Measure of non-proportional damping

Proportional or modal damping is often used as a simplified approach to model the effect of damping in linear vibrational mechanical systems. However, there are cases in which a general viscous damping is needed to simulate the dynamic of the system with sufficient accuracy. The scope of this paper is to investigate the difference between proportional and general viscous damping models. In case of general viscous damping, the modal marix of the underlying general eigenvalue problem depends on an orthonormal matrix, which represents the phase between different degrees of freedom of the model. It will be shown that in the case of proportional damping this orthogonal matrix becomes the identity matrix, which enables a real-valued normalisation of the modal matrix. Consequently, this orthogonal matrix can serve as a measure of the difference between proportional and general viscous damping models. Applications of the concept are demonstrated by two simulation examples. (C) 2000 Academic Press.