Dynamic Analysis of Harmonically Excited Non-Linear Structure System Using Harmonic Balance Method


초록

An analytical method is presented for evaluation of the steady state periodic behavior of nonlinear structural systems. This method is based on the substructure synthesis formulation and a harmonic balance procedure, which is applied to the analysis of nonlinear responses. A complex nonlinear system is divided into substructures, of which equations are approximately transformed to modal coordinates including nonlinear term under the reasonable procedure. Then, the equations are synthesized into the overall system and the nonlinear solution for the system is obtained. Based on the harmonic balance method, the proposed procedure reduces the size of large degrees-of-freedom problem in the solving nonlinear equations. Feasibility and advantages of the proposed method are illustrated using the study of the nonlinear rotating machine system as a large mechanical structure system. Results obtained are reported to be an efficient approach with respect to nonlinear response prediction when compared with other conventional methods.

키워드

참고문헌

  1. Choi, Y., Noah, S. T., 1987, 'Nonlinear steady state response of a rotor-support system,' Trans. ASME, Journal of Vibration, Acoustics, Stree and Reliability in Design, Vol. 109, pp. 255-261
  2. Dokainish, M. A., Subbaraj, K. 1989, 'A Survey of Direct Time-Integration Methods in Computational Structural Dynamics,' Computers and Structures, Vol. 32, pp. 1371-1386 https://doi.org/10.1016/0045-7949(89)90314-3
  3. Glisinn, D. E., 1982, 'A High Order Generalized Method of Averaging,' SIAM Journal on Applied Methematics, Vol. 42, No. 1, pp. 113-134 https://doi.org/10.1137/0142010
  4. Haquang, N., Mook, D. T., 1987, 'Non-linear Structural Vibration under Combined Parametric and External Excitation,' Journal of Sound and Vibration, Vol. 118-2, pp.291-306 https://doi.org/10.1016/0022-460X(87)90527-X
  5. Hassan A., 1994, 'Use of Transformations with The Higher Order Method of Multiple Scales to Determine The Steady Steate Periodic Respone of Harmonically Excited Non-linear oscillators:Transformation of Derivative,' Journal of Sound and Vibration, Vol. 178-1, pp. 1-19 https://doi.org/10.1006/jsvi.1994.1464
  6. Iwatsubo Takuzo, Kawamura Shozo, Moon Byungyoung, 1998, 'Non-Linear Vibration Analysis of Rotor System using Substructure Synthesis Method(Analysis with Consideration of non-linearity of rotor),' JSME International Journal Series C, Vol. 41, No. 4, pp 727-733
  7. Iwatsubo Takuzo, Shimbo Kenichi, Kawamura Shozo, Moon Byungyoung, 1999, 'Non-Lin-ear Vibration Analysis of Rotor System using Component Mode Synthsis Method (Proposition of construction method for the nonlinearrestoring force term by using modal coordinates,' Trans. Jpn. Soc. Mech. Eng.,Series C, Vol. 65, No. 637, pp 3499-3506
  8. Moon Byungyoung, Kim, Jin-Wook and Yang Bo-suk, 1999, 'Non-Linear Vibration Analysis of Mechanical Structure System using Substructure Synthesis Method,' KSME International Journal, Vol. 13, No. 9, pp 620-629
  9. Moon Byungyoung and Kang Beom-soo, 2001, 'Non-Linear Vibration Analysis of Mencnical System (Analysis with consideration of nonlinear sensitivity),' JSME International Journal Series C, Vol. 44, No. 1, pp. 12-20 https://doi.org/10.1299/jsmec.44.12