusoidal cycle goes into a safety margin. At the zero load, the absence of a rectangular cycle, the maximum stress, on average, is 5(%) lower (the durability is 2.5 times less) at the same number of cycles than that for a sinusoidal cycle and the loading period. The results are confirmed by experimental data on high- and very high fatigue of metals and alloys.

In this paper the motion of a spherical body with anisotropic magnetizable elastomer under the action of the magnetic field of an electromagnetic coil is studied experimentally and theoretically when the motion of the body is limited from below by an inclined plane. The dependences of the current in the coil on the angle of inclination of the plane, which separate the region in which the body either is at rest, or moves along an inclined plane, or first moves along an inclined plane and then breaks away from it, or immediately breaks away from the inclined plane are constructed experimentally. Based on the previously proposed mathematical model, which takes into account the interaction of the body (rolling, sliding) with the inclined plane and does not take into account the deformation of the body and surface roughness, similar dependences are calculated. The qualitative difference between the experiment and the theory proposed earlier is shown: in the experiment the body on the horizontal surface begins to move when the current in the coil reaches a certain value, while according to the previously proposed theory, the body begins to move at arbitrarily small currents. An improvement of the previously proposed theory is carried out: the moment of support reaction associated with the roughness of surfaces and the presence of a certain area of contact between the body and the plane is taken into account. The new model is shown to better describe the experimental results.

The paper considers the problems of motion of thin bodies in a viscous incompressible liquid. In the Stokes approximation, the equations of motion are linear. This assumption allows using the fundamental solutions to reduce the problem of motion of thin bodies of finite size to singular integral equations. A numerical method for solving the obtained integral equations for the three-dimensional motion of bodies int he form of a set of thin impermeable and permeable plates (not a direct boundary element method) is proposed. The solution to the problem in this method is obtained in the form of a finite series expansion according to the found basic functions. Using the fundamental solutions to the Stokes equations, the problem of three-dimensional motion of thin bodies in a viscous liquid is reduced to a system of singular integral equations. The program codes for solving the resulting system of singular integral equations are written. The program allows obtaining the velocity fields, stress components, vortex distribution, and forces and moments acting on the plates.

The paper discusses the challenges of inertial navigation in polar regions, where it is impossible to determine the longitude and true heading at the poles. To overcome this difficulty, it is proposed to use quasi-coordinates and quasi-attitude angles, as well as relevant quasi-ECEF and quasi-geodetic coordinate systems. It is proved that the quasi-geodetic (quasi-geocentric) coordinates, quasi-attitude angles, velocity of an object and inertial sensors readings can be simulated by using quasi-coordinates instead of traditional ones.