Random eigenvalue problems for large systems

摘要

The inherent uncertainties in geometry, material properties, etc. of engineering structures can be represented by stochastic models, where the parameters are described by probabilistic laws. Results from any analysis based on stochastic models inherit probabilistic information as well, which can be used e.g. for reliability analysis. Particularly in linear dynamics of structures the calculation and analysis of random eigenvalues and eigenvectors is crucial. A quite versatile, however computationally intensive way to analyze such systems is direct Monte Carlo simulation. In this paper procedures are shown, which allow a significant reduction of computational efforts of the simulation using a subspace iteration scheme with "optimally" selected start-vectors. As the subspace iteration procedure, although quite accurate, requires a factorization of the stiffness matrix, as an alternative, a procedure based on component mode synthesis is suggested.