Chaos and Bifurcation of Composite Laminated Cantilever Rectangular Plate

2012 ◽  
Author(s):  
Wei Zhang ◽  
Minghui Zhao ◽  
Xiangying Guo
Keyword(s):  
Rectangular Plate ◽  
Deformation Theory ◽  
Complex Dynamics ◽  
Equations Of Motion ◽  
Plate Boundary ◽  
Shear Deformation Theory ◽  
Governing Equations ◽  
Chaotic Motions ◽  
Cantilever Rectangular Plate ◽  
Two Degree Of Freedom

According to the Reddy’s high-order shear deformation theory and the von-Karman type equations for the geometric nonlinearity, the chaos and bifurcation of a composite laminated cantilever rectangular plate subjected to the in-plane and moment excitations are investigated with the case of 1:2 internal resonance. A new expression of displacement functions which can satisfy the cantilever plate boundary conditions are used to make the nonlinear partial differential governing equations of motion discretized into a two-degree-of-freedom nonlinear system under combined parametric and forcing excitations, representing the evolution of the amplitudes and phases exhibiting complex dynamics. The results of numerical simulation demonstrate that there exist the periodic and chaotic motions of the composite laminated cantilever rectangular plate. Finally, the influence of the forcing excitations on the bifurcations and chaotic behaviors of the system is investigated numerically.

scholarly journals Nonlinear Vibration of the Blade with Variable Thickness

2020 ◽  
Vol 2020 ◽  
pp. 1-18 ◽  
Author(s):  
Xiaobo Jie ◽  
Wei Zhang ◽  
Jiajia Mao
Keyword(s):  
Variable Thickness ◽  
Conical Shell ◽  
Deformation Theory ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Dynamic Responses ◽  
Nonlinear Ordinary Differential Equations ◽  
Nonlinear Relationship ◽  
Governing Equations ◽  
First Order

In this paper, the nonlinear dynamic responses of the blade with variable thickness are investigated by simulating it as a rotating pretwisted cantilever conical shell with variable thickness. The governing equations of motion are derived based on the von Kármán nonlinear relationship, Hamilton’s principle, and the first-order shear deformation theory. Galerkin’s method is employed to transform the partial differential governing equations of motion to a set of nonlinear ordinary differential equations. Then, some important numerical results are presented in terms of significant input parameters.

Bifurcations and Chaos of Composite Laminated Piezoelectric Rectangular Plate With One-to-Three Internal Resonance

2008 ◽  
Author(s):  
Zhi-Gang Yao ◽  
Wei Zhang
Keyword(s):  
Rectangular Plate ◽  
Multiple Scales ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Governing Equations ◽  
Third Order ◽  
Chaotic Motions ◽  
Piezoelectric Layers ◽  
Parametric And External Excitations ◽  
First Time

The bifurcations and chaotic motions of a simply supported symmetric cross-ply composite laminated piezoelectric rectangular plate are analyzed for the first time, which are forced by the transverse and in-plane excitations. It is assumed that different layers of symmetric cross-ply composite laminated piezoelectric rectangular plate are perfectly bonded to each other and with piezoelectric actuator layers embedded in the plate. Based on the Reddy’s third-order shear deformation plate theory, the nonlinear governing equations of motion for the composite laminated piezoelectric rectangular plate are derived by using the Hamilton’s principle. The excitation loaded by piezoelectric layers is considered. The Galerkin’s approach is employed to discretize partial differential governing equations to a two-degree-of-freedom nonlinear system under combined the parametric and external excitations. The method of multiple scales is utilized to obtain the four-dimensional averaged equation. Numerical method is used to find the periodic and chaotic motions of the composite laminated piezoelectric rectangular plate. The numerical results show the existence of the periodic and chaotic motions in the averaged equation. It is found that the chaotic responses are especially sensitive to the forcing and the parametric excitations. The influence of the transverse, in-plane and piezoelectric excitations on the bifurcations and chaotic behaviors of the composite laminated piezoelectric rectangular plate is investigated numerically.

Resonant Chaotic Dynamics of a Symmetric Cross-Ply Composite Laminated Plate Under Transverse and In-Plane Excitations

2020 ◽  
Vol 30 (07) ◽  
pp. 2050106
Author(s):  
W. S. Ma ◽  
W. Zhang
Keyword(s):  
Nonlinear System ◽  
Chaotic Dynamics ◽  
Equations Of Motion ◽  
Degree Of Freedom ◽  
Laminated Plate ◽  
Governing Equations ◽  
Partial Differential ◽  
Chaotic Motions ◽  
Composite Laminated Plate ◽  
Two Degree Of Freedom

The resonant chaotic dynamics of a symmetric cross-ply composite laminated plate are studied using the exponential dichotomies and an averaging procedure for the first time. The partial differential governing equations of motion for the symmetric cross-ply composite laminated plate are derived by using Reddy’s third-order shear deformation plate theory and von Karman type equation. The partial differential governing equations of motion are discretized into two-degree-of-freedom nonlinear systems including the quadratic and cubic nonlinear terms by using Galerkin method. There exists a fixed point of saddle-focus in the linear part for two-degree-of-freedom nonlinear system. The Melnikov method containing the terms of the nonhyperbolic mode is developed to investigate the resonant chaotic motions of the symmetric cross-ply composite laminated plate. The obtained results indicate that the nonhyperbolic mode of the symmetric cross-ply composite laminated plate does not affect the critical conditions in the occurrence of chaotic motions in the resonant case. When the resonant chaotic motion occurs, we can draw a conclusion that the resonant chaotic motions of the hyperbolic subsystem are shadowed for the full nonlinear system of the symmetric cross-ply composite laminated plate.

A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations

2017 ◽  
Vol 21 (6) ◽  
pp. 1906-1929 ◽  
Author(s):  
Abdelkader Mahmoudi ◽  
Samir Benyoucef ◽  
Abdelouahed Tounsi ◽  
Abdelkader Benachour ◽  
El Abbas Adda Bedia ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Elastic Foundation ◽  
Deformation Theory ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Refined Theory ◽  
Governing Equations

In this paper, a refined quasi-three-dimensional shear deformation theory for thermo-mechanical analysis of functionally graded sandwich plates resting on a two-parameter (Pasternak model) elastic foundation is developed. Unlike the other higher-order theories the number of unknowns and governing equations of the present theory is only four against six or more unknown displacement functions used in the corresponding ones. Furthermore, this theory takes into account the stretching effect due to its quasi-three-dimensional nature. The boundary conditions in the top and bottoms surfaces of the sandwich functionally graded plate are satisfied and no correction factor is required. Various types of functionally graded material sandwich plates are considered. The governing equations and boundary conditions are derived using the principle of virtual displacements. Numerical examples, selected from the literature, are illustrated. A good agreement is obtained between numerical results of the refined theory and the reference solutions. A parametric study is presented to examine the effect of the material gradation and elastic foundation on the deflections and stresses of functionally graded sandwich plate resting on elastic foundation subjected to thermo-mechanical loading.

scholarly journals Higher-Order Thermo-Elastic Analysis of FG-CNTRC Cylindrical Vessels Surrounded by a Pasternak Foundation

Nanomaterials ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 79 ◽  
Author(s):  
Masoud Mohammadi ◽  
Mohammad Arefi ◽  
Rossana Dimitri ◽  
Francesco Tornabene
Keyword(s):  
Deformation Theory ◽  
Volume Fraction ◽  
Effective Properties ◽  
Shear Deformation Theory ◽  
Pressure Vessels ◽  
Functionally Graded ◽  
Elastic Response ◽  
Governing Equations ◽  
Third Order ◽  
Reinforced Composite

This study analyses the two-dimensional thermo-elastic response of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) cylindrical pressure vessels, by applying the third-order shear deformation theory (TSDT). The effective properties of FG-CNTRC cylindrical pressure vessels are computed for different patterns of reinforcement, according to the rule of mixture. The governing equations of the problem are derived from the principle of virtual works and are solved as a classical eigenproblem under the assumption of clamped supported boundary conditions. A large parametric investigation aims at showing the influence of some meaningful parameters on the thermo-elastic response, such as the type of pattern, the volume fraction of CNTs, and the Pasternak coefficients related to the elastic foundation.

scholarly journals Unified theory of beam bending within flexoelectricity with including piezoelectricity

2020 ◽  
Vol 310 ◽  
pp. 00063
Author(s):  
Vladimir Sladek ◽  
Jan Sladek
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Electric Polarization ◽  
Unified Theory ◽  
Key Factors ◽  
Governing Equations ◽  
Proper Selection ◽  
Beam Bending ◽  
Selection Of

The behaviour of small size dielectric elastic beams is described within higher-grade theory with including electric polarization. The coupling between strain gradients and polarization is incorporated into the constitutive laws in the form of flexoelectricity, while piezoelectricity is involve in the classical form. Both the governing equations and boundary conditions are derived using variational formulation for electro-elastic continuous media and deformation assumptions employed in three various beam bending theories such as the classical theory (Euler-Bernoulli theory), the 1st order shear deformation theory (Timoshenko theory) and 3rd order shear deformation theory. The unified formulation allows switching between theories with various bending assumptions by a proper selection of two key factors.

Nonlinear Dynamic of Cantilever Functionally Graded Plates Under the Thermalmechanical Loads

2009 ◽  
Author(s):  
Yu-xin Hao ◽  
Wei Zhang ◽  
Jian-hua Wang
Keyword(s):  
Nonlinear System ◽  
Functionally Graded Materials ◽  
Nonlinear Dynamic ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Degree Of Freedom ◽  
Mode Shapes ◽  
Governing Equations ◽  
Graded Materials ◽  
Two Degree Of Freedom

An analysis on nonlinear dynamic of a cantilevered functionally graded materials (FGM) plate which subjected to the transverse excitation in the uniform thermal environment is presented for the first time. Materials properties of the constituents are graded in the thickness direction according to a power-law distribution and assumed to be temperature dependent. In the framework of the Third-order shear deformation plate theory, the nonlinear governing equations of motion for the functionally graded materials plate are derived by using the Hamilton’s principle. For cantilever rectangular plate, the first two vibration mode shapes that satisfy the boundary conditions is given. The Galerkin’s method is utilized to discretize the governing equations of motion to a two-degree-of-freedom nonlinear system under combined thermal and external excitations. By using the numerical method, the two-degree-of-freedom nonlinear system is analyzed to find the nonlinear responses of the cantilever FGMs plate. The influences of the thermal environments on the nonlinear dynamic response of the cantilevered FGM plate are discussed in detail through a parametric study.

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.

Dynamic Response of Cantilever FGM Cylindrical Shell

2011 ◽  
Vol 130-134 ◽  
pp. 3986-3993 ◽  
Author(s):  
Yu Xin Hao ◽  
Wei Zhang ◽  
L. Yang ◽  
J.H. Wang
Keyword(s):  
Cylindrical Shell ◽  
Volume Fraction ◽  
Nonlinear Oscillations ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Governing Equations ◽  
Temperature Dependent ◽  
Graded Materials ◽  
First Order ◽  
Two Degree Of Freedom

An analysis on the nonlinear dynamics of a cantilever functionally graded materials (FGM) cylindrical shell subjected to the transversal excitation is presented in thermal environment.Material properties are assumed to be temperature-dependent. Based on the Reddy’s first-order shell theory,the nonlinear governing equations of motion for the FGM cylindrical shell are derived using the Hamilton’s principle. The Galerkin’s method is utilized to discretize the governing partial equations to a two-degree-of-freedom nonlinear system including the quadratic and cubic nonlinear terms under combined external excitations. It is our desirable to choose a suitable mode function to satisfy the first two modes of transverse nonlinear oscillations and the boundary conditions for the cantilever FGM cylindrical shell. Numerical method is used to find that in the case of non-internal resonance the transverse amplitude are decreased by increasing the volume fraction index N.

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