Why the center-point of bridged carbon nanotube length is the most mass sensitive location for mass attachment?

The continuum mechanics method and a bending model were used to obtain the resonant frequencies of bridged single-walled carbon nanotubes (SWCNTs) with masses rigidly attached at various positions along the tube. The frequency response equations were derived using the Euler–Bernoulli theory. The resonant frequency decreased as the mass was increased, and the mass sensitivity increased as the attachment position approached the center of the bridged tube. The validity and accuracy of the equations were compared to other mass sensor models described in the literature. These new sensor equations may be used to model the behavior of CNT-based biosensors with reasonable accuracy. As a result, center point of bridged carbon nanotube is the most sensitive location for mass attachment.