Vol 63, No 7 (2018)

For the first time, the dynamic problem of plane-parallel rolling with the slip of an elastic cylinder along an elastic base of the same material is analyzed. The distribution of the normal and tangential stresses in the contact-interaction region consisting of relative slip and stick subregions corresponds to the solution of the quasi-static problem of the theory of elasticity. The solution obtained is compared with the solution of the problem of sliding of an absolutely rigid cylinder along an absolutely rigid plane with Amonton−Coulomb dry friction.

An algorithm for estimating the inhomogeneity of the microwave electromagnetic field is proposed for micro- and nano-heterogeneous media in a magnetic field. It is shown that the nonuniformity parameter for the microwave field in an artificial crystal containing ferrimagnetic particles depends significantly on the constant magnetic field, and the minimal value of the nonuniformity parameter corresponds approximately to the field of ferromagnetic resonance.

The dynamics of a double-link aerodynamic pendulum is considered. An airfoil-section blade is attached to the second pendulum link. The conditions whereby a spring mounted on the first pendulum link leads to the loss of stability of the equilibrium position, in which both links are directed along the incoming flow, have been derived. Experiments have been carried out in the wind tunnel of the Institute of Mechanics of the Moscow State University at various incoming flow speeds and blade positions. The experimental data agree qualitatively with the results of numerical simulations.

The highly reproducible effect of a giant (10 000-fold) increase in the electrical conductivity of a film sample of a high-resistivity MoS₂ semiconductor with a layered structure under continuous proton injection in dynamic equilibrium conditions is reported for the first time. The effect disappears when the process of proton injection is interrupted. The potential to control the composition and the properties of materials by doping them with charge carriers of different signs, masses, and energies (as a complement to traditional chemical doping) is noted.

A rigorous (inverse) hydromechanical solution of the new potential problem on the pulse punching of a plate adjacent to a rigid nondeformable medium based on the theory of the function of a complex variable is presented. An analytical relationship between the velocity-hodograph regions of the physical-flow region and the complex potential represented as a rectangle is obtained. An example of the calculation is given with determination of the plate-punching region boundaries and all the necessary hydrodynamic parameters of the potential flow in it.

The motion of a solid around a stationary point in a uniform gravity field is considered. The mass geometry of this body is such that it can perform regular precession around an axis inclined to a vertical (Grioli precession). The problem about the orbital stability of this precession is solved in the critical case of fourth-order resonance, when the terms to a power higher than the fourth with respect to perturbations (including the sixth-power terms) must be taken into account in the expansion of the Hamiltonian function.

For anisotropic elastic waveguides with cylindrical or periodic outlets to infinity, artificial integro-differential conditions are developed at the end face of a truncated waveguide, which simulate the Steklov–Poincaré operator for scalar problems. Asymptotically sharp error estimates are derived in the definition of both the elastic fields themselves in the waveguide and the corresponding scattering coefficients.