Effect of Distributed Mass on the Node, Frequency, and Sensitivity of Resonant-Mode Based Cantilevers

We derived an analytical expression for a resonant-mode based bi-layered cantilever with distributed mass load. The behavior of mode of vibration, nodal position, frequency shift, as well as sensitivity under different mass load distributions was theoretically studied. The theoretical results suggested that asymmetric mass load distribution leads to the shift of nodes as well as the sensitive regions of a resonant-mode based cantilever. n − 1 local maximal sensitivities and n − 1 local minimal sensitivities are observed when the cantilever vibrates in the nth-order resonance. The maximal sensitivity is found at the first local maximal sensitivity and the behavior of mass load length as a function of the maximal sensitivity follows the rule of an exponent decaying function. The sensitivity increases as the load mass increases for the same mass load distribution, but the corresponding slopes are different.