Methodological aspects of modeling stochastic vibrodynamic effects


Аuthors

Gerasimchuk V. V.*, Efanov V. V., Kuznetsov D. A.**, Telepnev P. P.***

Lavochkin Research and Production Association, NPO Lavochkin, 24, Leningradskay str., Khimki, Moscow region, 141400, Russia

*e-mail: gerasimchuk@laspace.ru
**e-mail: kuznetsovda@laspace.ru
***e-mail: telepnev@laspace.ru

Abstract

A methodological apparatus for the formation of a time series of random broadband exposure corresponding to the requirements set in the form of spectral densities of vibration accelerations for various frequency ranges is presented. The operation of the rocket engine at the expiration of the gas jet causes stochastic vibrations of the structure in the broadband range, which can negatively affect the correct operation of the spacecraft equipment, which actualizes the task of studying the vibration background of sensitive, low-vibration-resistant equipment at the early stages of design. The simulation model of such a stochastic system is studied using the method of statistical computer modeling, using the limit theorems of probabilities as a theoretical basis, and the vibrodynamic effect of the spacecraft correction engine is considered as the implementation of an ergodic and stationary random function. Using the inverse Fourier transform for the spectral density graph, the corresponding correlation function was determined and a variant of the input dynamic effect was formed to simulate the vibration background of the structure. The problem of finding a forming filter as a linear system forming a random function from "white" noise is solved. A family of correlation functions is considered as a mathematical model for approximating the functions of stochastic vibrodynamic action. The forming filter of a stationary random function is reduced to a forming filter in the form of a system of second-order differential equations. When solving differential equations on a computer, the high-order equation was replaced by a system of first-order equations and numerical integration by the Euler method was performed. The generated random broadband vibrodynamic effect is investigated. It is established that its spectrum corresponds to the initial requirements set in the form of spectral densities of vibration accelerations for various frequency ranges. The discrepancy for the RMS values of vibration accelerations was 13-21%, depending on the frequency band. The considered aspects of modeling stochastic vibrodynamic effects can make it possible to correctly form a time series having characteristics that quantitatively and qualitatively correspond to the characteristics of the specified spectral density of random oscillations caused by the operation of the correction engine, which will allow us to investigate the effect of broadband vibration on sensitive and low-vibration-resistant spacecraft equipment at early design stages.

Keywords:

spacecraft, spectral density, correlation function, stochastic vibration, vibration acceleration

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