Mechanical behaviour of micromachined sensor membranes under uniform external pressure affected by in-plane stresses using a Ritz method and Hermite polynomials

The mechanical behaviour (deflection and eigenvalues) of orthotropic micromachined sensor membranes under the combined action of out-of-plane pressure and internal in-plane stresses is discussed in this paper. Hermite polynomials of eighth order are used in combination with a Ritz method in order to solve the specific mechanical problems mentioned above. The solution procedure is presented and the results show excellent agreement with those obtained by other methods. In particular, simulations that have been carried out with the finite-element program ANSYS confirm this fact. The method presented here results in a quick, flexible and very accurate approximation of the mechanical behaviour. Furthermore, measurements of the centre deflection of sensor membranes are presented. A comparison with the theoretical results shows that the method used here leads to a sufficient prediction of the real deflection behaviour. Additionally, eigenfrequencies are evaluated and excellent agreement with the literature is also found in this case.