BIFURCATION TREES OF PERIODIC MOTIONS IN A PARAMETRICALLY EXCITED PENDULUM

被引：0

作者：

Guo, Yu ^{[1
]}

Luo, Albert C. J. ^{[2
]}

机构：

[1] Midwestern State Univ, McCoy Sch Engn, Wichita Falls, TX 76308 USA

[2] Southern Illinois Univ Edwardsville, Dept Mech & Ind Engn, Edwardsville, IL 62026 USA

来源：

PROCEEDINGS OF THE ASME INTERNATIONAL DESIGN ENGINEERING TECHNICAL CONFERENCES AND COMPUTERS AND INFORMATION IN ENGINEERING CONFERENCE, 2017, VOL 6 | 2017年

关键词：

RESONANT LAYERS; CHAOS;

D O I：

暂无

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

In this paper, the bifurcation trees of periodic motions in a parametrically excited pendulum are studied using discrete implicit maps. From the discrete maps, mapping structures are developed for periodic motions in such a parametric pendulum. Analytical bifurcation trees of periodic motions to chaos are developed through the nonlinear algebraic equations of such implicit maps in the specific mapping structures. The corresponding stability and bifurcation analysis of periodic motions is carried out. Finally, numerical results of periodic motions are presented. Many new periodic motions in the parametrically excited pendulum are discovered.

引用

页数：8

共 23 条

[11]

Luo A.C.J., 2015, Discontinuity, Nonlinearity, and Complexity, V4, P13, DOI 10.5890/dnc.2015.06.002

[12] The dynamics of stochastic and resonant layers in a periodically driven pendulum [J].

Luo, ACJ ;

Han, RPS .

CHAOS SOLITONS & FRACTALS, 2000, 11 (14) :2349-2359

[13] Resonant layers in a parametrically excited pendulum [J].

Luo, ACJ .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2002, 12 (02) :409-419

[14] Resonance and stochastic layer in a parametrically excited pendulum [J].

Luo, ACJ .

NONLINEAR DYNAMICS, 2001, 25 (04) :355-367

[15]

Luo ACJ., 2012, CONTINUOUS DYNAMICAL

[16] Periodic Motions to Chaos in Pendulum [J].

Luo, Albert C. J. ;

Guo, Yu .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2016, 26 (09)

[17] Periodic Flows to Chaos Based on Discrete Implicit Mappings of Continuous Nonlinear Systems [J].

Luo, Albert C. J. .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2015, 25 (03)

[18] Approximate solutions of periodic motions in nonlinear systems via a generalized harmonic balance [J].

Luo, Albert C. J. ;

Huang, Jianzhe .

JOURNAL OF VIBRATION AND CONTROL, 2012, 18 (11) :1661-1674

[19] ANALYTICAL DYNAMICS OF PERIOD-m FLOWS AND CHAOS IN NONLINEAR SYSTEMS [J].

Luo, Albert C. J. ;

Huang, Jianzhe .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2012, 22 (04)

[20]

Rand R.H., 1987, APPL MATH SCI

← 1 2 3 →