Optimization of Length and Thickness of Smart Transduction Layers on Beam Structures for Control and M/NEMS Applications

This work addresses the optimization of the geometry of smart sensors and actuators on cantilever beams. Three transduction principles are studied and compared in term of efficiency: piezoelectric, electrostatic and dielectric. For the piezoelectric transduction, an active layer of a shorter length than the one of the beam is added on its surfaces. For the electrostatic transduction, the beam is made of a conducting material and it is faced with a fixed electrode at a distance called the gap. This architecture is widely used for M/NEMS (Micro/Nano ElectroMechanical Systems). The last transduction principle, new and promising, is based on the use of dielectric layers on the beam surface. In this case, the excitation is based on electrostatic forces between the charged electrodes, causing transverse deformation of the dielectric film and bending of the multilayer structure; the detection of the vibration is capacitive, based on the fluctuation of the capacitance due to the deformation of the dielectric film. This work presents the optimization of the length and the thickness of the piezoelectric/dielectric layers and, for the electrostatic case, the optimization of the length and the gap of the electrostatic cavity. The study is based on an analytic model for a laminated beam and closed-form formula of the optimization parameters (coupling factor, driving efficiency, sensing efficiency) are obtained. The application of those three transduction principles mainly focus on resonating M/NEMS sensors, whereas the case of piezoelectric transduction is also useful for vibration control of macro-structures, especially with passive shunt techniques. General results on the comparison of the transduction efficiency, as a function of the device size and of the material properties, are also derived.