Damping Modelling and Identification Using Generalized Proportional Damping

In spite of a large amount of research, the understanding of damping forces in vibrating structures is not well developed. A major reason for this is that, by contrast with inertia and stiffness forces, the physics behind the damping forces is in general not clear. As a consequence, modelling of damping from the first principle is difficult, if not impossible, for real-life engineering structures. The common approach is to use the proportional damping model where it is assumed that the damping matrix is proportional to mass and stiffness matrices. The main limitation of the proportional damping approximation comes from the fact that the 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. Examples are provided to illustrate the proposed method.