The process of suppressing transverse vibrations of an elastic rod spinning in a horizontal plane and fixed at one of its ends is studied. It is supposed that the rod spins around the vertical axis at a constant angular velocity and performs transverse vibrations in the vertical plane, the vibrations are assumed small in amplitude. Transverse vibrations of the spinning rod are performed under external mechanical action. Lateral vibrations are described by the displacement function and considered in a rotating plane by using the classical beam model. The necessary conditions of optimality are derived and applied for suppressing elastic vibrations on a finite time-interval. The problem of optimal suppression of lateral vibrations caused by initial disturbances is formulated as a variational problem with constraints that take into account the suppressing effects on the rod. The limiting restrictions are presented in the form of inequalities. With the introduction of an additional variable, these restrictions are reduced to standard integral equality, while taking into account the energy constraints imposed on the control actions. The proposed iterative algorithm for solving the formulated problem is a numerical-analytical algorithm and consists in minimizing the quadratic quality criterion. This criterion characterizes the vibration suppression process and allows the implementation of improving variations. As a result of the operations carried out, the dependence of the vibration suppression process on the determining parameters, such as the angular velocity of rotation, the isoperimetric energy constant, and the length of the considered process of vibration suppression in time, has been clarified. An example that illustrates the implementation of the proposed algorithm and shows the effectiveness of this method for suppressing lateral vibrations is given.
An experimental study of the process of perforation of plates made of brittle materials by rigid strikers has been carried out. The strikers were accelerated to the required speed with a pneumatic gun. Both homogeneous plates and obstacles from several plates glued together, put together without gluing, or spaced relative to each other were considered as targets. The results of experiments on the perforation of plexiglass plates by rigid spherical bodies at impact velocities of 100–200 m/s are presented. Qualitative features of the fracture at different velocities of impact are revealed. For the samples considered, it was found that spaced plates reduce the velocity of the striker during penetration more effectively than the same plates putted together. A set of experiments were also carried out on perforation of two combined plates made of various brittle materials: plexiglass, ceramics, artificial stone (polyacryl, quartz) by a rigid spherical striker for a velocity range of 200–350 m/s. For each considered combination of plates, a ballistic limit (ballistic limit velocity, BLV, at which the striker penetrates the obstacle with zero exit speed) was experimentally established, which characterizes the protective properties of the barrier. The effect on the ballistic limit of the order of the layers was studied. As a result, it was found that for all selected pairs of materials, a larger ballistic limit was achieved when a less dense and less brittle plexiglass layer was located behind a denser plate (made of ceramic or artificial polyacrylic or quartz stone). The reverse order of the layers led to a decrease in the ballistic limit in all cases. Photographs illustrating the nature of the destruction of the plates are presented.
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