caa a22 4500 445361921 CHVBK 20180317142917.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s11071-011-9950-4 doi (NATIONALLICENCE)springer-10.1007/s11071-011-9950-4 A modified incremental harmonic balance method forrotary periodic motions [Elektronische Daten] [Chung-Jen Lu, Yu-Min Lin] The determination of periodic solutions is an essential step in the study of dynamic systems. If some of the generalized coordinates describing the configuration of a system are angular positions relative to certain reference axes, the associated periodic motions divide into two types: oscillatory and rotary periodic motions. For an oscillatory periodic motion, all the generalized coordinates are periodic in time. On the other hand, for a rotary periodic motion, some angular coordinates may have unbounded magnitude due to the persistent circulation about their pivots. In this case, although the behaviour of the system is periodic physically, those angular coordinates are not periodic in time. Although various effective methods have been developed for the determination of oscillatory periodic motion, the rotary periodic motion can only be determined by brute force integration. In this paper, the incremental harmonic balance (IHB) method is modified so that rotary periodic motions can be determined as well as oscillatory periodic motions in a unified formulation. This modified IHB method is applied to a practical device, a rotating disk equipped with a ball-type balancer, to show its effectiveness. Springer Science+Business Media B.V., 2011 Harmonic balance nationallicence Periodic motion nationallicence Unbalance vibration nationallicence Lu Chung-Jen Department of Mechanical Engineering, National Taiwan University, No. 1 Roosevelt Rd. Sec. 4, 10617, Taipei, Taiwan aut Lin Yu-Min Department of Mechanical Engineering, National Taiwan University, No. 1 Roosevelt Rd. Sec. 4, 10617, Taipei, Taiwan aut Nonlinear Dynamics Springer Netherlands 66/4(2011-12-01), 781-788 0924-090X 66:4<781 2011 66 11071 https://doi.org/10.1007/s11071-011-9950-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11071-011-9950-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lu Chung-Jen Department of Mechanical Engineering, National Taiwan University, No. 1 Roosevelt Rd. Sec. 4, 10617, Taipei, Taiwan aut NATIONALLICENCE 700 1- Lin Yu-Min Department of Mechanical Engineering, National Taiwan University, No. 1 Roosevelt Rd. Sec. 4, 10617, Taipei, Taiwan aut NATIONALLICENCE 773 0- Nonlinear Dynamics Springer Netherlands 66/4(2011-12-01), 781-788 0924-090X 66:4<781 2011 66 11071 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer