Subharmonics analysis of nonlinear flexural vibrations of piezoelectrically actuated microcantilevers

Using the method of multiple scales, an extensive frequency response and subharmonic resonance analysis of the equations of motion governing the nonlinear flexural vibrations of piezoelectrically actuated microcantilevers is performed. Such comprehensive understanding of the nonlinear response and subharmonics analysis of these microcantilevers is, indeed, justified by the applications of piezoelectrically actuated microcantilevers that are increasingly becoming popular in many science and engineering areas including scanning force microscopy, biosensors, and microactuators. Along this line, the method of multiple scales is used to derive the 2x and 3x subharmonic resonances appearing in nonlinear flexural vibrations of a piezoelectrically actuated microcantilever. An experimental examination is performed in order to verify the analytical results. The analytical and experimental results yield the same system response for the fundamental frequency. In addition, the experimental results demonstrate the presence of subharmonic resonances that are supported by numerical simulations of the equations of motion. The experimental mode shapes of these subharmonic frequencies are also measured and compared with fundamental frequency.