Анализ динамики нелинейных моделей конструкций ракетно-космической техники при нестационарных случайных нагрузках

Abstract

In aerospace engineering, it is customary to employ stochastic analysis methods at the design stage to investigate how the mechanical system responds to random external forces. This is relevant due to high reliability requirements for spacecraft. We developed a method for probabilistic estimation of the dynamic properties of a structure subjected simultaneously to external (additive) and parametric (multiplicative) vibrations. An ordinary non-linear vector differential equation describes the vibrations in the elastic structure. Non-linear position and velocity properties of kinematic pairs may have cusps and discontinuities. We assume that the probabilistic dispersions of respective phase coordinates are close to the normal distribution of probability density. The initial non-linear vibration equations are statistically linearised. The system of differential equations is not rewritten in the canonical form, which means that it is possible to carry out the probabilistic analysis of the system for any external non-steady-state effect. The fundamental matrix of the linearised system is used to find the expected value vector and the correlation function matrix of the phase coordinate vector. The solution consists of a matrix integro-power series containing linear and quadratic terms. Using the method makes it possible to assess the contribution of each external force component to the total result. We consider an example of a non-linear system responding to a stepwise non-steady-state external influence.