The effects of flow velocity on the vibration frequency and mode shape of the fluid-conveying single-walled carbon nanotube are analyzed using nonlocal elastic theory. Results show that the frequency and mode shape are significantly influenced by the nonlocal parameter e 0 a / L. Increasing the nonlocal parameter decreases the real component of frequency and the decrease is more obvious for a lower flow velocity and a higher-order mode. In addition, a higher mode shape is observed with increasing the value of e 0 a / L. When a critical flow velocity is reached, the combination of first and second modes takes place. The mode shape for the combination is large relative to mode 3 due to the coupled frequency effect, especially including negative imaginary frequency. Furthermore, the mode shape of the combination increases as the nonlocal effect increases.
The potential of using graphene as a nanomechanical resonator is explored. A graphene-resonator sensor is assumed to be a simply supported rectangular plate. The frequency equation of the sensor with an attached mass is derived analytically using nonlocal elasticity theory. The results indicate that increasing the nonlocal parameter markedly increases the frequency shift of the sensor, and the frequency shift becomes larger as the aspect ratio approaches 1. Therefore, in order to obtain the highest sensitivity, a square geometrical sensor should be used. The mass sensitivity can reach up to 10-27 g/Hz.
The frequency equation of carbon-nanotube-based cantilever sensor with an attached mass is derived analytically using nonlocal elasticity theory. According to the equation, the relationship between the frequency shift of the sensor and the attached mass can be obtained. When the nonlocal effect is not taken into account, the variation of frequency shift with the attached mass on the sensor is compared with the previous study. According to this study, the result shows that the frequency shift of the sensor increases with increasing the attached mass. When the attached mass is small compared with that of the sensor, the nonlocal effect is obvious and increasing nonlocal parameter decreases the frequency shift of the sensor. In addition, when the location of the attached mass is closer to the free end, the frequency shift is more significant and that makes the sensor reveal more sensitive. When the attached mass is small, a high sensitivity is obtained.
The modal frequencies of flexural vibration for an atomic force microscope (AFM)
cantilever have been evaluated using the Timoshenko beam theory, and a closed-form
expression for the frequencies of vibration modes has been obtained. In the analysis, the
effect of the ratios of different cantilever dimensions on frequency for the cantilever were
studied. The results show that increasing the ratio of cantilever thickness and
length decreases the vibration frequency. Increasing the ratio of the tip length
and cantilever length also increases the frequency. In addition, results using the
Bernoulli–Euler beam theory and the Timoshenko beam theory are compared. It can be
found that the Timoshenko beam theory is able to predict the frequencies of
flexural vibration of the higher modes with higher contact stiffness for the AFM
cantilever.
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