For the lumped mass model, the equa

For the lumped mass model, the equation of motion of
forced torsional vibrations is given by where M is the diagonal inertia matrix, and C and K are the
symmetric damping and stiffness matrices respectively. If
the marine propulsion shafting has a simple configuration
without any branches, the damping and stiffness matrixes are
tri-diagonal. For multi-branched systems, the damping and
stiffness elements can be defined according to the methods
given in [18]. The angular displacement and excitation torque
vectors are given by θ and t respectively. Detailed information on the Fourier analysis of the crankpin tangential force
and the method to establish the equation of motion can be
found in [7, 11, 19, 22].