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 language | English |
|---|---|
| Pages (from-to) | 1493-1506 |
| Number of pages | 14 |
| Journal | Chaos, solitons and fractals |
| Volume | 13 |
| Issue number | 7 |
| DOIs | |
| Publication status | Published - 2002 Jun 1 |
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All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematics(all)
- Physics and Astronomy(all)
- Applied Mathematics
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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 journal › Article
TY - JOUR
T1 - Chaotic and bifurcation dynamics for a simply supported rectangular plate of thermo-mechanical coupling in large deflection
AU - Yeh, Yen Liang
AU - Chen, Cha'o Kuang
AU - Lai, Steven Hsin-Yi
PY - 2002/6/1
Y1 - 2002/6/1
N2 - 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.
AB - 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.
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U2 - 10.1016/S0960-0779(01)00158-8
DO - 10.1016/S0960-0779(01)00158-8
M3 - Article
AN - SCOPUS:0036604640
VL - 13
SP - 1493
EP - 1506
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
SN - 0960-0779
IS - 7
ER -