Moscow University Mechanics Bulletin最新文献

The coupled unsteady vibrations of an underground pipeline and elastic soil caused by an inclined fall of a plane seismic wave are studied. The coupled self-similar problems are formulated. An analytical solution of the external problem for the soil is obtained. This solution leads to a theoretical expression for the force of interaction between the pipeline and the soil, for which only empirical relations were previously available. Solutions for pipeline in supersonic and subsonic cases demonstrate significantly different behavior, which should be taken into account during earthquake resistance calculations.

The problem of motion of a rigid body with a fixed point in a free molecular flow of particles is considered. It is shown that the equations of motion of this body generalize the classical Euler–Poisson equations of motion of a heavy rigid body with a fixed point, and they are represented in the form of the classical Euler–Poisson equations in the case when the surface of the body in a flow of particles is a sphere. The existence of first integrals in the considered system is discussed.

One kind of a descent of a heavy finned body in resisting medium is considered. It is shown that the gliding mode is possible for which blades are located in a horizontal plane. The stability of such modes of gliding is studied. Trajectories of gliding are constructed for various initial speeds.

From the standpoint of the linearized stability theory, two eigenvalue problems for the Orr–Sommerfeld equation with two groups of boundary conditions having a certain mechanical meaning are considered. The stability parameter, which is a real part of the spectral parameter, is estimated on the basis of the integral relations method operating with quadratic functionals. The technique of the method involves the application of the Friedrichs inequality for various classes of complex-valued functions. Using the minimizing property of the first positive eigenvalues in the corresponding problems, the values of the constants in some Friedrichs inequalities are increased, which entails the strengthening of the stability sufficient integral estimates for plane-parallel shear flows in a plane layer.

The paper investigates the possibility of pulsed control of an asteroid approaching the Earth. The control scheme is fixed: this is a two-pulse flight with a gravitational maneuver near the Earth. The purpose of the first pulse is to correct the approach to the Earth. With the help of a gravitational maneuver, the asteroid is transferred to an osculating heliocentric orbit with a period close to the period of the Earth’s revolution around the Sun. The purpose of the second pulse is to transfer the asteroid to an osculating orbit, the period of rotation of which makes long-period fluctuations near the period of the Earth. An approximate method for evaluating the feasibility of a flight is proposed. Two examples are considered: the asteroids Apophis 2004 MN4 and Duende 2012 DA14.

A linear time-invariant completely controllable second-order system is considered; all the eigenvalues of this system are different and have negative real parts. The control is considered to be a scalar piecewise continuous function bounded in absolute value. The size of the reachable region is defined as the maximum absolute value of the coordinates of the points of the reachable region on the phase plane. A monotonic dependence of the size of the reachable region on the parameters of the system is shown.

A variant of the constitutive equations for describing complex loading processes with deformation trajectories of arbitrary geometry and dimension is considered. The vector constitutive equations and a new method of mathematical modeling the five-dimensional complex loading processes are obtained. This method is validated for two- and three-dimensional processes of constant curvature. The constitutive equations describe the stages of active loading and unloading. Explicit representations of the stress vector in an arbitrary deformation process are obtained. It is shown that the state parameters of the model in the five-dimensional deformation space are the four angles from the representation of the stress director vector in the Frenet frame, not directly, but in the form of four special functions whose form is known. These functions are called the Vasin functions. The process of complex loading along a three-dimensional helical trajectory of deformation is also considered, where, after diving and subsequent additional loading, the equations of the steady-state loading process are established. Similar results are obtained for five-dimensional helical deformation trajectories. Hence, for this class of processes there exists a correspondence between the geometries of the deformation and reaction paths in the form of a loading path.

The trigger factors of various nature that lead to the excitation of seismic and volcanic activity are briefly considered. Based on the solution of the generalized Boussinesq problem for half-space and typical pressure differences in medium-power typhoons, some estimates of the trigger effect of such differences on the provocation of earthquakes are given. The possible mechanisms of the trigger effect of typhoons on seismicity, before they move from the sea area to the land, are discussed.

The paper considers parametric oscillations of a classical system under nonconservative loading—a flexible pipeline with a flowing liquid. The parametric effect on the system is determined by the variability of the fluid flow rate. The stability of the rectilinear form of the pipeline equilibrium according to the Floquet–Lyapunov theory is investigated by the monodromy matrix method. The main focus is the study of the influence the characteristics of the parametric effect have on the stability boundary position of the pipeline, assuming a harmonic deviation of the flow rate from a certain constant, in particular, the amplitude and frequency.

The article examines how the filtration theory should look from the point of view of the modern theory of disperse systems, which is a nontrivial generalization of the classical theory of Brownian motion.