On the validity of random matrix models in probabilistic structural dynamics
Adhikari, S.
2nd International Conference on Uncertainty in Structural Dynamics (USD 2009),
Sheffield, UK, June 15-17, 2009.
An accurate and efficient uncertainty quantification of the dynamic response of complex structural systems is crucial for their design and analysis. Among the many approaches proposed, the random matrix approach has received significant attention over the past decade. In this paper two new random matrix models, namely (a) inverted Wishart distribution and (b) generalized Wishart distribution have been proposed. The central aims behind the proposition of the new models are to (a) improve the accuracy of the statistical predictions, (b) simplify the analytical formulations and (c) improve computational efficiency. Identification of the parameters of the newly proposed random matrix models has been discussed. Closed-form expression have been derived using rigorous analytical approaches. It is considered that the dynamical system is proportionally damped and the mass and stiffness properties of the system are random. The newly proposed approaches are compared with the existing Wishart random matrix model. In total, five possible random matrix approaches are applied to the vibration problem of a cantilever plate with random properties. Relative merits and demerits of different random matrix formulations are discussed and based on extensive numerical studies recommendations for the best models for different scenarios have been outlined.
BiBTeX Entry
@INPROCEEDINGS{cp65,
AUTHOR={S. Adhikari},
TITLE={On the validity of random matrix models in probabilistic structural dynamics},
BOOKTITLE={2nd International Conference on Uncertainty in Structural Dynamics (USD)},
YEAR={2009},
page={281-290},
Address={Sheffield, UK},
Month={June}
}
by Sondipon Adhikari