Appropriation Effects in the Estimation of Modal Damping

Damping presents one of the most important physical aspects to model and estimate, since it plays a large role in determining the performance of a dynamic system and the amplitude of vibrations. The present study employs the modal strain energy method to estimate the modal damping associated with the localized dissipative interfaces of a global linear structure. This method is accurate in the case of proportional or classical damping model. But in the real case when modes are coupled with damping due to the localization of the dissipation, as in the case of most assembled structures, this method may present significant errors. In this paper an appropriation method is proposed and associated to the modal strain energy method in order to get a good estimation of the modal damping. The impact of appropriation on the modal damping estimation in the case of non-proportional viscous damping model is studied for a multi-degree of freedom system. Results are compared with the reference one obtained by the state space method. Simulated academic examples, where accurate estimations of the exact solutions are available, will be used to illustrate the methodology and to explore the potential difficulties that may arise in more complex industrial applications.