The analytical studies and chaotic behavior of forced vibration on Single-wall Carbon Nanotubes (SWCNTs) embedded in nonlinear viscous elastic medium subjected to parametric excitation are investigated. The analytical solution of the amplitude of nonlinear vibration is studied using Krylov–Bogoliubov–Mitropolsky (KBM) method. Both resonant and nonresonant cases are deduced. The computational techniques are used to draw graphs of time series, phase plot and Poincaré surface of section to analyze the chaotic behavior of the system considered. The plots are drawn for various values of different parameters like linear damping, nonlinear damping and amplitude of external forces in the considered model of SWCNTs. This work could be helpful in differentiating various elements of Carbon Nanotubes (CNTs) into the chaotic elements and controlling elements. The chaotic elements contributes to increase in the aging of CNTs while controlling elements can be used to control the irregular behavior of CNTs.

中文翻译：

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嵌入非线性粘弹性介质中的单壁碳纳米管及其各种参数的混沌效应分析研究

研究了嵌入非线性粘性弹性介质中的单壁碳纳米管（SWCNTs）受参量激发时受迫振动的解析研究和混沌行为。使用 Krylov-Bogoliubov-Mitropolsky (KBM) 方法研究非线性振动幅度的解析解。共振和非共振情况都被推导出来。计算技术用于绘制时间序列图、相位图和截面庞加莱曲面图，以分析所考虑系统的混沌行为。在所考虑的单壁碳纳米管模型中，绘制了不同参数的各种值，如线性阻尼、非线性阻尼和外力幅度。这项工作有助于将碳纳米管（CNT）的各种元素区分为混沌元素和控制元素。