A comparative analysis of modal motions for the gyroscopic and non-gyroscopic two degree-of-freedom conservative systems. (22nd December 2016) - Yang, Xiao-Dong; An, Hua-Zhen; Qian, Ying-Jing; Zhang, Wei; Melnik, Roderick V.N.
Abstract: The synchronous in-unison motions in vibrational mechanics and the non-synchronous out-of-unison motions are the most frequently found periodic motions in every fields of science and everywhere in the universe. In contrast to the in-unison normal modes, the out-of-unison complex modes feature a π /2 phase difference. By the complex mode analysis we classify the out-of-unison planar motion into two types, gyroscopic motions and elliptic motions. It is found that the gyroscopic and elliptic motions have different characteristics for a two degree-of-freedom (2DOF) system. The gyroscopic motion involves two distinct frequencies with, respectively, two corresponding complex modes. However, the elliptic motion the nonlinear non-gyroscopic 2DOF system with repeated frequencies involves only single frequency with corresponding two complex modes. The study of the differences and similarities of the gyroscopic and elliptic modes sheds new light on the in-depth mechanism of the planar motions in the universe and the man-made engineering systems.