Subharmonic Resonances of Piezoelectrically Actuated Microcantilevers

An extensive frequency response and subharmonic resonance analysis of the equations of motion governing the nonlinear flexural vibrations of piezoelectrically actuated microcantilevers is performed, using the method of Multiple Scales. A better understanding of the nonlinear response and subharmonics of such systems is needed to enhance the applications of piezoelectrically actuated microcantilevers that are increasingly becoming popular in many science and engineering areas including scanning force microscopy, biosensors, and microactuators. In this paper, the method of multiple scales is used to derive the 2× and 3× subharmonic resonances appearing in nonlinear flexural vibrations of a piezoelectrically actuated microcantilever. The analytical and numerical results yield the same system response for the fundamental and subharmonic frequencies.