Uncertainty analysis and stochastic characterization of carbon nanotube-based mass sensor with multiple deposited nanoparticles

Abstract

Input uncertainties on the location, mass, and geometry of multiple deposited nanoparticles for carbon nanotube-based mass sensor are investigated. The carbon nanotube (CNT) is modeled as an Euler-Bernoulli beam with end constrained boundary conditions and Eringen’s nonlocal elasticity theory to account for size-dependent phenomena. Additionally, the displacement field of the CNT is broken up into components to the left and right of each deposited particle. Utilizing the Hamilton’s principle and the discretized displacement fields, the nonlocal governing equations of motion, boundary conditions, and continuity conditions at the deposited particle locations are derived. The effects of the particle location, mass, and geometry on the inherent frequency shifts before and after deposition are studied. Following these parametric studies, sensitivity analysis and uncertainty quantification methods are applied for two different nominal configurations of the mass sensor. The importance of the input parameters is deeply discussed, focusing especially on the location effects on the first and second natural frequency shifts. It is shown that increasing the mass and size of the particle increases the overall frequency shift, while varying the location of the particles does not strictly lead to increased frequency shifts. Finally, it is shown that due to the high number of input parameters, there are multiple particle configurations that lead to identical frequency shifts. These findings may be used by other researchers to extend the usability, usefulness, and characterization of mass detection devices.