This paper presents a versatile platform named Variational Asymptotic Method (VAM), to model and analyze a piezoelectric cantilever sensor under static and dynamic load. Variational asymptotic method is a mathematically rigorous dimentional reduction methodology and has been previously used to model different structures which can be defined by an energy functional having one or more small inherent parameters; but, it has never been explicitly applied to capture the multiphysics behavior of a sensor. Piezoelectric based sensing technology has seen an explosive growth in the last decade with its various applications in different domain, such as energy harvesters, aerospace application, soft robotics, wind turbine, biomechanics, etc. So, an efficient mathematical model is highly required to get a better insight of the multiphysics behavior of an electromechanical structure. The present study highlights the capability of the theory to effectively capture the electromechanical response of a piezo-sensor under any static or dynamic load. The example problems considered in this present study include a single layer piezo-sensor as well as a double layer piezo-sensor bonded with aluminum. For static analysis, we have testified the model under a constant tip load. The discussed method effectively captures the voltage distribution across the thickness of the structure which is one of the fundamental parameter for a sensor model. The response accuracy obtained through variational asymptotic method is very good compared with the 3D simulation response performed in ABAQUS. For dynamic analysis a single layered piezo-sensor has been studied under a tip harmonic force. The structure response is studied for both damped as well as undamped conditions. Displacement and corresponding voltage output for specific excitation frequency which is close to its first natural frequency has been studied. The model efficacy under dynamic load has been validated with the experimental study performed by Ly et al. (2011). The present model has numerous potential applications like in PZT cantilever design for chemo-sensing, disease diagnostic, energy harvesting for self powered electronics, AFM higher harmonic imaging etc. The present theory along with the piezoelectric physics have been implemented in a modified version of VABS II (2004).
Banerjee, S., & Roy, S. (2016). Multiphysics analysis of an asymptotically correct piezoelectric sensor under static and dynamic load. International Journal of Solids and Structures, 92–93, 64–75. https://doi.org/10.1016/j.ijsolstr.2016.04.025