Nonlinear Dynamics of A Piezoelectrically-actuated Microcantilever Sensor
NanoMechanical Cantilever Sensors (NMCS) have recently emerged as an effective means for label-free chemical and biological species detection. They operate through the adsorption of species on the functionalized surface of cantilevers. Through this functionalization, molecular recognition is directly transduced into a micromechanical response. In order to effectively utilize these sensors in practice, the chief technical issue related to modeling must be addressed in order to correctly relate the micromechanical response to the adsorbed species. Along this line of reasoning, this paper presents a general nonlinear-comprehensive modeling framework for piezoelectrically-actuated microcantilevers and validate it both analytically and experimentally. The proposed model considers both longitudinal and flexural vibrations of the microcantilever sensor and their coupling in addition to the ever-present nonlinearities due to geometry of the microcantilever. More specifically, it is demonstrated that the electromechanical coupling in these sensors is also nonlinear which appears in quadratic form. Through extensive experimental measurements, the coefficient of such quadratic nonlinear term is determined which compares well with both analytical and numerical results. Taking into account the inextensibility feature of such sensors, the coupled longitudinal and flexural equations of motion are reduced to one nonlinear flexural equation. The resultant nonlinear equation of motion is then solved using the method of Multiple Scales to arrive at the frequency response of the system, analytically. Consequently, the system response to a number of periodic excitations with different amplitudes is experimentally and analytically investigated which matches the analytical results very well. Finally, the frequency response results clearly demonstrate the presence of nonlinear quadratic term in electromechanical coupling in these sensors. This is a critical observation when designing and employing such sensors in practice.