Energy-Based Solution Method for the Global Behavior of Diaphragms under Pneumatic and Electrostatic Pressure

摘要

In this paper, an approximate analytical solution is presented for the diaphragm's deflection based on energy minimization, through the use of a polynomial solution technique. Thanks to this method, we obtain not only the center deflection, but also the entire position under pneumatic pressure, thereby making it possible to compute the diaphragm's deflected volume. Regarding the geometrical and physical parameters, three cases can be distinguished, with the diaphragm: acting as a pure plate, acting as a pure membrane, or exhibiting the effects of both the elastic rigidity and the initial internal stress. For these three cases, a standardization of the diaphragm's behavior enables obtaining an abacus that can then be used for any geometrical or physical parameter. In order to validate this approach, some comparisons with other methods are performed. This energy-based approach has been extended to electrostatic actuation and yields more general results than do other more classical methods (i.e., the spring model). Lastly, a behavioral comparison of both the membrane and plate cases is presented for a conformable mirror with electrostatic actuation.