输送粘性流体的嵌入式碳纳米管振动中的非线性现象

Reza Ebrahimi
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引用次数: 0

摘要

碳纳米管响应中的各种非线性现象,如分岔和混沌,被认为是导致纳米机械系统不精确和不稳定的主要原因。因此,本文的主要目的是预测在非线性弹性基础上承载粘性流体的碳纳米管的非线性动力行为。该模型基于非局部欧拉-伯努利梁理论。采用伽辽金方法和摄动分析分别对运动偏微分方程进行离散化,得到频率响应方程。对非局部参数、基础系数、流体粘度、外力振幅和频率对系统非线性动力学的影响进行了详细的参数化研究。通过振动时程、频率响应曲线、分岔图、相位图、功率谱和庞加莱图揭示了亚谐波、准周期和混沌行为以及硬化非线性。结果表明,通过选择合适的参数,可以消除整个外力振幅范围内的不规则运动。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Nonlinear phenomena in vibrations of embedded carbon nanotubes conveying viscous fluid
Various nonlinear phenomena such as bifurcations and chaos in the responses of carbon nanotubes (CNTs) are recognized as being major contributors to the inaccuracy and instability of nanoscale mechanical systems. Therefore, the main purpose of this paper is to predict the nonlinear dynamic behavior of a CNT conveying viscous fluid and supported on a nonlinear elastic foundation. The proposed model is based on nonlocal Euler–Bernoulli beam theory. The Galerkin method and perturbation analysis are used to discretize the partial differential equation of motion and obtain the frequency-response equation, respectively. A detailed parametric study is reported into how the nonlocal parameter, foundation coefficients, fluid viscosity, and amplitude and frequency of the external force influence the nonlinear dynamics of the system. Subharmonic, quasi-periodic, and chaotic behaviors and hardening nonlinearity are revealed by means of the vibration time histories, frequency-response curves, bifurcation diagrams, phase portraits, power spectra, and Poincaré maps. Also, the results show that it is possible to eliminate irregular motion in the whole range of external force amplitude by selecting appropriate parameters.
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