Multi-pulse chaotic motions of high-dimension nonlinear system for a laminated composite piezoelectric rectangular plate

Meccanica ◽  
2013 ◽  
Vol 49 (2) ◽  
pp. 365-392 ◽  
Author(s):  
Minghui Yao ◽  
Wei Zhang
Keyword(s):  
Nonlinear System ◽  
Rectangular Plate ◽  
High Dimension ◽  
Laminated Composite ◽  
Chaotic Motions

scholarly journals Multipulse Heteroclinic Orbits and Chaotic Dynamics of the Laminated Composite Piezoelectric Rectangular Plate

2013 ◽  
Vol 2013 ◽  
pp. 1-27 ◽  
Author(s):  
Minghui Yao ◽  
Wei Zhang
Keyword(s):  
Rectangular Plate ◽  
Chaotic Dynamics ◽  
Multiple Scales ◽  
Nonlinear Oscillations ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Laminated Composite ◽  
Heteroclinic Orbits ◽  
Phase Method ◽  
Chaotic Motions

This paper investigates the multipulse global bifurcations and chaotic dynamics for the nonlinear oscillations of the laminated composite piezoelectric rectangular plate by using an energy phase method in the resonant case. Using the von Karman type equations, Reddy’s third-order shear deformation plate theory, and Hamilton’s principle, the equations of motion are derived for the laminated composite piezoelectric rectangular plate with combined parametric excitations and transverse excitation. Applying the method of multiple scales and Galerkin’s approach to the partial differential governing equation, the four-dimensional averaged equation is obtained for the case of 1 : 2 internal resonance and primary parametric resonance. The energy phase method is used for the first time to investigate the Shilnikov type multipulse heteroclinic bifurcations and chaotic dynamics of the laminated composite piezoelectric rectangular plate. The paper demonstrates how to employ the energy phase method to analyze the Shilnikov type multipulse heteroclinic bifurcations and chaotic dynamics of high-dimensional nonlinear systems in engineering applications. Numerical simulations show that for the nonlinear oscillations of the laminated composite piezoelectric rectangular plate, the Shilnikov type multipulse chaotic motions can occur. Overall, both theoretical and numerical studies suggest that chaos for the Smale horseshoe sense in motion exists.

scholarly journals Modeling and Chaotic Dynamics of the Laminated Composite Piezoelectric Rectangular Plate

2014 ◽  
Vol 2014 ◽  
pp. 1-19 ◽  
Author(s):  
Minghui Yao ◽  
Wei Zhang ◽  
D. M. Wang
Keyword(s):  
Rectangular Plate ◽  
Chaotic Dynamics ◽  
Multiple Scales ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Laminated Composite ◽  
Melnikov Method ◽  
Chaotic Motions ◽  
Extended Melnikov Method ◽  
Transverse Excitation

This paper investigates the multipulse heteroclinic bifurcations and chaotic dynamics of a laminated composite piezoelectric rectangular plate by using an extended Melnikov method in the resonant case. According to the von Karman type equations, Reddy’s third-order shear deformation plate theory, and Hamilton’s principle, the equations of motion are derived for the laminated composite piezoelectric rectangular plate with combined parametric excitations and transverse excitation. The method of multiple scales and Galerkin’s approach are applied to the partial differential governing equation. Then, the four-dimensional averaged equation is obtained for the case of 1 : 3 internal resonance and primary parametric resonance. The extended Melnikov method is used to study the Shilnikov type multipulse heteroclinic bifurcations and chaotic dynamics of the laminated composite piezoelectric rectangular plate. The necessary conditions of the existence for the Shilnikov type multipulse chaotic dynamics are analytically obtained. From the investigation, the geometric structure of the multipulse orbits is described in the four-dimensional phase space. Numerical simulations show that the Shilnikov type multipulse chaotic motions can occur. To sum up, both theoretical and numerical studies suggest that chaos for the Smale horseshoe sense in motion exists for the laminated composite piezoelectric rectangular plate.

Chaotic Dynamics of a Six-Dimensional Laminated Composite Piezoelectric Rectangular Plate

2009 ◽  
Author(s):  
Wei Zhang ◽  
Mei-juan Gao ◽  
Ming-hui Yao ◽  
Zhi-gang Yao
Keyword(s):  
Nonlinear System ◽  
Normal Form ◽  
Rectangular Plate ◽  
Chaotic Dynamics ◽  
Laminated Composite ◽  
Phase Method ◽  
Dynamical Characteristic ◽  
Theory Analysis ◽  
Theoretical Predictions ◽  
Pure Imaginary Eigenvalues

This paper focuses on the multi-pulse orbits and chaotic dynamics of the six-dimensional nonlinear system for the composite laminated piezoelectric rectangular plate using the theory of normal form and the energy-phase method. Taking into account that the averaged equation has a double zero and two pairs of pure imaginary eigenvalues, we use the theory of normal form to simplify the six-dimensional averaged equation to a simpler normal form. The energy-phase method is to be extended to study the dynamical characteristic of the six-dimensional nonlinear system. The global theory analysis indicates that there exist the homoclinic bifurcation and Shilnikov type multi-pulse jumping chaotic dynamics in the system under the small perturbation. In order to illustrate the theoretical predictions, the Runge-Kutta algorithm is used to perform numerical simulation. The results of numerical simulations also demonstrate that the jumping phenomena of orbits can occur in the composite laminated piezoelectric rectangular plate.

Multipulse Chaotic Dynamics of Six-Dimensional Nonautonomous Nonlinear System for a Honeycomb Sandwich Plate

2014 ◽  
Vol 24 (11) ◽  
pp. 1450138 ◽  
Author(s):  
W. L. Hao ◽  
W. Zhang ◽  
M. H. Yao
Keyword(s):  
Nonlinear System ◽  
Rectangular Plate ◽  
Chaotic Dynamics ◽  
Equations Of Motion ◽  
Melnikov Method ◽  
Global Bifurcations ◽  
Chaotic Motions ◽  
Simply Supported ◽  
Extended Melnikov Method ◽  
Honeycomb Sandwich

This paper studies the global bifurcations and multipulse chaotic dynamics of a four-edge simply supported honeycomb sandwich rectangular plate under combined in-plane and transverse excitations. Based on the von Karman type equation for the geometric nonlinearity and Reddy's third-order shear deformation theory, the governing equations of motion are derived for the four-edge simply supported honeycomb sandwich rectangular plate. The Galerkin method is employed to discretize the partial differential equations of motion to a three-degree-of-freedom nonlinear system. The six-dimensional nonautonomous nonlinear system is simplified to a three-order standard form by using the normal form method. The extended Melnikov method is improved to investigate the six-dimensional nonautonomous nonlinear dynamical system in a mixed coordinate. The global bifurcations and multipulse chaotic dynamics of the four-edge simply supported honeycomb sandwich rectangular plate are studied by using the improved extended Melnikov method. The multipulse chaotic motions of the system are found by using numerical simulation, which further verifies the result of theoretical analysis.

Flutter of high-dimension nonlinear system for a FGM truncated conical shell

2017 ◽  
Vol 25 (1) ◽  
pp. 47-61 ◽  
Author(s):  
Y. X. Hao ◽  
S. W. Yang ◽  
W. Zhang ◽  
M. H. Yao ◽  
A. W. Wang
Keyword(s):  
Nonlinear System ◽  
High Dimension ◽  
Conical Shell ◽  
Truncated Conical Shell

Nonlinear Vibrations and Chaotic Dynamics of the Laminated Composite Piezoelectric Beam

2015 ◽  
Vol 137 (1) ◽  
Author(s):  
Minghui Yao ◽  
Wei Zhang ◽  
Zhigang Yao
Keyword(s):  
Numerical Simulation ◽  
Axial Load ◽  
Nonlinear Vibrations ◽  
Dynamical Behavior ◽  
Laminated Composite ◽  
Transverse Load ◽  
Nonlinear Phenomenon ◽  
Periodic Motions ◽  
Chaotic Motions ◽  
Piezoelectric Beam

This paper investigates the complicated dynamics behavior and the evolution law of the nonlinear vibrations of the simply supported laminated composite piezoelectric beam subjected to the axial load and the transverse load. Using the third-order shear deformation theory and the Hamilton's principle, the nonlinear governing equations of motion for the laminated composite piezoelectric beam are derived. Applying the method of multiple scales and Galerkin's approach to the partial differential governing equation, the four-dimensional averaged equation is obtained for the case of principal parametric resonance and 1:9 internal resonance. From the averaged equations obtained, numerical simulation is performed to study nonlinear vibrations of the laminated composite piezoelectric beam. The axial load, the transverse load, and the piezoelectric parameter are selected as the controlling parameters to analyze the law of complicated nonlinear dynamics of the laminated composite piezoelectric beam. Based on the results of numerical simulation, it is found that there exists the complex nonlinear phenomenon in motions of the laminated composite piezoelectric beam. In summary, numerical studies suggest that periodic motions and chaotic motions exist in nonlinear vibrations of the laminated composite piezoelectric beam. In addition, it is observed that the axial load, the transverse load and the piezoelectric parameter have significant influence on the nonlinear dynamical behavior of the beam. We can control the response of the system from chaotic motions to periodic motions by changing these parameters.

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