I've found a number of references stating that the damping matrix, |C|, is:
|C| = a0 |M| + a1 |K|
a0 = 4πζ/(T1 + T2)
a1 = T1*T2*ζ/π*(T1 + T2)
T1 = Period of oscillation of a target mode (usually the first mode)
T2 = Period of oscillation of another target mode
ζ = Viscous damping ratio
Q1) Am I right in thinking that |M| is the mass matrix and |K| is the stiffness matrix? Are these the same matrices from a standard Euler-Bernoulli beam-column 1D 4DOF FE model?
Q2) Also, a few sources I've read state that these values should be lumped at the nodes rather than distributed - is this correct? Distributed values give more representative results, so I'm quite surprised by this 'lumping' if that is the case.
Q3) Can someone explain T1 and T2 to me in more detail? What are the target modes? Is this like 1P and 3P when it comes to wind turbines?
Q4) Is the viscous damping ratio the same damping ratio from soil test data? If not, how is it calculated?
Q5) Finally, am I right in thinking that the |C| matrix will be added to the |M| AND |K| matrices from the remainder of the beam-column formulation?
Thanks in advance for any answers to some or all of the above questions.