In RF-/DYNAM Pro, it is possible to find the Rayleigh damping. How do I determine these coefficients and what is their application?

Answer

For some solution methods, the Rayleigh coefficients are absolutely necessary. Since only the Lehr's damping values are given in the literature, they have to be converted.

The following formula is used for converting Lehr's damping values into Rayleigh coefficients:

${\mathrm D}_{\mathrm r}\:=\:\frac12\;\left(\frac{\mathrm\alpha}{{\mathrm\omega}_{\mathrm r}}\;+\;\mathrm\beta\;{\mathrm\omega}_{\mathrm r}\right)$

Where α and β are the Rayleigh coefficients. It is necessary to set up a system of equations always containing the natural angular frequencies of the two most dominant mode shapes. In the case of these two mode shapes, the structure will then be damped with the specified damping value. All other mode shapes of the structure will have different damping values. These result from the curve displayed in Figure 01. The curve shows an example of the two natural angular frequencies of 10 and 20 rad/s and Lehr's damping of 0.015.


It is also possible to use the 'Calculate from Lehr's Damping ...' button to activate corresponding conversion tool. 

Keywords

Damping Rayleigh Lehr´s Time history

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