The extended Melnikov method for non-autonomous nonlinear dynamical systems and application to multi-pulse chaotic dynamics of a buckled thin plate

2010 ◽  
Vol 11 (3) ◽  
pp. 1442-1457 ◽  
Author(s):  
W. Zhang ◽  
J.H. Zhang ◽  
M.H. Yao
Keyword(s):  
Dynamical Systems ◽  
Thin Plate ◽  
Chaotic Dynamics ◽  
Nonlinear Dynamical Systems ◽  
Melnikov Method ◽  
Nonlinear Dynamical ◽  
Extended Melnikov Method

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 Artificial Intelligence, Chaos, Prediction and Understanding in Science

2021 ◽  
Vol 31 (11) ◽  
pp. 2150173
Author(s):  
Miguel A. F. Sanjuán
Keyword(s):  
Artificial Intelligence ◽  
Machine Learning ◽  
Big Data ◽  
Deep Learning ◽  
Dynamical Systems ◽  
Chaotic Dynamics ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical ◽  
Constructive Dialogue ◽  
Learning Techniques

Machine learning and deep learning techniques are contributing much to the advancement of science. Their powerful predictive capabilities appear in numerous disciplines, including chaotic dynamics, but they miss understanding. The main thesis here is that prediction and understanding are two very different and important ideas that should guide us to follow the progress of science. Furthermore, the important role played by nonlinear dynamical systems is emphasized for the process of understanding. The path of the future of science will be marked by a constructive dialogue between big data and big theory, without which we cannot understand.

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.

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.

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