Elastic ties in the formation of the structure and dynamics of mechanical systems under conditions of vibrational loads of a forceful nature


Аuthors

Eliseev A. V.1*, Kuznetsov N. K.1**, Mironov A. S.2***

1. Irkutsk National Research Technical University, 83, Lermontov str., Irkutsk, 664074, Russia
2. Irkutsk State Transport University (IrGUPS), 15, Chernyshevsky str., Irkutsk, 664074, Russia

*e-mail: eavsh@ya.ru
**e-mail: knik@istu.edu
***e-mail: art.s.mironov@mail.ru

Abstract

A methodology for accounting for additional kinematic links in the problems of dynamic states estimation, correction and formation of the technological and transport machines actuators, operating under conditions of intensive loadings is being developed. The purpose of the study consists in developing a family of mathematical models in the form of mechanical oscillatory systems, in which the elastic elements stiffness varying would allow forming a plurality of dynamic states. Mechanical oscillatory systems formed by solid bodies interacting with account for elastic linkages are applied as computational schemes for vibration interactions of the technical objects elements. The problem of mechanical oscillatory systems mathematical models developing, enabling transformations in the form of joints representing the passage to the limit to the infinity of the elastic elements stiffness values to determine optimal structural and dynamic specifics of the engineering objects is being posed. The authors employ methods of theoretical mechanics, differential equations, vibration theory, integral equations and structural mathematical modeling methodology, based on comparing oscillatory systems to the dynamically equivalent structural diagrams of the automatic control systems. An approach to accounting for sequential joints in relative translational and rotational motion forms was developed. A theorem on the joining result independence from the order of sequential application of partial joints in the forms of translational and rotational relative movements was proven. The article demonstrates that the joints being considered as a process of the rigidity increasing while the two solids interaction, are being manifested by the unrestricted growth of the natural frequencies and frequencies of oscillations dynamic damping of the corresponding coordinates of the system. The methodology being developed for mathematical models constructing, is focused, in particular, on the design-and-technical solutions in the field of vibration testing equipment for the helicopter blade spars dynamic states assessing and forming.

Keywords:

structural mathematical modeling, mechanical oscillatory systems, transfer functions, natural frequencies, frequencies of dynamic vibration damping, stiffness coefficients, articulation of solids

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