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Symbolic computations in structural dynamics using stochastic second order perturbation method

Kamiński M.

Mechanics and Mechanical Engineering

2001

Vol. 5, nr 1

69-80

The main idea is to show the application of symbolic computations in analysis of engineering systems with random parameters. The general computational methodology is based on the stochastic second order perturbation method and its implementation in the mathematical package MAPLE. The entire approach is displayed on the example of a simple single degree of freedom dynamical system with random spring stiffness. The results of symbolic computations are derived numerically in the form of probabilistic moments of the structural response, computed for the whole analysis time domain. This methodology can be applied to all the engineering problems, where the response can be derived symbolically in the deterministic case, while input parameters of the system are random variables, fields or processes characterized by the probability density function (PDF) of any type.