Equiv. stiffness matrix (Mech. circuit) for hydraulic flow circuit?

reach_spk

Dear All,

I need to represent a hydraulic system into an equivalent mechanical (spring-mass-damper) system.

But actually, they have reverse analogy in terms of flow resistance and stiffness..
meaning, Force=stiffness(k)*displacement; but Flowrate=(Pressure drop)/Flow resistance
i.e., for series and parallel combinations, k and flow resistances will have reverse analogy additions..

I formed a stiffness matrix using concept of FE global elemental matrices assembly.. (1 dof @ each element nodes) - by considering the flow resistances of hydraulic circuit as spring stiffness directly...

Similarly, i used the same matrix assembly process to determine flow coefficients matrix for hyd. circuit - but ending up with FLowrate = Pressure drop * Flow resistance (wrong relation)
ie. Ab=X instead of AX=b

So, how can i represent my flow matrix now?? Only after achieving this, I can proceed forward..
Also let me know that whether I can replace all co-efficients of stiffness matrix with 1/R terms..
Or should I have to take inverse of that matrix and perform the calculations..

Help me out in reaching the soln..
Ur ideas/suggestions r most welcome…

Thanks in advance!!!