Damping Model Uncertainty in Structural Dynamics
Adhikari, S.,
International Conference on Noise and Vibration Engineering (ISMA2006),
Leuven, Belgium, 2006.
Uncertainties are unavoidable in the description of real-life
engineering systems. The quantification of uncertainties plays a
crucial role in establishing the credibility of a numerical model.
Uncertainties can be broadly divided into two categories. The
first type is due to the inherent variability in the system
parameters. This type of uncertainty is often referred to
as aleatoric uncertainty. If enough samples are present, it
is possible to characterize the variability using well established
statistical methods and consequently the probably density
functions (pdf) of the parameters can be obtained. The second type
of uncertainty is due to the lack of knowledge regarding a system,
often referred to as epistemic uncertainty or model
uncertainty. This kind of uncertainty generally arise in the
modelling of complex physical phenomenon such as damping.
Quantification of uncertainties associated with the damping forces
is difficult because, unlike inertia and stiffness forces, it is
not in general clear what are the state variables that
govern the damping forces. The most common approach is to use
`viscous damping' where the instantaneous generalized velocities
are the only relevant state variables. Several studies exist where
viscous damping coefficients are assumed to be random variables.
Considering randomness in the viscous damping parameters will
however not address the fundamental uncertainty that arises
due to the use of viscous damping model itself. Viscous damping by
no means the only damping model within the scope of linear
analysis. Any model which makes the energy dissipation functional
non-negative is a possible candidate for a valid damping model.
Therefore, to avoid any `model biases', in this study we have used
possibly the most general linear damping model[1, 2]
given by
|
F |
d(t) = |
ó
õ |
|
G (t,t) u(t) d t
(1) |
This paper is devoted to quantify uncertainty associated with the
use of the general damping model (not only the model parameters).
Two approaches, based on parametric and non-parametric methods are
developed. In the first approach, different equivalent functional
forms of G (t,t) are derived and their parameters are
selected. The collection of these different equivalent functional
forms are then assumed to form the random sample space. Under
these settings, the selection of any one model (such as the
viscous model) can be regarded as a random event in the sample
space of the admissible functions. In the second approach G
(t,t) is considered to be a matrix variate random process
whose distribution is obtained using the maximum entropy
principle[3, 4]. The results obtained from the
parametric and non-parametric methods are compared using
large-scale engineering dynamic problems.
References
-
[1]
-
Adhikari, S., ``Dynamics of non-viscously damped linear systems,'' ASCE Journal of Engineering Mechanics, Vol. 128, No. 3, March 2002,
pp. 328--339.
- [2]
-
Wagner, N. and Adhikari, S., ``Symmetric state-space formulation for a
class of non-viscously damped systems,'' AIAA Journal, Vol. 41, No. 5,
2003, pp. 951--956.
- [3]
-
Soize, C., ``A nonparametric model of random uncertainties for reduced
matrix models in structural dynamics,'' Probabilistic Engineering
Mechanics, Vol. 15, 2000, pp. 277--294.
- [4]
-
Soize, C., ``Maximum entropy approach for modeling random uncertainties
in transient elastodynamics,'' Journal of the Acoustical Society of
America, Vol. 109, No. 5, May 2001, pp. 1979--1996.
BiBTeX Entry
@INPROCEEDINGS{cp25,
AUTHOR={S. Adhikari},
TITLE={Damping model uncertainty in structural dynamics},
BOOKTITLE={International Conference on Noise and Vibration Engineering (ISMA2006)},
YEAR={2006},
Address={Leuven, Belgium},
Month={September},
Note={}
}
by Sondipon Adhikari