Response variability of viscoelastically damped systems

Adhikari, S. and Pascual, B.
International Conference on Mathematical Problems in Engineering, Aerospace and Sciences (ICNPAA 2008), Genoa, Italy, June 2008.

The characterization of energy dissipation or damping in complex vibrating structures such as aircrafts and helicopters is of fundamental importance. Noise and vibration are not only uncomfortable to the users of these complex dynamical systems, but also may lead to fatigue, fracture and even failure of such systems. Increasing use of composite structural materials, active control and health-monitoring systems in the industry requires the development of new reliable damping models and corresponding computational methods. During the design process of such damped dynamical systems, it is often required to make changes in the design parameters so that the design is optimal. This paper is aimed at developing computationally efficient and physically insightful approximate numerical methods for parametric sensitivity analysis of linear dynamical systems with viscoelastic damping. Frequency depended or non-viscous/viscoelastic damping can be incorporated in various ways. Here we use the Biot model which allows one to incorporate wide range of functions in the frequency domain by means of summation of simple 'pole residue forms'. Several authors have considered this model due to its simplicity and generality. Exact closed-form expressions are derived for the dynamic response sensitivities due to the changes in the system parameters for general forces and initial conditions. The response sensitivities in the frequency domain in turn are related to the sensitivities of eigensolutions of the system in the original space. Eigensolution sensitivity of the damped system are obtained approximately as functions of the undamped eigensolutions. This enables one to approximately calculate the dynamic response sensitivity of complex systems with viscoelastic damping by simple post-processing of the undamped eigensolutions. Suitable examples are given to illustrate the derived results.
BiBTeX Entry
@INPROCEEDINGS{cp51,
    AUTHOR={S. Adhikari and Blanca Pascual},
    TITLE={Response variability of viscoelastically damped systems},
    BOOKTITLE={International Conference on Mathematical Problems in Engineering ,Aerospace and Sciences (ICNPAA 2008)},
    YEAR={2008},
    Address={Genoa, Italy},
    Month={June}
}
by Sondipon Adhikari