SIMPLE VISUALIZATION THEORY FOR INVESTIGATING THE MECHANICAL BEHAVIOR OF A NOVEL FIBER

Abstract

In this paper, a simple theoretical and visualized explanation of a novel fiber with their mechanical behaviors have been derived to investigate a novel fabricated fibers made by the changing a natural garbage structure. By solving a simple string theory consisted of two to three coupled differential equations, the internal frequencies (w) and the fiber string constants (k) of two different fiber structures which have a uniform fiber structure and a not uniform fibers structure, respectively were obtained as follows: ω_1,2 = ± 7.312 Hz, for the value of k₁ = k₂ = k = 0.46 kg/s², and ω_1,2 = ± 12.657 Hz, for the values of k₁ = 0.5 kg/s², and k₂ = 0.426 kg/s². While the w and k of three different fiber structures in one fiber were found in the following values: ω_1,2 = ± 7.313 Hz, for k₁ = 1.974 kg/s², k₂ = 0.353 kg/s², and  k₃ = 0.989 kg/s² , and ω_1,2 = ± 7.313 Hz, for the value of k₁ = k₂ =k₃ = k = 0.69 kg/s², respectively. In addition, by incorporating a scientific mathematica 10.3 software, the visualizations from the coupled-two and coupled-three differential equations closely related to mechanical fiber behaviors produce the amplitude (A) ratio in those coupled equations.