Joint Distribution of Eigenvalues of Linear Stochastic Systems
Adhikari, S.,
46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics
& Materials Conference, Austin, Texas, USA, April 2005.
Description of real-life engineering structural systems is
associated with some amount of uncertainty in specifying material
properties, geometric parameters, boundary conditions and applied
loads. In the context of structural dynamics it is necessary to
consider random eigenvalue problems in order to account for these
uncertainties. Current methods to deal with such problems are
dominated by approximate perturbation methods. Some exact methods
to obtain joint distribution of the natural frequencies are
reviewed and their applicability in the context of real-life
engineering problems are discussed. A new approach based on an
asymptotic approximation of multidimensional integrals is
proposed. A closed-form expression for general order joint moments
of arbitrary number of natural frequencies of linear stochastic
systems is derived. The proposed method does not employ the `small
randomness' assumption unusually used in perturbation based
methods. Joint distributions of the natural frequencies are
investigated using numerical examples and the results are compared
with Monte Carlo Simulation.
BiBTeX Entry
@INPROCEEDINGS{cp13,
AUTHOR={S. Adhikari},
TITLE={Joint distribution of eigenvalues of linear stochastic systems},
BOOKTITLE={46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics \& Materials Conference},
YEAR={2005},
Address={Austin, Texas, USA},
Month={April},
Note={}
}
by Sondipon Adhikari