Equations of motion of the system “structure – reactive vibration dampener”

Abstract

The problem of damping vibrations of a mechanical system under seismic influences is considered. The construction of a mathematical model of the motion of a mechanical system with kinematic excitation of vibrations and simultaneous operation of a reactive damper is given. Transformations of differential equations of motion based on disturbing forces from a seismogram and damping action are shown. It is assumed that the jet extinguisher works constantly, changing the direction of the pulse depending on the sign of the speed of movement of the unit of its installation. The solution of the system of differential equations of motion is given. These transformations help to model more clearly the task of damping vibrations of mechanical systems during seismic disturbances