Subharmonic Melnikov method of four-dimensional non-autonomous systems and application to a rectangular thin plate

被引：10

作者：

Sun, M. ^{[1
]}

Zhang, W. ^{[2
]}

Chen, J. E. ^{[3
]}

Yao, M. H. ^{[2
]}

机构：

[1] Tianjin Chengjian Univ, Sch Sci, Tianjin 300384, Peoples R China

[2] Beijing Univ Technol, Coll Mech Engn, Beijing 100022, Peoples R China

[3] Tianjin Univ Technol, Tianjin Key Lab Design & Intelligent Control Adv, Tianjin 300384, Peoples R China

来源：

NONLINEAR DYNAMICS | 2015年 / 82卷 / 1-2期

基金：

中国国家自然科学基金;

关键词：

Subharmonic Melnikov method; Bifurcation; Periodic solution; Rectangular plate; COUPLED OSCILLATORS; LIMIT-CYCLES; PERIODIC-SOLUTIONS; BIFURCATION; ORBITS; CHAOS; VIBRATIONS; RESONANCE; MOTIONS;

D O I：

10.1007/s11071-015-2184-0

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

The existence and bifurcations of the subharmonic orbits for four-dimensional non-autonomous nonlinear systems are investigated in this paper. The improved subharmonic Melnikov method is presented by using the periodic transformations and Poincar, map. The theoretical results and the formulas are obtained, which can be used to analyze the subharmonic dynamic responses of four-dimensional non-autonomous nonlinear systems. The improved subharmonic Melnikov method is used to investigate the subharmonic orbits of a simply supported rectangular thin plate under combined parametric and external excitations for verifying the validity and applicability of the method. The theoretical results indicate that the subharmonic orbits can occur in the rectangular thin plate with 1:1 and 1:2 internal resonances. The results of numerical simulation also indicate the existence of the subharmonic orbits for the rectangular thin plate, which can verify the analytical predictions.

引用

页码：643 / 662

页数：20