Analysis of Flutter and Nonlinear Dynamics of a Composite Laminated Plate

2016 ◽  
Vol 16 (06) ◽  
pp. 1550019 ◽  
Author(s):  
J. Chen ◽  
Q. S. Li
Keyword(s):  
Nonlinear Dynamics ◽  
Mach Number ◽  
Rectangular Plate ◽  
Limit Cycle Oscillation ◽  
Laminated Plate ◽  
Governing Equations ◽  
Chaotic Motions ◽  
Critical Mach Number ◽  
Composite Laminated Plate ◽  
Transverse Excitation

This paper presents the analysis of flutter and nonlinear dynamics of an orthotropic composite laminated rectangular plate subjected to aerodynamic pressures and transverse excitation. The first-order linear piston theory is employed to model the air pressures. Based on Reddy’s third-order shear deformation plate theory and von Karman-type equation for the geometric nonlinearity, the nonlinear governing equations of motion are derived for the composite laminated rectangular plate by applying the Hamilton’s principle. The Galerkin method is utilized to discretize the partial differential governing equations to a set of nonlinear ordinary differential equations. The critical Mach number for occurrence of the flutter of the composite laminated plate is investigated by solving the eigenvalues problem. The relationship between the limit cycle oscillation and the critical Mach number is analyzed based on the nonlinear equations. The numerical simulation is conducted to study the influences of the transverse excitation on the nonlinear dynamics of the composited laminated plate. The numerical results, which include bifurcation diagram, phase plots and waveforms, demonstrate that there exist the bifurcation and chaotic motions of the composited laminated plate subjected to the aerodynamic pressures and the transverse excitation.

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.

Nonlinear Dynamics Simulation of Bending Deflection for Composite Laminated Plate Under Varied Temperature Using Lyapunov Exponent Parameter

2021 ◽  
Author(s):  
Louay S. Yousuf
Keyword(s):  
Nonlinear Dynamics ◽  
Lyapunov Exponent ◽  
Periodic Motion ◽  
Dynamics Simulation ◽  
Largest Lyapunov Exponent ◽  
Laminated Plate ◽  
Fiber Volume ◽  
Composite Laminated Plate ◽  
Volume Fractions ◽  
Aspect Ratios

Abstract This paper study the nonlinear dynamics behavior of the bending deflection of composite laminated plate based on largest Lyapunov exponent parameter. Wolf algorithm is used to quantify largest Lyapunov exponent in the presence of aspect ratios and fiber volume fractions. A power spectrum analysis has been added using the amplitude of Fast Fourier Transform (FFT) to detect the non-periodic motion of the bending deflection of the composite plate. The simulation process is done using ANSYS software Ver. 18.2. The temperature gradient of thermal shock is varied between (60C° and −15C°) through the laminate thickness. The experiment setup has been done through heating and cooling rig test environment. The non-periodic motion of the bending deflection is decreased with the increasing of aspect ratios, while the non-periodic motion of the bending deflection is increased wit the increasing of fiber volume fractions.

Chaotic Dynamics in a Higher-Dimensional Nonlinear System for a Composite Laminated Plate

2009 ◽  
Author(s):  
Wei Zhang ◽  
Mei-juan Gao
Keyword(s):  
Numerical Simulation ◽  
Nonlinear System ◽  
Normal Form ◽  
Chaotic Dynamics ◽  
Phase Method ◽  
Laminated Plate ◽  
Internal Resonances ◽  
Chaotic Motions ◽  
Composite Laminated Plate ◽  
Higher Dimensional

In this paper, we first analyze the chaotic dynamics of a higher-dimensional nonlinear system for a composite laminated plate in the case of 1:3:3 internal resonances with the theory of normal form and the energy-phase method. The theory of normal form is used to obtain the simpler normal form of the system. The energy-phase method is employed to analyze the multi-pulse chaotic dynamics of the higher-dimensional nonlinear system for a composite laminated plate. Moreover, the numerical simulation is performed to find the multi-pulse chaotic motion of the composite laminated plate. The global theory analysis and the results of numerical simulation demonstrate that the existence of the periodic motions and chaotic motions with the jumping phenomena in the composite laminated plate.

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.

scholarly journals Modeling and Chaotic Dynamics of the Laminated Composite Piezoelectric Rectangular Plate

2014 ◽  
Vol 2014 ◽  
pp. 1-19 ◽  
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.

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.

Multi-Pulse Chaotic Dynamics of a Composite Laminated Plate with Strong Coupling

2014 ◽  
Vol 548-549 ◽  
pp. 431-437
Author(s):  
Y. Zhao ◽  
W. Xu ◽  
J.H. Zhang
Keyword(s):  
Strong Coupling ◽  
Chaotic Dynamics ◽  
Nonlinear Dynamical System ◽  
Melnikov Method ◽  
Laminated Plate ◽  
Chaotic Motions ◽  
Nonlinear Dynamical ◽  
Simply Supported ◽  
Composite Laminated Plate ◽  
Two Degree Of Freedom

In this paper, the multi-pulse chaotic dynamics of a simply-supported symmetric cross-ply composite laminated rectangular plate with the parametric and forcing excitations is investigated by using the extended Melnikov method. The two-degree-of-freedom non-autonomous nonlinear dynamical system of the plate with strong coupling is considered. The results obtained here indicate that multi-pulse chaotic motions can occur in the plate. Numerical simulation is also employed to find the multi-pulse chaotic motions of the plate based on the theoretical analysis.

ABOUT CONSTRUCTION OF FLAT BODIES WITH INCREASED CRITICAL MACH NUMBER

2016 ◽  
Vol 47 (6) ◽  
pp. 563-579
Author(s):  
Sergey Alexandrovich Takovitskii
Keyword(s):  
Mach Number ◽  
Critical Mach Number

Nonlinear Vibrations of Two-Span Composite Laminated Plates with Equal and Unequal Subspan Lengths

2017 ◽  
Vol 9 (6) ◽  
pp. 1485-1505
Author(s):  
Lingchang Meng ◽  
Fengming Li
Keyword(s):  
Multiple Scales ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Laminated Plates ◽  
Laminated Plate ◽  
Composite Laminated Plate ◽  
Vibration Localization ◽  
Composite Laminated Plates ◽  
Localization Phenomenon ◽  
Harmonic Resonance

AbstractThe nonlinear transverse vibrations of ordered and disordered two-dimensional (2D) two-span composite laminated plates are studied. Based on the von Karman's large deformation theory, the equations of motion of each-span composite laminated plate are formulated using Hamilton's principle, and the partial differential equations are discretized into nonlinear ordinary ones through the Galerkin's method. The primary resonance and 1/3 sub-harmonic resonance are investigated by using the method of multiple scales. The amplitude-frequency relations of the steady-state responses and their stability analyses in each kind of resonance are carried out. The effects of the disorder ratio and ply angle on the two different resonances are analyzed. From the numerical results, it can be concluded that disorder in the length of the two-span 2D composite laminated plate will cause the nonlinear vibration localization phenomenon, and with the increase of the disorder ratio, the vibration localization phenomenon will become more obvious. Moreover, the amplitude-frequency curves for both primary resonance and 1/3 sub-harmonic resonance obtained by the present analytical method are compared with those by the numerical integration, and satisfactory precision can be obtained for engineering applications and the results certify the correctness of the present approximately analytical solutions.

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