Dynamic Behaviour Analysis of a Dual-Rotor System Using the Transfer Matrix Method

%$ &$ ' Represent transfer matrices, each of dimension (33 ! 33) Bearing matrix !B" ' Direct damping coefficients Cyy,Czz ' Cross coupled damping coefficients Cyz,Czy ' High and low rotor damping, respectively CH,CL ' E Modulus of elasticity ' e Eccentricity ' Field matrix !F" ' Overall field matrix !F" ' h Thickness of the disk ' Unit matrix !I" ' Transverse mass moment of inertia of the disk IT ' Polar mass moment of inertia of the disk IP ' Direct stiffnesses Kyy,Kzz ' Cross coupled stiffnesses Kyz,Kzy ' High and low rotor stiffness, respectively KH,KL ' l Sectional length ' Moments about yand z-axes, respectively My,Mz ' High and low rotor mass, respectively MH,ML ' m Mass of the element per unit length ' Mass of the shaft at bearing station mb ' Unbalance mass me ' Point matrix !P" ' Overall point matrix !P" ' Unbalance components Uy,Uz ' Shear force in yand z-directions, respectively Vy,Vz ' Deflection along yand z-axes, respectively v,w ' Fixed co-ordinate system X,Y,Z ' Rotating co-ordinate system X ,Y ,Z ' Modified State vector at any station S ' S OA, S OB S OC, Z OD #$