Effects of thermal loads representations on the dynamics and characteristics of carbon nanotubes-based mass sensors

Uniform, linear, and nonlinear temperature gradients are considered to perform buckling and vibration analyses of carbon nanotube (CNT)-based mass sensors modeled as a clamped-clamped Euler-Bernoulli nanobeam with a deposited atomic-scale particle. Size dependent effects are taken into account using the Eringen's nonlocal elasticity theory. Employing the Hamilton's principle, the governing equations of motion considering the three types of temperature distribution are derived. To investigate the effects of various thermal loadings on the mass detection sensitivity of clamped CNT-mass detectors, four distinct noble gas atoms, namely Helium (He), Neon (Ne), Argon (Ar), and Krypton (Kr) with very low chemical reactivity are considered as attached atomic-scale masses. The influence of important parameters, such as the length and diameter of the CNT, the deposited mass and its location, the nonlocal parameter, the surface temperature difference, the temperature rise, and the type of temperature distribution on the errors in thermal buckling loads and frequency shifts are also studied. Assessing the impacts of the inaccuracies of uniform and linear temperature distributions on the critical thermal buckling load and the frequency shift of the CNT-based mechanical resonator is the primary contribution of the work. The numerical results indicate that in the pre-buckling region, the assumptions of uniform and linear temperature distributions through the thickness of the CNT estimate higher values of the natural frequency and the frequency shift compared to the nonlinear temperature gradient. On the contrary, the nonlinear thermal gradient across the radius of the CNT-based mass detector yields the largest values of the frequency shift and hence the highest mass detection sensitivities of the CNT-based mass sensor in the post-buckling configuration.