Hi

I am not sure I understand your definition of non-classical but, here is how I would do it

• Use modal substructuring for your superstructure and apply your modal damping values.
• Model you isolation system, as appropriate, using dashpots and/or complex spring elements and add them to the model.
• Compute a new set of complex modes

If the above for some reason is too complex, a simpler approach is to use the modal strain energy method. Compute the modal strain for your superstructure (A) and the modal strain for your isolator system (B). Compute the system damping as

Eta_Total = Eta_A*%SE_A + Eta_B*%SE_B,

where %SE_X is the % of total modal strain energy for domain X and Eta_X is the structural loss factor for domain X.

If you are interested, you find some other ramblings on the topic of damping and isolation here

http://qringtech.com/2014/06/22/designed-damping-types-mechanisms-application-limitation/

http://qringtech.com/2014/01/28/need-to-know-about-vibration-isolation/

Sincerely

Claes

Hi,

Claes’s answer is correct. For details, if I’m facing this situation, I would,

1. Perform modal test on isolation system and your superstructure,

2. If all the resonance frequencies of isolation system are far from those of your superstructure, the effect of isolation can be ignored.

3. if that is not the case, modal synthesis technique should be used as follows

Step 1: List differential equations of structure and isolation under nodal coordinate system,

Step 2: Concerning the coordinates of a connecting-nodes-pair are equal, the unknown interaction forces between these nodes pairs can be eliminated using coordinate reduction,

Step 3: Transferring to substructure modal coordinate space, physical mass, damping and stiffness matrices will be transferred to modal mass, damping and stiffness matrices,

Step 4: Using eigenvalue decomposition to find the complex modal frequencies, damping factors and modal vectors of the system.

Dear Anastasia,

I'm not sure what you are going to do with the damping matrix of the isolated structure. I assume you were trying to construct the equation of motion of the isolated structure. I made a short derivation with substructure method. Please take a look at the attachment. 

Thank you all very much for your valuable input !

Use modal substructuring for your superstructure and apply your modal damping values.

Model you isolation system, as appropriate, using dashpots and/or complex spring elements and add them to the model.

Compute a new set of complex modes

If the above for some reason is too complex, a simpler approach is to use the modal strain energy method. Compute the modal strain for your superstructure (A) and the modal strain for your isolator system (B). Compute the system damping as

Eta_Total = Eta_A*%SE_A + Eta_B*%SE_B,

where %SE_X is the % of total modal strain energy for domain X and Eta_X is the structural loss factor for domain X.

If you are interested, you find some other ramblings on the topic of damping and isolation here