Modal analysis of microcantilever sensors with environmental damping

The vibration response of microcantilevers to simple harmonic base motion is formulated in terms of base motion plus modal responses relative to the moving base frame. Environmental damping is evaluated. The analysis gives the frequency responses of the first four modes and shows that the phase angle of each mode relative to the moving base frame is constant but that the phase angle of the absolute motion varies along the length of cantilevers. This finding is verified with experimental data. Phase changes along cantilevers depend on frequency ratios and the magnitude of environmental damping. Experimental data are used to establish damping factors, and phase angles are measured experimentally and compared with theoretical predictions.