Normalized Abacus for the Global Behavior of Diaphragms : Pneumatic, Electrostatic, Piezoelectric or Electromagnetic Actuation

The aim of this paper is to propose a complete normalized study of a diaphragm's behavior under classical excitation encountered in microsystem: pneumatic, electrostatic, piezoelectric and magnetic. The principle of modeling is widely described in order to be easily applied to other structure. First, a traditional analytical solution is recalled for the diaphragm's deflection based on energy minimization, through the use of a polynomial solution technique. Regarding the geometrical and physical parameters, three cases can be distinguished. They concern the diaphragm: acting as a pure plate, acting as a pure membrane, or exhibiting the effects of both elastic rigidity and initial internal stress. For these three cases, a standardization of the diaphragm's behavior under pneumatic actuation makes it possible to obtain an abacus that can then be used for any geometrical or physical parameter. The most interest of this paper is to establish simple abacuses for the diaphragm deflection under piezoelectric, magnetic or electrostatic actuation. The initial analytical formulae are obtained from the study of the physical phenomena. The abacuses for the piezoelectric and electromagnetic actuation can be deduced from the well known pneumatic actuation presented at the beginning of this paper. For the electrostatic actuation, the classical energy-based approach has been extended and allows to obtain abacuses for the center deflection, for the volume stroke and for the electrical capacitance. These abacuses have been compared with measurements made on silicon plates under electrostatic actuation. Although the results presented are obtained by making certain approximations, this study provides order of magnitude results for the deflection, and in particular it can be used to find the effect of each parameter (current, voltage, thickness, length, material properties, etc.). The use of these abacuses is easy and numerous potential applications exist: electrostatic or piezoelectric micropump, accelerometers, microphones, microspeaker, etc.