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Vol 73, No 4 (2018)
- Year: 2018
- Articles: 5
- URL: https://journals.rcsi.science/0027-1330/issue/view/10028
Article
Mechanical Systems with Rapidly Vibrating Constraints
Abstract
We consider a natural Lagrangian system on which an additional holonomic rheonomic constraint is imposed; the time dependence is included in this constraint by a parameter performing rapid periodic oscillations. Such a constraint is said to be a vibrating constraint. The equations of motion are obtained for a system with a vibrating constraint in the form of Hamilton’s equations. It is shown that the structure of the Hamiltonian of the system has a special form convenient for deriving the averaged equations. Usage of the averaging method allows us to obtain the limit equations of motion of the system as the frequency of vibrations tends to infinity and to prove the uniform convergence of the solutions of Hamilton’s equations to the solutions of the limit equations on a finite time interval. Some examples are discussed.
73-78
Diffraction of Plane Sound Waves on a Hard-Soft Half-Plane
Abstract
A simple method is proposed for solving the problems of diffraction of plane sound waves on a half-plane with different-type boundary conditions on its surfaces (the Neumann condition on one surface and the Dirichlet condition on the opposite surface). In contrast to existing techniques, the proposed method allows one to obtain analytical solutions valid near the half-plane edge and at far distances from the edge.
79-83
Reaction Forces under Static Loading of a Wheel Pair with Camber
Abstract
The static loading of a wheel pair with a deformable periphery is considered when the wheels are mounted on a common axle with a non-zero camber angle. A tire tread (protector) is modeled by a set of elastic rods interacting with the motion plane according to the dry friction law. The wheel camber effect on the slip in the contact zone and on the magnitude of reaction forces from the road is studied. An analog of the continuous model for a rod tread is discussed. The normal and tangential reaction forces are found depending on the vertical displacement of the center of the mechanical system under discussion.
84-90
Maintenance of Oscillations in Three-Dimensional Traveling Waves in Plane Poiseuille Flows
Abstract
Two solutions of three-dimensional Navier–Stokes equations are studied numerically. These solutions describe the fluid motion in a plane channel, are of the traveling-wave form, and are periodic in the streamwise and spanwise directions. It is shown that, in each solution, the oscillations arise as a result of linear instability in the streamwise averaged velocity field. This instability is due to the existence of streamwise streaks known as the regions where the velocity is higher or lower than the mean velocity. A mechanism for the maintenance of streamwise vortices causing the formation of streaks is revealed. The obtained results confirm and extend the existing knowledge about the mechanism for the formation of near-wall turbulent structures.
91-96
Parametrization of Saccade Trajectories
Abstract
The problem of description and classification of rapid eye movements called saccades is considered. It is well known that the saccades are of various types. A classification of saccades is proposed according to the presence and types of pre-saccadic and post-saccadic movements. An algorithm is developed to determine the parameters that can be used to formally assign the saccade to one of the given types.
97-100