THE GENERALIZED PROBLEM OF A MECHANICAL IMPACT IN THE HERZ THEORY
Olshanskiy Vasiliy Pavlovich – Doctor of Physical and Mathematical Sciences, Professor, Kharkiv Petro Vasylenko National Technical University of Agriculture, Kharkov.
Olshanskiy Stanislav Vasilevich – PhD in Physics and Mathematics, Kharkiv Petro Vasylenko National Technical University of Agriculture, Kharkov; (e-mail: email@example.com).
The generalization of the well-known classical Hertz problem of the impact of two solids, taking into account contact deformations, was achieved by introducing into consideration the internal hysteresis energy losses, accompanying the dynamic deformation of bodies upon impact. In contrast to the classical version of the theory, in the generalized problem they do not coincide, but the graphs of the dependence of the impact force on the convergence of the centers of mass of the bodies at the stages of their compression and stretching differ. Therefore, the differential equations of motion at these stages have different values of the coefficients. They also correspond to different durations in time of the mentioned stages, and the duration of compression is longer than the duration of decompression. The first integrals of the nonlinear differential equations of motion are expressed in elementary functions and the second integrals are expressed through periodic Ateb-functions. Compact formulas have been derived for calculating the maxima: the convergence of the centers of mass of the bodies, the impact force, the dimensions of the contact area, the pressure at the center of this area. A compact expression was also obtained for the coefficient of speed recovery for a direct central impact, moreover, its value is less than unity and does not depend on the speed of the collision and the masses of the bodies subjected to the impact. This is consistent with the well-known Newton hypothesis, which is traditionally used in the theory of partially elastic stereomechanical shock.
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In June 1994 the 2nd International Scientific and Technical Conference "Application of vibrations for technological purposes" was organized on the basis of Vinnytsia State Agricultural Institute. Leading experts in this field, noting the significant contribution to the school of Vibration Engineering under the leadership of P. S. Bernyk, proposed to create a professional all-Ukrainian scientific and technical journal "Vibration in engineering and technology..The journal was foundedat Vinnytsia State Agricultural Institute and P.S. Bernyk was elected to be the chief editor .
For all these years (since 1994) theJournal "vibration in engineering and technology" published 94 issues wherestudy of vibration effects, the creation of progressive energy saving technologies and equipment for their implementation were highlighted.
Currently Kaletnik H.M PhD , professor, academician NAAS is the chief editor of the "Vibrations in engineering and Technology"
The journal "Vibration in Engineering and technology", which has no analogues on the territory of Ukraine, is well known abroad.