2.10. Damping

Damping allows to account for energy dissipation, for example due to internal friction/hysteresis of the materials. It only has an effect in dynamic analysis.

damping
Figure 18. Screenshot of the damping dialog

Since modelling all the different forms of energy dissipation in a bow in an exact way would be too complex, the damping is reduced to two empirical values: The damping ratio of the Limbs and the damping ratio of the String.

The damping ratio characterizes how quickly oscillations decay over time. An oscillation with a damping ratio of 0% is undamped, it doesn’t dissipate any energy and just keeps going with a constant amplitude. The higher the damping ratio the faster the amplitudes decay over time, losing energy with each oscillation. Once the damping ratio reaches 100% there is no longer any oscillation (no overshoot), this is called critical damping. See Table 2 for a visual explanation of those three cases.

Table 2. Examples for different values of the damping ratio
Damping Amplitude

0%

damping ratio 00

10%

damping ratio 01

100%

damping ratio 10

Note
The damping ratios of a bow’s limbs and string are mostly empirical and there isn’t yet much practical experience. Realistic values are probably in the range of 1 - 10% though.
Note
In more technical terms, the limb’s damping ratio applies to its first eigenmode in unbraced state and the string’s damping ratio applies to its first eigenmode in longitudinal direction.