Chaotic and bifurcation dynamics for a simply supported rectangular plate of thermo-mechanical coupling in large deflection

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

Research output: Contribution to journalArticle

33 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 of thermo-mechanical coupling by utilizing the criteria of the fractal dimension and the maximum Lyapunov exponent. The governing partial differential equation of the simply supported rectangular plate of thermo-mechanical coupling is first derived and simplified to a set of three ordinary differential equations by the Galerkin method. Several different features including power spectra, phase plot, Poincaré map and bifurcation diagram are then numerically computed. 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 the thermo-mechanical coupling rectangular plate possesses many bifurcation points, chaotic motions and period-double phenomena under various lateral loads, bi-axial loads, thermo-mechanical coupling factors and aspect ratios. The modeling results of numerical simulation indicate that the chaotic motion may occur in the range of lateral loads Q̄ = 1.25 to 3.35 and near the bi-axial load η2 = 1.5. The dynamic motion of the thermal-couple plate is periodic if the aspect ratio is within a specific range or the thermo-mechanical coupling factor is within a specific range. 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 the thermo-mechanical coupling plate in large deflection.

Original languageEnglish
Pages (from-to)1493-1506
Number of pages14
JournalChaos, solitons and fractals
Volume13
Issue number7
DOIs
Publication statusPublished - 2002 Jun 1

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Thermo-mechanical Coupling
Large Deflection
Rectangular Plate
Bifurcation
Chaotic Motion
Biaxial
Aspect Ratio
Lateral
Modeling
Range of data
Motion
Bifurcation Point
Bifurcation Diagram
Power Spectrum
Galerkin Method
Fractal Dimension
Lyapunov Exponent
Dynamic Behavior
Ordinary differential equation
Partial differential equation

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematics(all)
  • Physics and Astronomy(all)
  • 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 of thermo-mechanical coupling by utilizing the criteria of the fractal dimension and the maximum Lyapunov exponent. The governing partial differential equation of the simply supported rectangular plate of thermo-mechanical coupling is first derived and simplified to a set of three ordinary differential equations by the Galerkin method. Several different features including power spectra, phase plot, Poincar{\'e} map and bifurcation diagram are then numerically computed. 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 the thermo-mechanical coupling rectangular plate possesses many bifurcation points, chaotic motions and period-double phenomena under various lateral loads, bi-axial loads, thermo-mechanical coupling factors and aspect ratios. The modeling results of numerical simulation indicate that the chaotic motion may occur in the range of lateral loads Q̄ = 1.25 to 3.35 and near the bi-axial load η2 = 1.5. The dynamic motion of the thermal-couple plate is periodic if the aspect ratio is within a specific range or the thermo-mechanical coupling factor is within a specific range. 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 the thermo-mechanical coupling plate in large deflection.",
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Chaotic and bifurcation dynamics for a simply supported rectangular plate of thermo-mechanical coupling in large deflection. / Yeh, Yen Liang; Chen, Cha'o Kuang; Lai, Steven Hsin-Yi.

In: Chaos, solitons and fractals, Vol. 13, No. 7, 01.06.2002, p. 1493-1506.

Research output: Contribution to journalArticle

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