Mathematical Modeling of Vibration Dampers of Vibration-Insulated Structures

Abstract

Vibration dampers are installed on the machine foundations in order to reduce the vibration level. Such technological solutions are most expedient in the case of a harmonic load with a low instability of the vibration frequency. Unfortunately, dampers do not provide such a large reduction in the dynamic effect on the base, as vibration isolation, but in some cases their efficiency turns out to be quite sufficient with a relatively simple implementation and low manufacturing cost. The use of dynamic vibration dampers gives a great effect when an increased vibration of foundations occurs during the operation of equipment in metallurgical production, for example, when processing materials by pressure, reconstructing enterprises and replacing heavy equipment. During the operation of heavy forging equipment and manipulators for various purposes, the foundations of these devices can be considered as a rigid body. The model soil on which this foundation is installed can be considered a homogeneous elastic isotropic half-space. When calculating with such mathematical models, one can use solutions of the corresponding dynamic contact problems. A comparative analysis of the effectiveness of damping foundation vibrations using different foundation models, including the model of an elastic, homogeneous half-space and a system of semi-infinite rods, the modulus of elasticity of which increases with depth according to the quadratic law, shows a fairly close agreement.