Nonlinear oscillations and chaotic dynamics of an antisymmetric cross-ply laminated composite rectangular thin plate under parametric excitation

2005 ◽  
Vol 287 (4-5) ◽  
pp. 723-758 ◽  
Author(s):  
Min Ye ◽  
Yanhong Sun ◽  
Wei Zhang ◽  
Xueping Zhan ◽  
Qian Ding
Keyword(s):  
Thin Plate ◽  
Parametric Excitation ◽  
Chaotic Dynamics ◽  
Nonlinear Oscillations ◽  
Laminated Composite ◽  
Rectangular Thin Plate

The Extended Melnikov Method for Non-Autonomous Higher Dimensional Nonlinear Systems and Multi-Pulse Chaotic Dynamics of Laminated Composite Piezoelectric Plate

2009 ◽  
Author(s):  
Wei Zhang ◽  
Jun-Hua Zhang
Keyword(s):  
Thin Plate ◽  
Chaotic Dynamics ◽  
Plate Theory ◽  
Nonlinear Dynamical System ◽  
Laminated Composite ◽  
Melnikov Method ◽  
Type Equation ◽  
Rectangular Thin Plate ◽  
Chaotic Motions ◽  
Extended Melnikov Method

The global bifurcations and multi-pulse chaotic dynamics of a simply supported laminated composite piezoelectric rectangular thin plate under combined parametric and transverse excitations are investigated in this paper for the first time. The formulas of the laminated composite piezoelectric rectangular plate are derived by using the von Karman-type equation, the Reddy’s third-order shear deformation plate theory 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 laminated composite piezoelectric rectangular thin plate. The results obtained here indicate that the multi-pulse chaotic motions can occur in the laminated composite piezoelectric rectangular thin plate. Numerical simulation is also employed to find the multi-pulse chaotic motions of the laminated composite piezoelectric rectangular thin plate.

FURTHER STUDIES ON NONLINEAR OSCILLATIONS AND CHAOS OF A SYMMETRIC CROSS-PLY LAMINATED THIN PLATE UNDER PARAMETRIC EXCITATION

2006 ◽  
Vol 16 (02) ◽  
pp. 325-347 ◽  
Author(s):  
WEI ZHANG ◽  
CHUNZHI SONG ◽  
MIN YE
Keyword(s):  
Thin Plate ◽  
Parametric Excitation ◽  
Multiple Scales ◽  
Nonlinear Oscillations ◽  
Equations Of Motion ◽  
Laminated Composite ◽  
Chaotic Motions ◽  
Parametrically Excited ◽  
Simply Supported ◽  
Analysis Of Stability

In this paper, the nonlinear oscillations and chaotic dynamics of a parametrically excited simply supported symmetric cross-ply laminated composite rectangular thin plate are further investigated. Considering geometric nonlinearity and nonlinear damping, a two-degree-of-freedom nonlinear system under parametric excitation is obtained to give the nonlinear governing equations of motion for laminated composite plate subjected to in-plane load. The method of multiple scales is utilized to obtain the averaged equations that are numerically solved to obtain the steady bifurcation responses and analysis of stability for laminated composite thin plate. It is illustrated that under certain conditions laminated composite thin plate may have the multiple steady bifurcation solutions and jumping may occur. The chaotic motion of rectangular symmetric cross-ply laminated composite thin plate is also found by using numerical simulation. It is found that the occurrence of the periodic, quasi-periodic and chaotic motions for a parametrically excited four-edges simply supported rectangular symmetric cross-ply laminated composite thin plate depends on the parametric excitation.

scholarly journals Multipulse Chaotic Dynamics for a Laminated Composite Piezoelectric Plate

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
J. H. Zhang ◽  
W. Zhang
Keyword(s):  
Thin Plate ◽  
Chaotic Dynamics ◽  
Piezoelectric Plate ◽  
Equations Of Motion ◽  
Laminated Composite ◽  
Phase Portraits ◽  
Rectangular Thin Plate ◽  
Governing Equations ◽  
Chaotic Motions ◽  
Simply Supported

We investigate the global bifurcations and multipulse chaotic dynamics of a simply supported laminated composite piezoelectric rectangular thin plate under combined parametric and transverse excitations. We analyze directly the nonautonomous governing equations of motion for the laminated composite piezoelectric rectangular thin plate. The results obtained here indicate that the multipulse chaotic motions can occur in the laminated composite piezoelectric rectangular thin plate. Numerical simulations including the phase portraits and Lyapunov exponents are used to analyze the complex nonlinear dynamic behaviors of the laminated composite piezoelectric rectangular thin plate.

Nonlinear Oscillations of a Composite Laminated Plate with Parametrically and Externally Excitations

2013 ◽  
Vol 699 ◽  
pp. 641-644
Author(s):  
Xiao Li Bian ◽  
Shuang Bao Li
Keyword(s):  
Thin Plate ◽  
Nonlinear Oscillations ◽  
Plate Theory ◽  
Laminated Plate ◽  
Rectangular Thin Plate ◽  
Third Order ◽  
Composite Laminated Plate ◽  
Strain Relationship ◽  
Relationship Of ◽  
Equations Of Motions

Nonlinear oscillations of a simply-supported symmetric cross-ply composite laminated rectangular thin plate are investigated in this paper. The rectangular thin plate is subjected to the transversal and in-plane excitations. Based on the Reddy’s third-order shear deformation plate theory and the stress-strain relationship of the composite laminated plate, a two-degree-of-freedom non-autonomous nonlinear system governing equations of motions for the composite laminated rectangular thin plate is derived by using the Galerkin’s method. Numerical simulations illustrate that there exist complex nonlinear oscillations for composite laminated rectangular thin plate.

Multi-Pulse Chaotic Motion for a Non-Autonomous Buckled Plate by Using the Extended Melnikov Method

2007 ◽  
Author(s):  
Wei Zhang ◽  
Jun-Hua Zhang ◽  
Ming-Hui Yao
Keyword(s):  
Thin Plate ◽  
Chaotic Dynamics ◽  
Melnikov Method ◽  
Type Equation ◽  
Rectangular Thin Plate ◽  
Governing Equations ◽  
Chaotic Motions ◽  
Simply Supported ◽  
Extended Melnikov Method ◽  
Two Degree Of Freedom

The multi-pulse Shilnikov orbits and chaotic dynamics for a parametrically excited, simply supported rectangular buckled thin plate are studied by using the extended Melnikov method. Based on von Karman type equation and the Galerkin’s approach, two-degree-of-freedom nonlinear system is obtained for the rectangular thin plate. The extended Melnikov method is directly applied to the non-autonomous governing equations of the thin plate. The results obtained here show that the multipulse chaotic motions can occur in the thin plate.

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 With a Melnikov Method and Chaotic Dynamics in Motion of Composite Laminated Rectangular Thin Plate

2008 ◽  
Author(s):  
Ming-Hui Yao ◽  
Wei Zhang ◽  
Xiang-Ying Guo ◽  
Dong-Xing Cao
Keyword(s):  
Numerical Simulation ◽  
Normal Form ◽  
Differential Equations ◽  
Thin Plate ◽  
Chaotic Dynamics ◽  
Equations Of Motion ◽  
Melnikov Method ◽  
Rectangular Thin Plate ◽  
Partial Differential ◽  
Chaotic Motions

This paper presents an analysis on the nonlinear dynamics and multi-pulse chaotic motions of a simply-supported symmetric cross-ply composite laminated rectangular thin plate with the parametric and forcing excitations. Firstly, based on the Reddy’s three-order shear deformation plate theory and the model of the von Karman type geometric nonlinearity, the nonlinear governing partial differential equations of motion for the composite laminated rectangular thin plate are derived by using the Hamilton’s principle. Then, using the second-order Galerkin discretization approach, the partial differential governing equations of motion are transformed to nonlinear ordinary differential equations. The case of the primary parametric resonance and 1:1 internal resonance is considered. Four-dimensional averaged equation is obtained by using the method of multiple scales. From the averaged equation obtained here, the theory of normal form is used to give the explicit expressions of normal form. Based on normal form, the extended Melnikov method is utilized to analyze the global bifurcations and multi-pulse chaotic dynamics of the composite laminated rectangular thin plate. The results obtained above illustrate the existence of the chaos for the Smale horseshoe sense in a parametrical and forcing excited composite laminated thin plate. The chaotic motions of the composite laminated rectangular thin plate are also found by using numerical simulation. The results of numerical simulation also indicate that there exist different shapes of the multi-pulse chaotic motions for the composite laminated rectangular thin plate.

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