Can anyone please tell me how should I optimize a geometry for damping issues ?
Consider a laminated composite beam with a SMA thin film in the middle. And let's think the beam is vibrating in it's first mode.
I am about to optimize the shape of SMA thin film , in order to reduce the mass but yet have enough damping.
does any function exists which define the dissipated energy through the beam ?
As a rule of thumb, add damping material where the curvature is higher and save weight everywhere else. If needed, use this as a first solution for an optimization algorithm.
For the beam, the below is similar to what is suggested by A.M.R. Ribeiro. In my answer, I assume you will be using Finite Element analysis.
If you compute modal strain energy, you do not need to visually inspect how your structure is vibrating, i.e.you get a procedure you can use for optimization. You can usually compute also a % of total modal strain energy (%SE).
Concentrate your damping material into regions with high %SE.
The effect of the damping material can be assessed by computing complex modes or by the modal strain energy approach, where the total modal loss factor is assessed as Eta_total = sum(Eta_j*%SE_j), where Eta_total is the loss factor for a single mode, Eta_j is the damping loss factor for region j and %SE_j is the % of modal strain energy for region j. Note that your film would have to be modelled as a separate layer when using the modal strain energy approach.
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