Damping modelling using generalized proportional damping

Proportional damping is the most common approach to model dissipative forces in complex engineering structures and it has been used in various dynamic problems for more than 10 decades. One of the main limitation of the mass and stiffness proportional damping approximation comes from the fact that the arbitrary variation of damping factors with respect to vibration frequency cannot be modelled accurately by using this approach. Experimental results, however, suggest that damping factors can vary with frequency. In this paper a new generalized proportional damping model is proposed in order to capture the frequency-variation of the damping factors accurately. A simple identification method is proposed to obtain the damping matrix using the generalized proportional damping model. The proposed method requires only the measurements of natural frequencies and modal damping factors. Based on the proposed damping identification method, a general approach for modelling of damping in complex systems has been proposed. Examples are provided to illustrate the proposed method.