Abstract

This novel study presents a framework to investigate the effects of transient heat conduction on the nonlinear deflection and vibration of single-walled carbon nanotubes (SWCNTs) based on Eringen’s nonlocal elasticity and nonlocal heat conduction theories. The first phase of this research involves modifying the hyperbolic heat conduction theory by including a nonlocality term, in which the scale of energy transport is taken into account. The next phase includes a thermoelasticity solution for carbon nanotubes (CNTs), which is developed by Eringen’s nonlocal theory and implementing the obtained temperature. The differential quadrature method (DQM) is used to solve the transversely induced nonlocal heat conduction. We have shown the effect of thermal waves on the mode shapes and nonlinear vibration of a SWCNT by considering phase lag parameters. All boundaries are considered under a temperature-jump at the nanometer scale to consider the boundary phonon scattering. The effects of several parameters, including time-dependent boundary conditions, time lag, nonlocal parameter, length and radius, and end supports on the frequency response of SWCNTs are investigated.

摘要

这项新颖的研究提出了一个框架，基于 Eringen 的非局域弹性和非局域热传导理论，研究瞬态热传导对单壁碳纳米管 (SWCNT) 的非线性偏转和振动的影响。这项研究的第一阶段涉及通过引入非定域项来修改双曲热传导理论，其中考虑了能量传输的规模。下一阶段包括碳纳米管 (CNT) 的热弹性解决方案，该解决方案由 Eringen 的非局域理论开发并实现所获得的温度。微分求积法（DQM）用于求解横向引起的非局部热传导。我们通过考虑相位滞后参数，展示了热波对单壁碳纳米管模态形状和非线性振动的影响。所有边界均在纳米尺度的温度跳跃下考虑，以考虑边界声子散射。研究了几个参数的影响，包括时间相关边界条件、时滞、非局部参数、长度和半径以及端部支撑对单壁碳纳米管频率响应的影响。