Multi-pulse chaotic dynamics of non-autonomous nonlinear system for a laminated composite piezoelectric rectangular plate

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

Discrete Dynamics in Nature and Society ◽

10.1155/2013/958219 ◽

2013 ◽

Vol 2013 ◽

pp. 1-27 ◽

Cited By ~ 2

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.

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Multi-pulse chaotic dynamics of six-dimensional non-autonomous nonlinear system for a composite laminated piezoelectric rectangular plate

Nonlinear Dynamics ◽

10.1007/s11071-013-0849-0 ◽

2013 ◽

Vol 73 (1-2) ◽

pp. 1005-1033 ◽

Cited By ~ 19

Author(s):

W. Zhang ◽

W. L. Hao

Keyword(s):

Nonlinear System ◽

Rectangular Plate ◽

Chaotic Dynamics

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Modeling and Chaotic Dynamics of the Laminated Composite Piezoelectric Rectangular Plate

Mathematical Problems in Engineering ◽

10.1155/2014/345072 ◽

2014 ◽

Vol 2014 ◽

pp. 1-19 ◽

Cited By ~ 4

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.

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

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127414501387 ◽

2014 ◽

Vol 24 (11) ◽

pp. 1450138 ◽

Cited By ~ 8

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.

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

Meccanica ◽

10.1007/s11012-013-9800-1 ◽

2013 ◽

Vol 49 (2) ◽

pp. 365-392 ◽

Cited By ~ 20

Author(s):

Minghui Yao ◽

Wei Zhang

Keyword(s):

Nonlinear System ◽

Rectangular Plate ◽

High Dimension ◽

Laminated Composite ◽

Chaotic Motions

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Analysis of Stress and Strain with Variation in Elastic Properties in Symmetric Laminated Composite Rectangular Plate

International Journal for Research in Applied Science and Engineering Technology ◽

10.22214/ijraset.2017.8334 ◽

2017 ◽

Vol V (VIII) ◽

pp. 2336-2347

Author(s):

Yogesh Pratap Singh

Keyword(s):

Rectangular Plate ◽

Elastic Properties ◽

Laminated Composite ◽

Stress And Strain

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Multi-Pulse Chaotic Dynamics of Four-Dimensional Non-Autonomous Nonlinear System for a Truss Core Sandwich Plate

Volume 8: 26th Conference on Mechanical Vibration and Noise ◽

10.1115/detc2014-34133 ◽

2014 ◽

Author(s):

Wei Zhang ◽

Qi-liang Wu

Keyword(s):

Nonlinear System ◽

Chaotic Dynamics ◽

Sandwich Plate ◽

Melnikov Method ◽

Order Mode ◽

Simply Supported ◽

Truss Core ◽

Extended Melnikov Method ◽

Kagome Truss ◽

Truss Core Sandwich Plate

In this paper, an extended high-dimensional Melnikov method is used to investigate global and chaotic dynamics of a simply supported 3D-kagome truss core sandwich plate subjected to the transverse and the in-plane excitations. Based on the motion equation derived by Zhang and the method of multiple scales, the averaged equation is obtained for the case of principal parametric resonance and 1:2 sub-harmonic resonance for the first-order mode and primary resonance for the second-order mode. From the averaged equation obtained, the system is simplified to a three order standard form with a double zero and a pair of pure imaginary eigenvalues by using the theory of normal form. Then, the extended Melnikov method is utilized to investigate the Shilnikov-type multi-pulse heteroclinic bifurcations and existence of chaos. The analysis of the extended Melnikov method demonstrates that there exist the Shilnikov-type multi-pulse heteroclinic bifurcations and chaos in the four-dimensional non-autonomous nonlinear system. Finally, the results of numerical simulations also show that for the nonlinear system of simply supported 3D-kagome truss core sandwich plate with the transverse and the in-plane excitations, the Shilnikov-type multi-pulse motion of chaos can happen and further verify the result of theoretical analysis.

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