Moscow University Mechanics Bulletin最新文献

A basic model of a cylindrical quasi-force-free solenoid for the generation of strong and superstrong magnetic fields is considered in this paper for the resulting stress-strain state under the influence of current and magnetic induction. For a single-layer model, the parameterization problem satisfying the local Maxwell equations for the magnetic quantities in poloidal and toroidal directions has been solved. Analytical minimization problem of the integral radial component of the Lorentz mechanical force through conductor thickness is performed by taking into account the introduced parameterization of the system. In the formulation of the linear elasticity theory, the quasi-static axisymmetric problem of mechanics of a deformable solid under the action of a volumetric radial force is considered analytically. Taking into account the introduced parameterization, the optimal induction ratio in the conductor from the point of view of minimizing the maximum value of the von Mises stress normalized to magnetic pressure mechanical stress is found.

To solve the problem of rescuing a multilegged robot from an emergency upside-down position, an original method is used to find optimal control of the oscillation amplitude in the vicinity of the equilibrium position for a scleronomic mechanical system with an underactuated one oscillatory degree of freedom. The control is implemented by changing the position of a specially selected group of legs relative to the robot’s body. The effectiveness of the developed control algorithm is confirmed by the results of computer simulation of the full dynamics of the robot.

A model of the afferent primary neuron in the form of the Hodgkin–Huxley equations modified by Aleksandrov–Soto to third-order model and two simplified second-order models is under consideration. Stationary solutions of these models, periodic solutions, stationary solutions attraction regions, and bistability intervals are compared. It is concluded that the simplified model with a functional representation of the inactivation parameter better approximates the full third-order model.

We consider the inverse problem of bending an elastic circular plate when it is necessary to determine the values of the forces acting at some points and causing a given approximately values of deflection at that points.

For the case of a simplified plane stress state and plane deformation trajectories, the constitutive relations between stresses and strains beyond the elastic limit in derivatives with respect to the parameter of tracing the loading process are obtained. The necessity of taking into account the sign of the approach angle between the tangent to the strain trajectory and the stress vector in the constitutive relations is shown.

The article considers the interaction of two spherical bodies made of an anisotropic magnetizable material in an applied uniform magnetic field. The force acting on one of these bodies from the nonuniform magnetic field induced by the other body is obtained and investigated analytically. It is shown that this force can be represented as the force of interaction of two dipoles with special magnetic moments. Calculations of the magnetic force values for different directions of the body’s anisotropy vectors and the magnetic field are made. A significant effect of anisotropy on the magnitude and direction of the magnetic force between the bodies is shown.

Comparison of mass distributions of unevaporated fragments of meteoroids and asteroids disrupted in the atmosphere and fragments of bodies disrupted in impact experiments modeling the destruction of asteroids in outer space is carried out. For the analytical description of the distributions, a relation is used that is derived under the assumption that the distribution density of the number of fragments over masses obeys a power law. The ranges of variation in the power index are estimated in both cases. Approximate dependences of the power index on the specific impact energy (destruction in experiments) and on the number of fragments (destruction in the atmosphere) are obtained.

On the example of a mathematical model of a spring pendulum, the paper considers the algorithmic and computer implementation of the dynamic regularization method in application to the problem of restoring perturbations acting on periodic movements of the systems.

The application-oriented problem of two-stage compression of a plane layer (laminate), which is nonhomogeneous over the thickness and infinite in two directions, is considered. The constitutive relations of the layer material are consistent with the theory of small elastoplastic deformations. At the first step, one-dimensional compression takes place according to an active process described by a two-link polygonal line. At the second step, controlled unloading is carried out, as a result of which the thickness of the layer takes a given value at a given compression stress.

A method of approximate solution to the characteristic equation describing the heat dissipation during oscillations of bubbles in a liquid is presented in this article. An analytical formula for the damping decrement is derived.