Objectives. The article reflects the results of the numerical analysis of the earthquake-resistant building on kinematic supports. To this end, the problem is reduced to solving the nonlinear stochastic Cauchy problem. The solution is constructed by the method of successive approximations. The probabilistic characteristics of the oscillation of the building are determined without the use of linearization techniques. An algorithm for solving this problem, which allows to perform numerical experiments on a computer to study the operation of a earthquake-resistant building on kinematic sup-ports, is given.Method. The acceleration of the earth's surface during an earthquake is represented as a non-stationary random Gaussian process. This approach is now generally accepted and beyond doubt. The study of vibrations of the building on kinematic supports under the influence of strong earthquakes is reduced to the solution of the stochastic nonlinear Cauchy equation. This equation is solved by iteration. The acceleration of the earth's surface is a function of three random variables. The required probability is represented as a triple integral, which is calculated using a computer.Result. The basic information about the considered kinematic supports is given. The Cauchy problem is formulated for the case of oscillations of a earthquake-resistant building on kinematic supports under the influence of strong earthquakes. The algorithm allowing to solve this equation is described in detail. The probability of finding the movements of the building within certain limits is represented as a triple integral. The results of numerical experiments carried out on a computer are given. The corresponding graphs are constructed using real accelerograms of strong earthquakes that occurred in the cities of Taft (USA) and Gazli (Uzbekistan).Conclusion. This article describes the method of calculation of earthquake-resistant buildings on kinematic supports, using the data of real strong earthquakes. Based on the results of numerical experiments conducted on a computer, graphs of the reliability of seismic stability of the building in earthquakes. The constructed algorithm and the developed technique can be used in the calculation and design of earthquake-resistant buildings both on conventional supports and on kinematic supports.
