Mathematics (Jun 2022)
Largest Lyapunov Exponent Parameter of Stiffened Carbon Fiber Reinforced Epoxy Composite Laminated Plate Due to Critical Buckling Load Using Average Logarithmic Divergence Approach
Abstract
The purpose of this study is to calculate the bending deflection which is used to investigate the largest Lyapunov exponent due to buckling load. The design methodology is to calculate the largest Lyapunov exponent parameter at different thickness ratios and different fiber volume fractions using one and two stiffeners in order to reduce the chaotic phenomenon. The practical implication is to find the bending deflection using a strain gauge through a strain meter, in which this bending deflection is used in the algorithm of average logarithmic divergence to calculate the largest Lyapunov exponent experimentally. The experiment set up is carried out using Southwell plot when the upper head of the servo hydraulic cylinder moves downward. There are no limitations to this research, since it works on all kinds of composite materials, different thickness ratios, and different number of layers, different fiber volume fractions, and different boundary conditions. The findings of this work will allow us to detect the chaotic phenomenon in a stiffened carbon fiber reinforced epoxy composite laminated plate using the conception of the largest Lyapunov exponent parameter. The higher order shear deformation theory (HOSDT) of plates is used to analytically calculate the set of data of the bending deflection against time. All the systems used in this paper have non-periodic motion and chaos because the value of the Lyapunov parameter is above zero. The originality of this paper is the use of the algorithm code of average logarithmic divergence to investigate the value of the largest Lyapunov exponent parameter in the presence of stiffeners based on the bending deflection of a carbon epoxy composite laminated plate.
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