Nonlocal Mechanics Based Computational Methods for Nano-mechanical Sensors (Keynote Address)

Technology behind nano-scale mass sensor has been growing rapidly in the recent years. This paper outlines a non-local mechanics based computational approach by which using the frequency-shift of the fundamental vibration mode the mass on an attached object can be predicted. We develop new nonlocal frequency sensor equations utilizing energy principles. Two physically realistic configurations of the added mass, namely, point mass and distributed masses are considered. Exact closed-form expressions relating the frequency-shift and the added mass have been derived for both the cases. The proposed nonlocal sensor-equation is general in nature and depends on three non-dimensional calibrations constants namely, the stiffness calibration constant, the mass calibration constant and the nonlocal calibration constant. Explicit analytical expressions of these calibration constants are derived. An example of a single wall carbon nanotube with attached multiple strands of deoxythimidine is considered to illustrate the analytical results. Molecular mechanics simulation is used to validate the new nonlocal sensor equations. The optimal values of nonlocal parameter are obtained from the molecular mechanics simulation results. The nonlocal approach generally predicts the frequency shift accurately compared to the local approach. Numerical results show the importance of considering the distributed nature of the added mass while using the nonlocal theory.