Measure of non-proportional damping

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