Random Matrix Theory for Stochastic Structural Dynamics
Adhikari, S.
6th International Congress on Industrial and Applied Mathematics (ICIAM 2007),
Zurich, Switzerland, July 2007.
Uncertainties need to be taken into account for credible results
from high fidelity, physics and engineering-based numerical
simulations. As a result, the quantification and propagation of
uncertainties play a crucial role in today's predictive
engineering science. Uncertainties can be broadly divided into
parametric uncertainty (inherent variability/data
uncertainty) and nonparametric uncertainty (lack of
knowledge/model uncertainty). Within the past three decades the
deterministic finite element method has been generalized to
consider parametric uncertainties in a systematic manner by means
of the Stochastic Finite Element Method (SFEM). In the context
structural dynamics, using SFEM one usually obtains the random
mass, stiffness and damping matrices. More recently a systematic
approach to model nonparametric uncertainty is proposed. Using
this method one can obtain the probability density function of the
system matrices. Therefore, both parametric and nonparametric
uncertainty modelling lead to matrix variate distributions
describing the system matrices of a linear dynamic system. In this
paper it is first proved that both parametric and non-parametric
uncertainty can be modelled using a unified matrix variate
distribution (similar to a noncentral Wishart distribution).
Parametric and nonparametric uncertainty models can be identified
as special cases of this general distribution. Once the random
system matrices are `known' via this distribution, using the
random matrix theory exact analytical methods have been proposed
for the solution of a set of random algebraic equations
(K y = f) and the random eigenvalue
problem (K fj = lj M fj).
BiBTeX Entry
@INPROCEEDINGS{cp41,
AUTHOR={S. Adhikari},
TITLE={Random matrix theory for stochastic structural dynamics},
BOOKTITLE={6th International Congress on Industrial and Applied Mathematics (ICIAM 2007)},
YEAR={2007},
Address={Zurich, Switzerland},
Month={July},
Note={}
}
by Sondipon Adhikari