Critically damped cantilever beam

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BeamStudent
I need to design a multi-layer cantilever beam with alternate visco-elastic and elastic layers. The goal is a beam with 18" unsupported and 4" glued to a firm support. In operation, this firm support will be vibrating in the audio range and the beam wants to damp out those vibrations and not pass them to the far end.

What FEM software deals with vibration analysis with material having elastic moduli expressed as complex numbers?

Has anybody done this sort of analysis and design?
 
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I can't make much sense of that problem description

Please start again and clearly describe what it is that you are trying to achieve .