Double-mode modeling of chaotic and bifurcation dynamics for a simply supported rectangular plate in large deflection

Steven Hsin-Yi Lai, Cha'o Kuang Chen, Yen Liang Yeh

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

This paper presents a new approach to characterize the conditions that can possibly lead to chaotic motion for a simply supported large deflection rectangular plate by utilizing the criteria of the fractal dimension and the maximum Lyapunov exponent. The governing partial differential equation of the simply supported rectangular plate is first derived and simplified to a set of two ordinary differential equations by the Galerkin method. Several different features including Fourier spectra, state-space plot, Poincaŕe map and bifurcation diagram are then numerically computed by using a double-mode approach. These features are used to characterize the dynamic behavior of the plate subjected to various excitation conditions. Numerical examples are presented to verify the validity of the conditions that lead to chaotic motion and the effectiveness of the proposed modeling approach. The numerical results indicate that large deflection motion of a rectangular plate possesses many bifurcation points, two different chaotic motions and some jump phenomena under various lateral loading. The results of numerical simulation indicate that the computed bifurcation points can lead to either a transcritical bifurcation or a pitchfork bifurcation for the motion of a large deflection rectangular plate. Meanwhile, the points of pitchfork bifurcation can gradually lead to chaotic motion in some specific loading conditions. The modeling result thus obtained by using the method proposed in this paper can be employed to predict the instability induced by the dynamics of a large deflection plate.

Original languageEnglish
Pages (from-to)331-343
Number of pages13
JournalInternational Journal of Non-Linear Mechanics
Volume37
Issue number2
DOIs
Publication statusPublished - 2002 Mar 1

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Large Deflection
Rectangular Plate
Chaotic Motion
Bifurcation
Pitchfork Bifurcation
Bifurcation Point
Fractal dimension
Galerkin methods
Modeling
Ordinary differential equations
Partial differential equations
Transcritical Bifurcation
Fourier Spectrum
Motion
Computer simulation
Bifurcation Diagram
Galerkin Method
Fractal Dimension
Lyapunov Exponent
Dynamic Behavior

All Science Journal Classification (ASJC) codes

  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

Cite this

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abstract = "This paper presents a new approach to characterize the conditions that can possibly lead to chaotic motion for a simply supported large deflection rectangular plate by utilizing the criteria of the fractal dimension and the maximum Lyapunov exponent. The governing partial differential equation of the simply supported rectangular plate is first derived and simplified to a set of two ordinary differential equations by the Galerkin method. Several different features including Fourier spectra, state-space plot, Poincaŕe map and bifurcation diagram are then numerically computed by using a double-mode approach. These features are used to characterize the dynamic behavior of the plate subjected to various excitation conditions. Numerical examples are presented to verify the validity of the conditions that lead to chaotic motion and the effectiveness of the proposed modeling approach. The numerical results indicate that large deflection motion of a rectangular plate possesses many bifurcation points, two different chaotic motions and some jump phenomena under various lateral loading. The results of numerical simulation indicate that the computed bifurcation points can lead to either a transcritical bifurcation or a pitchfork bifurcation for the motion of a large deflection rectangular plate. Meanwhile, the points of pitchfork bifurcation can gradually lead to chaotic motion in some specific loading conditions. The modeling result thus obtained by using the method proposed in this paper can be employed to predict the instability induced by the dynamics of a large deflection plate.",
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Double-mode modeling of chaotic and bifurcation dynamics for a simply supported rectangular plate in large deflection. / Lai, Steven Hsin-Yi; Chen, Cha'o Kuang; Yeh, Yen Liang.

In: International Journal of Non-Linear Mechanics, Vol. 37, No. 2, 01.03.2002, p. 331-343.

Research output: Contribution to journalArticle

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