Dynamic Response Variability of General FE-Systems

Abstract

In this paper a general formulation is proposed for the dynamic analysis of stochastic structures with uncertain material properties. A straightforward generalization of the mean and variability response function concept is introduced leading to closed form integral expressions for the dynamic mean and variability response of statically indeterminate beam/frame structures as well as for more general stochastic finite element systems. As in the case of classical variability functions, these integral expressions involve the spectral density function of a stochastic field modeling the uncertain material properties and so-called dynamic mean and variability response functions, recently established for linear stochastic statically determinate single degree of freedom oscillators. A finite element method-based fast Monte Carlo simulation procedure is used for the accurate and efficient numerical evaluation of these functions. Numerical examples are provided including a statically indeterminate beam/frame structure and a plane stress problem. The dynamic mean and variability response functions can be used consequently to perform sensitivity/parametric analyses with respect to various probabilistic characteristics involved in the problem (i.e., correlation distance, standard deviation) and to establish realizable upper bounds on the dynamic mean and variance of the response.