Analysis of the Operation of Kinematic Seismically Isolated Foundations Taking into Account the Vertical Component of the Seismic Impact

Abstract

The analysis of the work of kinematic foundations under seismic impact is carried out. In this case, the seismic action is set by two harmonic functions, one of which describes the vertical component of the movement of points on the day surface during an earthquake. The equation of motion of the considered seismically isolated supports is reduced to the form of the well-known Mathieu-Hill equation, the solutions of which can be both bounded and infinitely increasing functions. Thus, the possibility of occurrence in the considered system of seismic isolation of the phenomenon of parametric resonance has been proved and the parameters of the system and the parameters of seismic impact, on which the occurrence of this phenomenon depends, have been identified. The values of the damping parameters in the system and the amplitude of the vertical component of the seismic action, at which the movement of the kinematic supports is unstable, have been established. The construction of the zones of instability of oscillations of supports on the plane of change of the coefficients of the Mathieu-Hill equation is carried out. Also, the value of damping in the seismic isolation system is obtained, which is necessary to ensure the stability of motion under the combined action of the vertical and horizontal components of the seismic action.