Higher-dimensional chaotic dynamics of a composite laminated piezoelectric rectangular plate

2009 ◽  
Vol 52 (12) ◽  
pp. 1989-2000 ◽  
Author(s):  
Wei Zhang ◽  
MeiJuan Gao ◽  
MingHui Yao ◽  
ZhiGang Yao
Keyword(s):  
Rectangular Plate ◽  
Chaotic Dynamics ◽  
Higher Dimensional

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.

Multi-pulse orbits and chaotic dynamics of a composite laminated rectangular plate

2011 ◽  
Vol 24 (5) ◽  
pp. 383-398 ◽  
Author(s):  
Xiangying Guo ◽  
Wei Zhang ◽  
Minghui Yao
Keyword(s):  
Rectangular Plate ◽  
Chaotic Dynamics

Chaotic Dynamics in a Higher-Dimensional Nonlinear System for a Composite Laminated Plate

2009 ◽  
Author(s):  
Wei Zhang ◽  
Mei-juan Gao
Keyword(s):  
Numerical Simulation ◽  
Nonlinear System ◽  
Normal Form ◽  
Chaotic Dynamics ◽  
Phase Method ◽  
Laminated Plate ◽  
Internal Resonances ◽  
Chaotic Motions ◽  
Composite Laminated Plate ◽  
Higher Dimensional

In this paper, we first analyze the chaotic dynamics of a higher-dimensional nonlinear system for a composite laminated plate in the case of 1:3:3 internal resonances with the theory of normal form and the energy-phase method. The theory of normal form is used to obtain the simpler normal form of the system. The energy-phase method is employed to analyze the multi-pulse chaotic dynamics of the higher-dimensional nonlinear system for a composite laminated plate. Moreover, the numerical simulation is performed to find the multi-pulse chaotic motion of the composite laminated plate. The global theory analysis and the results of numerical simulation demonstrate that the existence of the periodic motions and chaotic motions with the jumping phenomena in the composite laminated plate.

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.

Multi-Pulse Chaotic Dynamics for Composite Laminated Plates

2010 ◽  
Author(s):  
Jun-Hua Zhang ◽  
Wei Zhang ◽  
Qian Wang
Keyword(s):  
Rectangular Plate ◽  
Chaotic Dynamics ◽  
Equations Of Motion ◽  
Nonlinear Dynamical System ◽  
Melnikov Method ◽  
Laminated Plates ◽  
Chaotic Motions ◽  
Nonlinear Dynamical ◽  
Simply Supported ◽  
First Time

The heteroclinic bifurcation and multi-pulse chaotic dynamics of a simply-supported symmetric cross-ply composite laminated rectangular plate with parametric and forcing excitations are investigated in this paper for the first time. The formulas of the simply-supported composite laminated rectangular plate are derived by using Hamilton’s principle and the Galerkin’s approach. The extended Melnikov method is improved to enable us to analyze directly the non-autonomous nonlinear dynamical system, which is applied to the non-autonomous governing equations of motion for the simply-supported composite laminated rectangular plate. The results obtained here indicate that the multi-pulse chaotic motions can occur in the simply-supported composite laminated rectangular plate. Numerical simulation is also employed to find the multipulse chaotic motions of the simply-supported composite laminated rectangular plate.

Multipulse Chaotic Dynamics for Nonautonomous Nonlinear Systems and Application to a FGM Plate

2014 ◽  
Vol 24 (05) ◽  
pp. 1450068 ◽  
Author(s):  
Junhua Zhang ◽  
Wei Zhang ◽  
Yuxin Hao
Keyword(s):  
Dynamical System ◽  
Rectangular Plate ◽  
Chaotic Dynamics ◽  
Nonlinear Dynamical System ◽  
Melnikov Method ◽  
Functionally Graded ◽  
Chaotic Motions ◽  
Nonlinear Dynamical ◽  
Simply Supported ◽  
Extended Melnikov Method

The extended Melnikov method is improved to investigate the nonautonomous nonlinear dynamical system in Cartesian coordinate. The multipulse chaotic dynamics of a simply supported functionally graded materials (FGM) rectangular plate subjected to transversal and in-plane excitations is investigated in this paper for the first time. The formulas of the FGM rectangular plate are two-degree-of-freedom nonautonomous nonlinear system with coupling of nonlinear terms including several square and cubic terms. The extended Melnikov method is improved to enable us to analyze directly the nonautonomous nonlinear dynamical system of the simply-supported FGM rectangular plate. The results obtained here indicate that multipulse chaotic motions can occur in the simply-supported FGM rectangular plate. Numerical simulation is also employed to find the multipulse chaotic motions of the simply-supported FGM 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.

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