Dynamic Modeling and Control of Integrated Micro- and Nano- systems: A.1. Coupled Flexural-Torsional Nonlinear Vibrations of PZT-actuated Microcantilevers: The problem of coupled flexural-torsional nonlinear vibrations of a piezoelectrically-actuated microcantilever beam as a typical configuration utilized in microcantilever-based sensing

The problem of coupled flexural-torsional nonlinear vibrations of a piezoelectrically-actuated microcantilever beam as a typical configuration utilized in microcantilever-based sensing is being investigated. The actuation and sensing are both facilitated through bonding a piezoelectric layer (here, ZnO) on the microcantilever surface. Considering different geometrical configurations for the beam, it is demonstrated that how beam geometry or piezoelectric properties can bring different nonlinear coupling terms into the equations. An experimental setup consisting of a commercial piezoelectric microcantilever installed on the stand of an ultramodern laser-based microsystem analyzer is designed and utilized to verify the theoretical developments. First and second flexural natural frequencies are experimentally obtained, which are shown to be in good agreement with their theoretical values. Both linear and nonlinear simulation results are compared with experimental results and it is observed that nonlinear modeling response matches the experimental findings very closely. More importantly, it is disclosed that the initial twisting in the microcantilever can influence the value of the flexural vibration resonance. Such unique and unexplored coupling effect may lead to the possibility of indirectly measuring small torsional vibration without the need for any angular displacement sensor. This observation could significantly extend the application of friction force microscopy to measure the friction of a surface indirectly.