Extended transfer matrix method with complex numbers for branched torsional systems

The extended transfer matrix method with complex numbers and the Newton-Raphson technique is used to analyze torsional vibration for branched systems. The relationship between the first station and the last station is established. Equivalent contact disks of the power train with a contact transfer matrix are used to simplify a branched torsional system into a single shaft system. This method reduces calculation of some elements in the complicated procedures of matrix multiplication. A system with three free-end boundaries is analyzed. The calculated results of the eigenvalues and eigenvectors of an undamped branched system are compared and show good agreement with the data obtained by the MATLAB software program. The eigensolutions of a damped branched system are calculated and the results are acceptable. Therefore, the methodology used is feasible for the torsional vibration analysis of damped branched systems.