Probabilistic model for non-proportional damping in structural dynamics

Damping in structural dynamics is an important source of uncertainty. Whereas it has a great influence in most of the systems, the nature of the dissipative phenomenon is seldom simple, and information regarding it is not necessarily straightforward. Usually, simplified damping models are employed to facilitate the analyses conducted in several systems. Maybe the most common approach is the Rayleigh proportional damping, as it preserves the modes from the undamped dynamical system. A generalization was introduced by Caughey and O'Kelly [8] , where this proportional damping condition could be achieved by power series of the generalized mass and stiffness matrices. Further on, Adhikari [1] proposed a methodology to adjust arbitrary damping curves into a proportional damping model, configuring another generalization of this set of models. While proportional damping models are practical, the presence of non-proportional damping encompasses a large por The complexity behind dissipative phenomenon is still a major source of uncertainty in structural dynamics. This phenomenon is usually simplified to a deterministic proportional damping, disregarding the effects of modal coupling in the analysis. In this work, a proba-bilistic model is developed for non-proportional damping by adding uncertainties globally in the damping operator. The two main hypotheses of the resulting random damping ma-trix are: (i) it is symmetric positive definite and (ii) it is expected to be diagonal dominant. Several analyses are conducted, comparing proportional and non-proportional models. In addition, experimental data are used in the identification procedure of the random model. The proposed probabilistic model might be employed to other matrices, if the fundamental hypotheses are respected. (c) 2021 Elsevier Ltd. All rights reserved.