Response variability of linear stochastic systems: A general solution using random matrix theory
Adhikari, S.
49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics
& Materials Conference,Schaumburg, IL, USA, April 2008.
Uncertainties need to be taken into account for credible
predictions of the dynamic response of complex structural systems.
Such uncertainties should include uncertainties in the system
parameters and those arising due to the modelling of a complex
system. In spite of extensive research over the past four decades
a general purpose probabilistic predictive code for real-life
structural dynamical systems is still not available. The reasons
behind this include: (a) the computational time can be
prohibitively high compared to a deterministic analysis, and (b)
the detailed and complete information regarding parametric and
model uncertainties are in general not available. In this paper a
Wishart random matrix based approach is proposed to address the
above two issues. Closed-form approximate analytical expressions
are developed to obtain the mean and covariance of the amplitude
of the frequency response function. The method utilizes analytical
inversion of the random dynamic stiffness matrix in the frequency
domain. The method is applied to vibration of a cantilever plate
with uncertainties. The dynamic response obtained using the
Wishart random matrix model agree well with the results obtained
from the stochastic finite element method.
BiBTeX Entry
@INPROCEEDINGS{cp44,
AUTHOR={S. Adhikari},
TITLE={Response variability of linear stochastic systems: \uppercase{a} general solution using random matrix theory},
BOOKTITLE={49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics \& Materials Conference},
YEAR={2008},
Address={Schaumburg, IL, USA},
Month={April},
Organization={AIAA},
Note={}
}
by Sondipon Adhikari