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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.

Nonlocal thermoelasticity: Transient heat conduction effects on the linear and nonlinear vibration of single-walled carbon nanotubes