On the nonlinear-flexural response of piezoelectrically driven microcantilever sensors

This paper undertakes a comprehensive analysis and detailed comparative study of two types of microcantilever sensors (MCS). The first configuration is actuated using a piezoelectric stack embedded under the sensor base yielding a base-type actuation while the second is actuated via a piezoelectric ZnO layer deposited on the surface of the sensor. Along these lines, a comprehensive distributed-parameters nonlinear model that includes both geometric and material nonlinearities is developed. The method of multiple scales is then implemented to study the asymptotic behavior of the sensors' response. Results demonstrate that each of the aforedescribed sensors exhibits a completely different nonlinear behavior. More specifically, similar to a base-excited macrocantilever, the first mode of a base-excited MCS has a hardening-type behavior. On the other hand, the first vibration mode of the piezoelectrically actuated MCS has a softening-type response. This softening behavior can be attributed to the presence of quadratic material nonlinearities in the piezoelectric layer (ZnO here). Such nonlinearities, which describe the nonlinear relation between the stress and strain in some piezoelectric materials are usually neglected in the modeling of piezoelectrically actuated macrocantilever beams. Here, we demonstrate by extensive theoretical development and experimental results that material nonlinearities associated with ZnO materials are large and have a considerable effect altering the response from the commonly expected hardening to the softening type. As such, it becomes evident that such detailed and comprehensive-nonlinear modeling effort is a key step towards the design and development of practical MCS.