Modal hysteretic and viscous damping ratios

Let

be the modal hysteretic and modal viscous damping ratios for the r-th normal modes.

The damping effects can be written into equations of motion (in the modal space) as

	Equation 1

where

mr	= modal mass of the r-th mode
kr	= modal stiffness of the r-th mode
	= modal displacement
	= modal velocity
	= modal acceleration
Cc	= critical damping of the r-th mode
	=

Therefore, the modal viscous and modal hysteretic dampings are defined as

	Equation 2

and

	Equation 3

Look up more details

Equivalent viscous damping ratio

Rayleigh's damping method

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Modal hysteretic and viscous damping ratios , Simcenter 3D 2021.1 Series

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