Let's say you have string (e.g. guitar), which is fixed on both ends; and you want to place a discrete number of actuators to damp natural frequencies of it.
How can I find the best position to damp for example the first five modes?
Or the other way around: There is an actuator on a fixed position and you want to know the damping characteristic on an specific mode?
If it is a single mode you want to deal with, locate your actuators at locations of the anti-nodes (peaks) of that mode.
If you want to deal with more than one mose simultaneously, this an optimisation problem. You need to specify an objective function that contains a weighted sum of peak values of all the modes of concern.
If you google for 'optimal actuator placement', you should find papers on this topic. Even though these papers are not a string, the general principle should apply.
In addition, you can use dampers too. Again, it is an optimisation problem where you place them to deal with multiple modes simultaneously.
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