Modern machines and aerospace facilities are equipped with rather complex, multi-link high-level vibration protection systems. Therefore, it is of interest to carry out work on the formation of dynamic models of vibration-protective properties of the apparatus, taking into account the properties of their real design features. The plane-parallel motion of a viscoelastic suspended rigid body with an axis of symmetry and imitating the motion of the table of an electrodynamic stand is considered. In the calculated dynamic scheme, the action of the suspension membranes and the hanging shock absorber is represented as the action of some linear springs. It is assumed that a periodic perturbing force (the action of a pulsating magnetic field) directed vertically is applied at the body’s center of gravity. Nonlinear integro-differential equations of motion are compiled, in expansions of trigonometric functions and power series, only small second2 nd order are kept. The method of averaging is used to reduce to normal coordinates. The conditions for indirect excitation of axial lateral vibrations (torsional vibrations about the horizontal axis) under the stability of the parametric resonance of the vertical are obtained. Formulas providing the suspendet object are obtained.
Increased machine efficiency, increased speeds of working bodies, reduced material consumption, increased load, the need to ensure reliable operation of equipment and safe working conditions are the main factors, that determine attention to vibration protection problems. This constitutes the current trend in the modern dynamics of machines. In this work, we propose a method for the dynamic synthesis of dynamic vibration dampers of a viscoelastic mechanical system having the structure of several (two) bodies elastically attached to the object. The aim of the work is to develop methods of mathematical and computer modeling of the processes of dynamics of active and passive vibration protection systems, as well as to increase the efficiency of using passive and active vibration protection of objects. When developing a system for protecting radio-electronic devices (RED) at resonant frequencies, elements of the theory of automatic control and mathematical modeling were used. An algorithm for generating feedback signals for the information-measuring system for active control of vibration-protective radio-electronic devices is proposed. A method is developed for numerically - analytical study of oscillatory processes of nonlinear mechanical systems consisting of spatial rigid bodies interconnected by massless viscoelastic elements.
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