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Equivalent viscous damping ratio

Assuming sinusoidal response, such as

and, substituting into Equation 1, you get:

Equation 4

The equivalent viscous damping is thus

Equation 5

and if

Equation 5 can be rewritten as

Equation 6

We can thus calculate the equivalent viscous damping ratio as

Equation 7
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Modal hysteretic and viscous damping ratios

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Source: https://docs.sw.siemens.com/en-US/doc/289054037/PL20200601120302950.advanced/id631216 · retrieved 2026-07-17