You cannot calculate damping. It is one of the system characteristic. It is the same as for mass or stiffness - you cannot calculate them either. You have to always measure them or represent them using other measured characteristics (density, Young's modulus etc.).  

Hi

I advice you to see these documents. You will find what you need.

Best regards

http://www.myphysicslab.com/spring1.html

http://physics.stackexchange.com/questions/166106/calculate-damping-constant-coefficient

https://www.google.fr/url?sa=t&rct=j&q=&esrc=s&source=web&cd=5&cad=rja&uact=8&ved=0ahUKEwjJ4bvloN7JAhVJORoKHTdWDuIQFghFMAQ&url=http%3A%2F%2Fwww.wceng-fea.com%2Fdil.pdf&usg=AFQjCNFcw7-cqfF6mN36fqZ12wYUBXMzoQ&sig2=VdnUeCuX9F-HOFjrYeLgMA&bvm=bv.110151844,d.d2s

Be aware that damping effect is most of the time underestimated. It depends if you want to simulate with models or estimate it from experimental tests.

The most easy way with a virtual model is to consider it as proportional to the mass and stiffness matrices ([C]=a[M]+b[K]), so that the system behaves with real valued eigenmodes. Thus, once you have modelled your mass and stiffness distribution, you can try to introduce damping without altering the system too much, just lowering part of the resonances in your mathematical model. A structural damping of few percentage points is already enough. If you have dampers that might be more tricky.

From tests, you can always try an estimation from free vibration decay in time domain (logarithmic decrement), or with forced vibration in frequency domain (half power band) approaches. This works well for 1 single dof system, whereas you need a complete modal analysis when you have multi dof systems.

Hope this can be a good start for your enquiry,

my regards,

Alessandro

Hi, maybe the authors of this article can help you 

http://hebergement.u-psud.fr/joovon/pdf/ApplPhysLett_102_022407.pdf

Hi maybe this note can be useful for you

http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/readings/supp_notes/MIT18_03S10_chapter_13.pdf