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.

Nonlinear Dynamics Behavior of a Pear Cam With Roller Follower Mechanism

2019 ◽  
Author(s):  
Louay S. Yousuf ◽  
Dan B. Marghitu
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Analysis ◽  
Lyapunov Exponent ◽  
Periodic Motion ◽  
Angular Speed ◽  
Largest Lyapunov Exponent ◽  
Infrared Sensor ◽  
The Largest Lyapunov Exponent

Abstract A pear cam and roller follower system is studied for distinct values of cam rotational speeds. Different values of clearance (C = 1, 1.5, and 2 mm) are used. SolidWorks is used for the numerical analysis. The largest Lyapunov exponent was calculated for the mechanism and the non-periodic motion is analyzed for different clearances and angular speeds. The displacement of follower motion is processed using OPTOTRAK / 3020 with a 3-D infrared sensor experimentally. The system with clearance C = 2 mm has largest value of (LLE) at N = 400 rpm, while the lowest value of (LLE) is at N = 100 rpm at the same value of angular speed.

The Dynamics of a Flexible Levitated Droplet

2001 ◽  
Author(s):  
Mihai Dupac ◽  
Dan B. Marghitu ◽  
David G. Beale
Keyword(s):  
Nonlinear Dynamics ◽  
Time Series ◽  
Lyapunov Exponent ◽  
Time Series Data ◽  
Simulated Data ◽  
Series Data ◽  
Largest Lyapunov Exponent ◽  
Dynamics Analysis ◽  
Attractor Dimension ◽  
Levitated Droplet

Abstract In this paper, a nonlinear dynamics analysis of the simulated data was considered to study the time evolution of an electro-magnetically levitated flexible droplet. The main goals of this work are to study the behavior of the levitated droplet and to investigate its stability. Quantities characterizing time series data such as attractor dimension or largest Lyapunov exponent were computed.

ON THE WAVELET TRANSFORM APPLICATION TO A STUDY OF CHAOTIC VIBRATIONS OF THE INFINITE LENGTH FLEXIBLE PANELS DRIVEN LONGITUDINALLY

2009 ◽  
Vol 19 (10) ◽  
pp. 3347-3371 ◽  
Author(s):  
J. AWREJCEWICZ ◽  
A. V. KRYSKO ◽  
V. SOLDATOV
Keyword(s):  
Nonlinear Dynamics ◽  
Lyapunov Exponent ◽  
Chaotic Dynamics ◽  
Wavelet Spectrum ◽  
Largest Lyapunov Exponent ◽  
Infinite Length ◽  
Continuous Wavelets ◽  
Linear Vibrations ◽  
Plate Strip ◽  
Flexible Panels

Both classical Fourier analysis and continuous wavelets transformation are applied to study non-linear vibrations of infinitely long flexible panels subject to longitudinal sign-changeable external load actions. First the governing PDEs are derived and then the Bubnov–Galerkin method is applied to yield 2N first order ODEs. The further used Lyapunov exponent computation is described. Transition scenarios from regular to chaotic dynamics of the being investigated plate strip are analyzed using different wavelets, and their suitability and advantages/disadvantages to nonlinear dynamics monitoring and quantifying are illustrated and discussed. A few novel results devoted to the beam nonlinear dynamics behavior are reported. In addition, links between the largest Lyapunov exponent computation and the wavelet spectrum numerical estimation are also illustrated and discussed.

Buckling Analysis of Stitched and Unstitched Glass Epoxy Composites

2011 ◽  
Vol 337 ◽  
pp. 594-597
Author(s):  
R. Muruganandhan ◽  
Murali Vela
Keyword(s):  
Epoxy Composite ◽  
Composite Plates ◽  
Buckling Load ◽  
Epoxy Composites ◽  
Laminated Plate ◽  
Critical Buckling Load ◽  
Composite Laminated Plate ◽  
Finite Element Software ◽  
Aspect Ratios ◽  
Teflon Film

In this paper, the effects of delamination on critical buckling load failure of unidirectional E-glass/epoxy composite laminated plate consisting of delamination at the middle of the mid plane were studied. Experimental work was carried out to determine the buckling load for rectangular composite plates consisting of delamination for various aspect ratios ranging from 0.5 to 3. Stitched and unstitched laminates were prepared by introducing inplane delamination at the mid of the mid plane using Teflon film. These specimens were made with unidirectional fiber of orientation of (0o/-45o/45o/90o)s with single inplane delamination at the mid of the mid plane of through width and various lengths of 130 mm and 50 mm. The Plates were made to buckle experimentally by simply supporting the top and bottom edges, and sides were kept free. Buckling load has been found from the graph. The critical buckling load is found to be increased in the stitched laminates when compared with unstitched laminates and is decreased in both stitched and unstitched laminates as the aspect ratio increases. The experimental results were validated by using commercial finite element software of ANSYS.

scholarly journals Nonlinear Dynamics of an Unsymmetric Cross-Ply Square Composite Laminated Plate for Vibration Energy Harvesting

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1261
Author(s):  
Guoqing Jiang ◽  
Ting Dong ◽  
Zhenkun Guo
Keyword(s):  
Thermal Stress ◽  
Energy Harvesting ◽  
Periodic Motion ◽  
Stable Equilibrium ◽  
Excitation Amplitude ◽  
Laminated Plate ◽  
Base Excitation ◽  
Composite Laminated Plate ◽  
Piezoelectric Patch ◽  
Nonlinear Behaviors

The nonlinear behaviors and energy harvesting of an unsymmetric cross-ply square composite laminated plate with a piezoelectric patch is presented. The unsymmetric cross-ply square composite laminated plate has two stable equilibrium positions by applying thermal stress, thus having snap-through with larger amplitude between the two stable equilibrium positions relative to the general laminated plate. Based on the von-Karman large deformation theory, the nonlinear electromechanical coupling equations of motion of the unsymmetric composite laminated plate with a piezoelectric patch are derived by using Hamilton’s principle. The influence of the base excitation amplitude on nonlinear behaviors and energy harvesting are investigated. For different base excitation amplitudes, the motions of the system demonstrate periodic motion, quasi-periodic motion, chaotic motion and snap-through, and two single-well chaotic attractors and a two-well chaos attractor coexist. Moreover, the power generation efficiency is optimal when the excitation amplitude is in a certain range due to its own unique nonlinear characteristics. The unsymmetric cross-ply square composite laminated plate subjected to thermal stress can actually be called a kind of bistable composite shell structure that has a broad application prospect in combination with morphing aircraft, large deployable antenna and solar panel, which are very likely to have nonlinear vibration.

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.

Lyapunov Exponent for a Globoidal Cam With a Roller Follower Mechanism Using Wolf Algorithm

2020 ◽  
Author(s):  
Louay S. Yousuf ◽  
Dan B. Marghitu
Keyword(s):  
Numerical Simulation ◽  
Fourier Transform ◽  
Lyapunov Exponent ◽  
Angular Velocity ◽  
Fast Fourier Transform ◽  
Periodic Motion ◽  
Phase Plane ◽  
Largest Lyapunov Exponent ◽  
Cam Follower ◽  
The Impact

Abstract A globoidal cam and roller follower system is analyzed and discussed for non-periodic motion of the follower. Wolf algorithm is used to calculate the largest Lyapunov exponent. The impact between the cam, follower and the two guides is occurred due to the impulse and momentum phenomenon. The effect of the internal dimension of the follower guide on the non-periodic motion of the follower is considered at distinct angular velocity of the cam. The numerical simulation has been done using SolidWorks software. Follower movement is processed experimentally through an infrared 3-D camera device. Phase plane diagram is used to explain the variation in follower motion. Phase-plane diagram and Fast Fourier Transform (FFT) are used to investigate follower non-periodicity. The follower motion is non-periodic when the orbit of phase-plane diagram diverges with no limit of spiral cycles.

scholarly journals Nonlinear dynamics behavior of cam-follower system using concave curvatures profile

2020 ◽  
Vol 12 (9) ◽  
pp. 168781402094592
Author(s):  
Louay S Yousuf ◽  
Dan B Marghitu
Keyword(s):  
Nonlinear Dynamics ◽  
Lyapunov Exponent ◽  
Damping Ratio ◽  
Three Dimensional ◽  
Largest Lyapunov Exponent ◽  
Momentum Theory ◽  
Cam Follower ◽  
Cam Profile ◽  
The Impact ◽  
Contact Parameters

Nonlinear dynamics behavior of the roller follower is discussed for different follower guides’ internal dimensions and cam angular speeds. A dynamic tool such as Wolf algorithm is used to extract largest Lyapunov exponent parameter. Positive value of Lyapunov exponent parameter indicates non-periodic motion and chaos. The influence of flank curvature of the cam profile on the nonlinear dynamic behavior of the roller follower is investigated. Impulse and momentum theory is used to describe the impact phenomenon based on the contact force between the follower and its guides. Contact parameters such as exponent, sliding contact velocity, contact bodies stiffness, penetration, and damping ratio are used in SolidWorks software to simulate follower movement numerically. Experiment setup has been done by taking into consideration the use of an infrared three-dimensional camera device through a high precision optical sensor. The follower motion is non-periodic when the cross-linking of phase-plane diagram diverges with no limit of spiral cycles.

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