THE APPLICATIONS OF A MODIFIED NORMAL FORM APPROACH

Applied Mathematics and Mechanics (English Edition) ›› 2001, Vol. 22 ›› Issue (7): 802-807.

THE APPLICATIONS OF A MODIFIED NORMAL FORM APPROACH

张伟亿^1,2, Koncay Huseyin², 叶敏¹

1. Department of Mechanics, Tianjin University, Tianjin 300072, P. R. China;
2. Department of Systems Design Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

收稿日期:2000-01-12 修回日期:2001-01-20 出版日期:2001-07-18 发布日期:2001-07-18
基金资助:
the Key Projects of National Natural Science Foundation of China(19990510);the NSERC Foundation of Canada;the National Natural Science Foundation of China(10072037)

THE APPLICATIONS OF A MODIFIED NORMAL FORM APPROACH

ZHANG Wei-yi^1,2, Koncay Huseyin², YE Min ¹

1. Department of Mechanics, Tianjin University, Tianjin 300072, P. R. China;
2. Department of Systems Design Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

Received:2000-01-12 Revised:2001-01-20 Online:2001-07-18 Published:2001-07-18
Supported by:
the Key Projects of National Natural Science Foundation of China(19990510);the NSERC Foundation of Canada;the National Natural Science Foundation of China(10072037)

摘要/Abstract

摘要： The modified normal form approach presented by ZHANG Wei-yi, K Huseyin and CHEN Yu-shu is further extended and a different procedure is introduced which lends itself readily to symbolic calculations, like MAPLE. This provides a number of significant advantages over the previous approach, and facilitates the associated calculations. To illustrate the new approach, three examples are presented.

中图分类号:

O322

张伟亿;Koncay Huseyin;叶敏. THE APPLICATIONS OF A MODIFIED NORMAL FORM APPROACH[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(7): 802-807.

ZHANG Wei-yi;Koncay Huseyin;YE Min . THE APPLICATIONS OF A MODIFIED NORMAL FORM APPROACH[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(7): 802-807.

[1]	Canchang LIU, Qian DING, Qingmei GONG, Chicheng MA, Shuchang YUE. Axial control for nonlinear resonances of electrostatically actuated nanobeam with graphene sensor[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(4): 527-542.
[2]	R. NAZEMNEZHAD, P. FAHIMI. Free torsional vibration of cracked nanobeams incorporating surface energy effects[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(2): 217-230.
[3]	Lei HOU, Yushu CHEN. Bifurcation analysis of aero-engine's rotor system under constant maneuver load[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(11): 1417-1426.
[4]	Xiaodong WANG, Yushu CHEN, Lei HOU. Nonlinear dynamic singularity analysis of two interconnected synchronous generator system with 1:3 internal resonance and parametric principal resonance[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(8): 985-1004.
[5]	Demin ZHAO, Jianlin LIU, C. Q. WU. Stability and local bifurcation of parameter-excited vibration of pipes conveying pulsating fluid under thermal loading[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(8): 1017-1032.
[6]	A. G. ARANI, G. S. JAFARI. Nonlinear vibration analysis of laminated composite Mindlin micro/nano-plates resting on orthotropic Pasternak medium using DQM[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(8): 1033-1044.
[7]	Xuan XIE;Lingcheng KONG;Yuxi WANG;Jun ZHANG;Yuantai HU. Coupled vibrations and frequency shift of compound system consisting of quartz crystal resonator in thickness-shear motions and micro-beam array immersed in liquid[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(2): 225-232.
[8]	B. AMIRIAN;R. HOSSEINI-ARA;H. MOOSAVI. Surface and thermal effects on vibration of embedded alumina nanobeams based on novel Timoshenko beam model[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(7): 875-886.
[9]	马宇立;陈继伟;刘咏泉;苏先樾. Vibration analysis of foam plates based on cell volume distribution[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(12): 1493-1504.
[10]	李凤明;刘春川. Parametric vibration stability and active control of nonlinear beams[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(11): 1381-1392.
[11]	李双宝;张伟. Global bifurcations and multi-pulse chaotic dynamics of rectangular thin plate with one-to-one internal resonance[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(9): 1115-1128.
[12]	陈洋洋;燕乐纬;佘锦炎;陈树辉. Generalized hyperbolic perturbation method for homoclinic solutions of strongly nonlinear autonomous systems[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(9): 1137-1152.
[13]	张华彪;陈予恕;李军. Bifurcation on synchronous full annular rub of rigid-rotor elastic-support system[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(7): 865-880.
[14]	李忠刚;陈予恕. Research on 1:2 subharmonic resonance and bifurcation of nonlinear rotor-seal system[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(4): 499-510.
[15]	沈建和;陈树辉. 混沌Mathieu_Duffing振子的开闭环控制[J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(1): 19-27 .

THE APPLICATIONS OF A MODIFIED NORMAL FORM APPROACH

THE APPLICATIONS OF A MODIFIED NORMAL FORM APPROACH

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价