No 1 (2024)

It is noted that, based on observations of fluctuations of the ice cover in natural conditions under the influence of moving loads, i. e., when excitation of flexural gravity waves (FGW), the latter behaves similarly to an elastic isotropic plate. On this basis, a new direction has been proposed in modeling some problems of deformation of the FGW ice cover on elastic films in conventional experimental basins. The possibility of this technology is confirmed by the results of comparing records of deformation by moving loads of an elastic model layer and a natural ice cover. Based on the theory of similarity and dimensions, dependencies were obtained for converting model test data to full scale. It is noted that the costs of conducting such model experiments are disproportionately less than the costs of conducting experiments in ice basins. Ice engineering problems are listed, in solving which the developed FGW modeling technique can be used.

The study of the “bifurcation memory” effect plays an important role in the study of dynamic features of real systems. Practical interest lies in studying the possibility of predicting a temporary decrease in response to control, which can significantly improve navigation safety. The effect of “bifurcation memory” is a temporary decrease in the phase velocity of the imaging point when passing through a certain area (“phase spot”) on the phase plane. A “phase spot” appears near the equilibrium state that disappeared during bifurcation. Over the almost half-century history of studying this dynamic feature, very few methods have been proposed that make it possible to unambiguously and with sufficient accuracy identify the “bifurcation memory” effect. This article proposes an improved phase plane method, which consists in constructing a phase velocity hodograph. A distinctive feature of the proposed method is not only that it surpasses previously developed methods in accuracy, but also covers both phase coordinates, and also gives an adequate result for any initial conditions. The method is quite universal and can be used to study the effect of “bifurcation memory” in various dynamic systems. Information about the boundary values of the parameter – the rudder angle, at which the effect of “bifurcation memory” begins (ends) to manifest itself can be used, for example, in the problem of optimizing the design of the hull and rudders or when creating control algorithms.

The problem of constructing the worst-case disturbance for an oscillator with quadratic damping is considered. The disturbance is carried out by an external force, which is applied to the oscillator body, does not change the direction of its action and has a given impulse (time integral). It is assumed that before the onset of the disturbance the oscillator is in a state of equilibrium. The worst disturbance is considered to be one in which the absolute value of the displacement of the oscillator body from the equilibrium position reaches its maximum value. In the class of disturbances of a rectangular profile with a given impulse, the worst disturbance and the corresponding largest displacement and the time to reach it were found, depending on the parameters of the oscillator.

Structural models for three-dimensional fiber-reinforced hybrid composite media and for particular two-dimensional problems have been developed. Using these models, one can calculate the surfaces and yield curves of the composition. The three-dimensional stress state in all components is taken into account. The materials of the composition components are homogeneous and anisotropic, their mechanical behavior is described by the associated flow law for a rigid-plastic body with general quadratic yield conditions. Components have different resistance to tension and compression. To perform constructions, stresses in components are presented in parametric form. The yield curves are calculated for a model in-plane reinforced composition of orthotropic phase materials. The influence of the direction of reinforcement, transverse normal stress and anisotropy parameters of the composition components on the shape and dimensions of the yield curves of the composite material under consideration has been studied. It has been shown that the anisotropy of the binder has a greater effect on the shape and dimensions of the yield surface of the composition than the anisotropy of the reinforcing fibers. It has been demonstrated that plastic flow in a reinforced medium is associated with the calculated yield curves (surfaces) of the composition. It is shown that in the presence of strongly pronounced anisotropy in the reinforcement, a structural model with a one-dimensional stress state in the fibers does not allow adequate calculation of the yield curves and surfaces of the composite medium.

The contact problem of steady sliding of a rigid cylinder over an elastic half-space in the presence of liquid menisci is considered, taking into account the hysteresis of the contact angle, which leads to different adhesion conditions at the entrance to the contact and at the exit from it. The problem was considered in a flat formulation and was solved by reducing it to the Riemann–Hilbert problem. An analytical expression for the contact pressure and a system of four equations for the numerical determination of the coordinates of the ends of the contact area and the meniscus zones are obtained. The calculation was carried out in the range of input parameters corresponding to the situation when a sliding cylinder models a separate protrusion of a rough surface. The distribution of contact pressure, the size of the contact area and its displacement relative to the axis of symmetry of the cylinder, the width of the menisci at the entrance to and exit from the contact, as well as the friction force caused by capillary adhesion were studied. It has been established, in particular, that the friction force significantly depends on the value of the contact angle hysteresis, and especially on the surface tension of the liquid, but weakly depends on the capillary pressure in the menisci, which, under conditions of thermodynamic equilibrium of the meniscus with the environment, is determined by the humidity of the surrounding air.

The problem on optimal rotation of a solid (spacecraft) from an arbitrary initial to a prescribed final angular position in the presence of restrictions on the control variables is studied. The turnaround time is set. To optimize the rotation control program, a combined quality criterion that reflects energy costs is used. The minimized functional combines in a given proportion the integral of the rotational energy and the contribution of control forces to the maneuver. Based on the Pontryagin’s maximum principle and quaternion models of controlled motion of a solid, an analytical solution of the problem has been obtained. The properties of optimal motion are revealed in analytical form. To construct an optimal rotation program, formalized equations and calculation formulas are written. Analytical equations and relations for finding optimal control are given. The key relations that determine the optimal values of the parameters of the rotation control algorithm are given. In addition, a constructive scheme for solving the boundary value problem of the maximum principle for arbitrary turning conditions (initial and final positions and moments of inertia of a solid) is described. For a dynamically symmetric solid, a closed-form solution for the reorientation problem is obtained. A numerical example and mathematical modeling results that confirm the practical feasibility of the developed method for controlling the orientation of a spacecraft are presented.

We consider the problem of controlling a spherical robot with a pendulum actuator rolling on a platform that is capable of moving translationally in the horizontal plane of absolute space. The spherical robot is subject to holonomic and nonholonomic constraints. Some point target moves at the level of the geometric center of the spherical robot and does not touch the moving platform itself. The motion program that allows the spherical robot to pursue a target is specified through two servo-constraints. The robot can follow a target from any position and with any initial conditions. Two ways to control this system in absolute space are proposed: by controlling the forced motion of the platform (the pendulum oscillates freely) and by controlling the torque of the pendulum (the platform is stationary or oscillates inconsistently with the spherical robot). The equations of motion of the system are constructed. In the case of free oscillations of the pendulum, the system of equations of motion has first integrals and, if necessary, can be reduced to a fixed level of these integrals. When a spherical robot moves in a straight line, for a system reduced to the level of integrals, phase curves, graphs of the distance from the geometric center of the spherical robot to the target, the trajectory of the selected platform point when controlling the platform, and the square of the control torque when controlling the pendulum drive are constructed. When the robot moves along a curved path, integration is carried out in the original variables. Graphs of the squares of the angular velocity of the pendulum and the spherical robot itself are constructed, as well as the trajectory of the robot’s motion in absolute space and on a moving platform. Numerical experiments were performed in the Maple software package.

The article proposes a spatial model of an exoskeleton for the human musculoskeletal system, represented by three movable links of variable length and two-point masses. The stiffness of the links is controlled by changing the voltage supplied to the magnetic rheological fluid, which fills sections of variable length. The model can be used to develop comfortable exoskeletons, the kinematic characteristics of which are close to the kinematic characteristics of the human musculoskeletal system. The model dynamics equations are constructed using local coordinate systems.

The required laws of change of generalized coordinates are specified by the equations of program connections that determine the dependence of differentiable periodic functions on time. Control moments and longitudinal forces are determined by methods of solving inverse dynamics problems and are realized by changing the magnetic field strengths, which affect the change in the stiffness of the magnetic-rheological fluid. The magnetic field strengths that control the stiffness of the link are implemented by step functions. An animation of the movement of the mechanism has been synthesized, showing the adequacy of the proposed modeling procedure. The connections of the links are modeled by joints and motors that implement the necessary rotational motion. The dynamics of the model is controlled by changing the lengths of the links and the angles between the links.