Effect of temperature on vibrations and buckling behavior of carbon nanotube-based mass sensors using a new temperature-dependent structural model

Abstract

In last decade, structural mechanics (SM) approach has been one of the most known and effective tools for the determination of the mechanical properties of carbon nanotubes (CNTs) such as elastic modulus, shear modulus, natural frequency, and critical axial buckling strain. Considering increasing applications of CNTs as resonators at low and high temperatures, a new temperature-dependent structural mechanics model is presented here. The proposed model can be utilized to predict the effect of temperature on the mechanical response of CNTs as functional resonators. Mechanical and geometrical properties of equivalent beam element are correlated to the CNT's coefficient of thermal expansion (CTE). Owing to elaborate series of finite element simulations, the frequency shift of a CNTs-based mass sensor with different attached mass and aspect ratio in temperature range of 0–1600 K is calculated. Afterwards, the critical buckling temperature of CNTs-based mass sensor due to increasing the axial force by changing ambient temperature is obtained. Results show that decreasing the first natural frequency is clearly appeared by attaching a mass more than about 1 zg on the CNTs structure. In other words, CNTs can be used to detect particles with mass above 1 zg. Moreover, it is shown that the variation of CTE versus temperature is a critical parameter that influences the vibration and buckling behavior of CNTs-based mass sensors. Increasing temperature leads to decreasing natural frequency due to rising axial forces along the CNTs axis. As a result, the natural frequency approaches to zero when the temperature rises up to the critical buckling temperature. In addition, increase in temperature over the critical buckling temperature changes the mode shape of CNT vibration to the next mode shape.