Frequency analysis of carbon-nanotube-based mass sensor using non-local Timoshenko beam theory

The characteristic equation of carbon-nanotube-based cantilever sensor with an attached mass is derived analytically using non-local Timoshenko beam theory. The relationship between the resonant frequency of the sensor and the attached mass can be obtained from the equation. The result shows that the effects of shear deformation and rotary inertia on the frequency of the sensor obviously increase when the mode number increases and the attached mass is small relative to the sensor. When the value of aspect ratio of the sensor is small, the effects of shear deformation and rotary inertia on the frequency are large particularly at high-order modes. In addition, the variation of frequency shift with the attached mass on the sensor is compared with the previous studies when the non-local effect is not taken into account.