Free vibration of micromembranes subject to prestress and pressure

Circular micromembranes, subject to in-plane tension and transverse pressure and, actuated by a piezoelectric film, are modeled via a geometrically exact approach that accounts for finite motions. The free vibration properties (i.e., frequencies and mode shapes) about the nonlinear equilibrium due to the in-plane prestress state and the pressure field are investigated in a wide range of pressures to purposefully explore the nonlinear range. Given the pronounced hardening membrane nonlinearity, there is a high sensitivity of the fundamental frequency with respect to the applied pressure. This is due to the nonlinear increase of the membrane tension caused by the pressure. Analytical laws can be obtained by curve fitting to describe the variation of the membrane lowest frequencies with the prestress tension and the applied pressure. Such laws are useful in feasibility studies on the design of micromembranes as pressure sensors.