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Due to the rapid development in advanced complex machinery, the analysis of torsional vibrations for multi-junction, multi-branch systems is becoming a subject of increasing interest. Torsional vibration may occur within an operation range in a rotating system and cause a serious failure in the machine. This is the case when an excitating frequency gets close to the natural frequency of the system. In this paper, an efficient and accurate method has been developed to calculate torsional natural frequencies of complex rotating systems. The method is used in designing a drive-train of a chassis dynamometer simulating a multi-junction, multi-branch rotating system. Natural frequencies and mode shapes of the drive-train have been determined and used for further development in the components of the system.