Shilnikov Type Multi-Pulse Orbits of Functionally Graded Materials Rectangular Plate

2010 ◽  
Author(s):  
Wei Zhang ◽  
Ming-Hui Yao ◽  
Dong-Xing Cao
Keyword(s):  
Normal Form ◽  
Rectangular Plate ◽  
Functionally Graded Materials ◽  
Chaotic Dynamics ◽  
Functionally Graded ◽  
Phase Method ◽  
Global Dynamics ◽  
Graded Materials ◽  
Chaotic Motions ◽  
Simply Supported

Multi-pulse chaotic dynamics of a simply supported functionally graded materials (FGMs) rectangular plate is investigated in this paper. The FGMs rectangular plate is subjected to the transversal and in-plane excitations. The properties of material are graded in the direction of thickness. Based on Reddy’s third-order shear deformation plate theory, the nonlinear governing equations of motion for the FGMs plate are derived by using the Hamilton’s principle. The four-dimensional averaged equation under the case of 1:2 internal resonance, primary parametric resonance and 1/2-subharmonic resonance is obtained by directly using the asymptotic perturbation method and Galerkin approach to the partial differential governing equation of motion for the FGMs rectangular plate. The system is transformed to the averaged equation. From the averaged equation, the theory of normal form is used to find the explicit formulas of normal form. Based on normal form obtained, the energy phase method is utilized to analyze the multi-pulse global bifurcations and chaotic dynamics for the FGMs rectangular plate. The analysis of global dynamics indicates that there exist the multi-pulse jumping orbits in the perturbed phase space of the averaged equation. From the averaged equations obtained, the chaotic motions and the Shilnikov type multi-pulse orbits of the FGMs rectangular plate are found by using numerical simulation. The results obtained above mean the existence of the chaos for the Smale horseshoe sense for the simply supported FGMs rectangular plate.

Multi-Pulse Chaotic Dynamics of the Cantilevered Pipe Conveying Pulsating Fluid

2009 ◽  
Author(s):  
Ming-Hui Yao ◽  
Wei Zhang ◽  
Dong-Xing Cao
Keyword(s):  
Normal Form ◽  
Chaotic Dynamics ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Phase Method ◽  
Global Dynamics ◽  
Pipe Material ◽  
Chaotic Motions ◽  
Cantilevered Pipe ◽  
Pulsating Fluid

The multi-pulse orbits and chaotic dynamics of the cantilevered pipe conveying pulsating fluid with harmonic external force are studied in detail. The nonlinear geometric deformation of the pipe and the Kelvin constitutive relation of the pipe material are considered. The nonlinear governing equations of motion for the cantilevered pipe conveying pulsating fluid are determined by using Hamilton principle. The four-dimensional averaged equation under the case of principle parameter resonance, 1/2 subharmonic resonance and 1:2 internal resonance and primary parametric resonance is obtained by directly using the method of multiple scales and Galerkin approach to the partial differential governing equation of motion for the cantilevered pipe. The system is transformed to the averaged equation. From the averaged equation, the theory of normal form is used to find the explicit formulas of normal form. Based on normal form obtained, the energy phase method is utilized to analyze the multi-pulse global bifurcations and chaotic dynamics for the cantilevered pipe conveying pulsating fluid. The analysis of global dynamics indicates that there exist the multi-pulse jumping orbits in the perturbed phase space of the averaged equation. From the averaged equations obtained, the chaotic motions and the Shilnikov type multi-pulse orbits of the cantilevered pipe are found by using numerical simulation. The results obtained above mean the existence of the chaos for the Smale horseshoe sense for the pulsating fluid conveying cantilevered pipe.

Multi-Pulse Heteroclinic Orbits and Chaotic Dynamics of Laminated Composite Piezoelectric Rectangular Plate

2009 ◽  
Author(s):  
Ming-Hui Yao ◽  
Wei Zhang ◽  
Dong-Xing Cao
Keyword(s):  
Normal Form ◽  
Chaotic Dynamics ◽  
Multiple Scales ◽  
Laminated Composite ◽  
Heteroclinic Orbits ◽  
Global Dynamics ◽  
Rectangular Plates ◽  
Internal Resonances ◽  
Chaotic Motions ◽  
Simply Supported

The multi-pulse orbits and chaotic dynamics of the simply supported laminated composite piezoelectric rectangular plates under combined parametric excitation and transverse loads are studied in detail. It is assumed that different layers are perfectly bonded to each other with piezoelectric actuator patches embedded. The nonlinear equations of motions for the laminated composite piezoelectric rectangular plates are derived from von Karman-type equation and third-order shear deformation laminate theory of Reddy. The four-dimensional averaged equation under the case of primary parametric resonance and 1:2 internal resonances is obtained by directly using the method of multiple scales and Galerkin approach to the partial differential governing equation of motion for the laminated composite piezoelectric rectangular plates. The system is transformed to the averaged equation. From the averaged equation, the theory of normal form is used to find the explicit formulas of normal form. Based on normal form obtained, the extended Melnikov method is utilized to analyze the multi-pulse global bifurcations and chaotic dynamics for the laminated composite piezoelectric rectangular plates. The analysis of global dynamics indicates that there exist the multi-pulse jumping orbits in the perturbed phase space of the averaged equation. From the averaged equations obtained, the chaotic motions and the Shilnikov type multi-pulse orbits of the laminated composite piezoelectric rectangular plates are found by using numerical simulation. The results obtained above mean the existence of the chaos for the Smale horseshoe sense for the simply supported laminated composite piezoelectric rectangular plates.

A Mathematical Model of Functionally Graded Materials Thin Plates and Levy Solutions

2013 ◽  
Vol 740 ◽  
pp. 574-577
Author(s):  
Ming Lu Wang
Keyword(s):  
Mathematical Model ◽  
Rectangular Plate ◽  
Thin Plate ◽  
Functionally Graded Materials ◽  
Governing Equation ◽  
Functionally Graded ◽  
Thin Plates ◽  
Graded Materials ◽  
Simply Supported ◽  
Static Responses

The governing equation of elastic FGM thin plates was obtained by degenerating the governing equation of viscoelastic FGM thin plates. A Levy solution of a simply supported FGM rectangular plate was gotten. Based on the Levy solution, the influence of considering and ignoring mid-plane stain, due to the inhomogeneous property of the functionally graded materials, on the static responses of the functionally graded materials thin plate is investigated.

Thermoelastic Deformations of Functionally Graded Materials Plates

2013 ◽  
Vol 740 ◽  
pp. 570-573
Author(s):  
Ming Lu Wang
Keyword(s):  
Thermal Stress ◽  
Rectangular Plate ◽  
Thin Plate ◽  
Functionally Graded Materials ◽  
Governing Equation ◽  
Functionally Graded ◽  
Thin Plates ◽  
Graded Materials ◽  
Navier Solution ◽  
Simply Supported

The governing equation of thermoelastic FGM thin plates was obtained by degenerating the governing equation of thermoviscoelastic FGM thin plates. A Navier solution of a simply supported FGM rectangular plate under thermal loads was get. Based on the Navier solution, the influence of considering and ignoring mid-plane stain, due to the inhomogeneous property of the functionally graded materials, on the maximal deflection and thermal stress of the functionally graded materials thin plate is investigated.

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.

Multi-Pulse Chaotic Dynamics of Laminated Composite Piezoelectric Rectangular Plate

2009 ◽  
Author(s):  
Wei Zhang ◽  
Ming-Hui Yao ◽  
Dong-Xing Cao
Keyword(s):  
Normal Form ◽  
Chaotic Dynamics ◽  
Multiple Scales ◽  
Laminated Composite ◽  
Type Equation ◽  
Global Dynamics ◽  
Rectangular Plates ◽  
Internal Resonances ◽  
Chaotic Motions ◽  
Simply Supported

The multi-pulse orbits and chaotic dynamics of the simply supported laminated composite piezoelectric rectangular plates under combined parametric excitation and transverse loads are studied in detail. It is assumed that different layers are perfectly bonded to each other with piezoelectric actuator patches embedded. The nonlinear equations of motions for the laminated composite piezoelectric rectangular plates are derived from von Karman-type equation and third-order shear deformation laminate theory of Reddy. The four-dimensional averaged equation under the case of primary parametric resonance and 1:2 internal resonances is obtained by directly using the method of multiple scales and Galerkin approach to the partial differential governing equation of motion for the laminated composite piezoelectric rectangular plates. The system is transformed to the averaged equation. From the averaged equation, the theory of normal form is used to find the explicit formulas of normal form. Based on normal form obtained, the extended Melnikov method is utilized to analyze the multi-pulse global bifurcations and chaotic dynamics for the laminated composite piezoelectric rectangular plates. The analysis of global dynamics indicates that there exist the multi-pulse jumping orbits in the perturbed phase space of the averaged equation. From the averaged equations obtained, the chaotic motions and the Shilnikov type multi-pulse orbits of the laminated composite piezoelectric rectangular plates are found by using numerical simulation. The results obtained above mean the existence of the chaos for the Smale horseshoe sense for the simply supported laminated composite piezoelectric rectangular plates.

The Levy Solution of Functionally Graded Materials Elastic Thin Plates

2013 ◽  
Vol 681 ◽  
pp. 329-332
Author(s):  
Feng Zheng ◽  
Ming Lu Wang
Keyword(s):  
Rectangular Plate ◽  
Thin Plate ◽  
Functionally Graded Materials ◽  
Governing Equation ◽  
Functionally Graded ◽  
Thin Plates ◽  
Graded Materials ◽  
Simply Supported ◽  
Static Responses

The governing equation of elastic FGM thin plates was obtained by degenerating the governing equation of viscoelastic FGM thin plates. A Levy solution of a simply supported FGM rectangular plate was gotten. Based on the Levy solution, the influence of considering and ignoring mid-plane stain, due to the inhomogeneous property of the functionally graded materials, on the static responses of the functionally graded materials thin plate is investigated.

Analysis of Thermal Deformations of FGM Thin Plates

2013 ◽  
Vol 681 ◽  
pp. 333-336
Author(s):  
Ming Lu Wang
Keyword(s):  
Thermal Stress ◽  
Rectangular Plate ◽  
Thin Plate ◽  
Functionally Graded Materials ◽  
Governing Equation ◽  
Functionally Graded ◽  
Thin Plates ◽  
Graded Materials ◽  
Navier Solution ◽  
Simply Supported

The governing equation of thermoelastic FGM thin plates was obtained by degenerating the governing equation of thermoviscoelastic FGM thin plates. A Navier solution of a simply supported FGM rectangular plate under thermal loads was get. Based on the Navier solution, the influence of considering and ignoring mid-plane stain, due to the inhomogeneous property of the functionally graded materials, on the maximal deflection and thermal stress of the functionally graded materials thin plate is investigated.

MULTIPULSE SHILNIKOV ORBITS AND CHAOTIC DYNAMICS FOR NONLINEAR NONPLANAR MOTION OF A CANTILEVER BEAM

2005 ◽  
Vol 15 (12) ◽  
pp. 3923-3952 ◽  
Author(s):  
MINGHUI YAO ◽  
WEI ZHANG
Keyword(s):  
Phase Space ◽  
Normal Form ◽  
Cantilever Beam ◽  
Parametric Resonance ◽  
Chaotic Dynamics ◽  
Phase Portraits ◽  
Phase Method ◽  
Global Dynamics ◽  
Governing Equations ◽  
Chaotic Motions

The multipulse Shilnikov orbits and chaotic dynamics for the nonlinear nonplanar oscillations of a cantilever beam are studied in this paper for the first time. The cantilever beam studied here is subjected to a harmonic axial excitation and two transverse excitations at the free end. The nonlinear governing equations of nonplanar motion with parametric and external excitations are obtained. The Galerkin procedure is applied to the partial differential governing equations to obtain a two-degree-of-freedom nonlinear system under combined parametric and forcing excitations. The resonant case considered here is principal parametric resonance-1/2 subharmonic resonance for the first mode and fundamental parametric resonance-primary resonance for the second mode. The parametrically and externally excited system is transformed to the averaged equation by using the method of multiple scales. From the averaged equation, the theory of normal form is used to find their explicit formulas. Based on normal form obtained above, the dissipative version of the energy-phase method is utilized to analyze the multipulse global bifurcations and chaotic dynamics for the nonlinear nonplanar oscillations of the cantilever beam. The energy-phase method is further improved to ensure the equivalence of topological structure for the phase portraits. The analysis of global dynamics indicates that there exist the multipulse jumping orbits in the perturbed phase space of the averaged equation for the nonlinear nonplanar oscillations of the cantilever beam. These results show that the multipulse Shilnikov type chaotic motions can occur for the nonlinear nonplanar oscillations of the cantilever beam. Numerical simulations are given to verify the analytical predictions. It is also found from the results of numerical simulation in three-dimensional phase space that the multipulse Shilnikov type orbits exist for the nonlinear nonplanar oscillations of the cantilever beam.

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