Study of node and mass sensitivity of resonant mode based cantilevers with concentrated mass loading

Resonant-mode based cantilevers are an important type of acoustic wave based mass-sensing devices. In this work, the governing vibration equation of a bi-layer resonant-mode based cantilever attached with concentrated mass is established by using a modal analysis method. The effects of resonance modes and mass loading conditions on nodes and mass sensitivity of the cantilever were theoretically studied. The results suggested that the node did not shift when concentrated mass was loaded on a specific position. Mass sensitivity of the cantilever was linearly proportional to the square of the point displacement at the mass loading position for all the resonance modes. For the first resonance mode, when mass loading position xc satisfied 0 < xc < ∼ 0.3l (l is the cantilever beam length and 0 represents the rigid end), mass sensitivity decreased as the mass increasing while the opposite trend was obtained when mass loading satisfied ∼0.3l ≤ xc ≤ l. Mass sensitivity did not change when concentrated mass was loaded at the rigid end. This work can provide scientific guidance to optimize the mass sensitivity of a resonant-mode based cantilever.