Numerical free vibration analysis of multi shaft-disc systems

As it is known, multi shaft-disc systems are subjected to the bending, axialand torsional effects under static/dynamic forces. Among those, the shearing stressesdue to the torsional moment are known as the most dangerous stresses on rotatingshafts. Therefore, free or forced torsional vibration analysis of rotating shafts is ofutmost importance in the dynamic design stage. The torsional vibration analysis maybe carried out by both numerical and analytical methods such as the transfer matrixmethod, the finite element method and Holzer method.In this study, the numerical free vibration analysis of multi shaft-disc systemsis studied. A Fortran code is developed for the undamped free vibration analysis ofthe simple/branched shaft-discs systems based on the lumped-parameter model withthe help of the transfer matrix method. For the same purpose, software packageANSYS is also used to perform the finite element analysis. The results obtained fromboth the transfer matrix and finite element methods are compared with thoseavailable in the literature. After verification of the present results, a parametric studyis performed to investigate the effects of variation of the number of discs, thetorsional rigidity of shafts, inertia of the discs, the mass of the shaft and the boundaryconditions on the first three natural frequencies. Parametric results are given ingraphical forms. The mode shapes are also presented.Keywords: Shaft-Disc, Free Vibration, Transfer Matrix, Natural Frequency,Torsional Vibration.