Mode Superposition Method

We know that in Dynamic Analysis , to solve the equations of the form:



[M]{D² X} +[C]{D¹X}+[K]{X} = {R} ---------------- EQ.1



Where [M], [C],[K] are square matrices of mass, damping and stiffness matrices respectively.



D is derivative wrt time, {X}, {R} are the column matrices of displacement, external load respectevily.



We
use either direct step by step integration method or mode superposition
method. Both of them have advantages one over the other. Say, I am
solving the set of equations using Mode Superposition Method. Here
using a transformation for {X} we convert the set equations into 'n'
number of individual equations of single degree of freedom each.
Earlier in the set of equations these equatione were coupled, now after
applying the transformation these equations got uncoupled and we could
get 'n' individual equations. Those equations are easy to solve and we
can proceed.



My question is, is it always possible to
decouple the EQ.1 into 'n' number of equations of single degree of
freedom. (I think it is not so). In what cases we cannot decouple the
EQ.1.( In that case nonlinearities come into picture I think) If we
cannot decouple the EQ.1, then who is the culprit? It is [C] or [K]. I
want to know the cases where we cannot decouple EQ.1 due to [K].



Any good references for this study? I checked in Bathe but I am not
satisfied with the information given in there. Any articles or link?



Please help................