A Measure of Non-proportional Damping
U Prells & MI Friswell (University of Wales Swansea)
Mechanical Systems and Signal Processing, Vol. 14, No. 2, March 2000, pp. 125-137
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 acuracy. 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 matrix 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 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.
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Link to paper using doi:10.1006/mssp.1999.1280
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