Natural vibration frequencies of silicon diaphragms

It is postulated that the behavior of square and rectangular silicon diaphragms used in pressure sensors is governed by a Lagrange-Newton differential system. Estimation of the natural vibration frequencies using Galerkin´s method shows that the anisotropic characteristic of silicon does not significantly influence the results. Excitation and detection of the first vibration modes are carried out in a straightforward manner with a capacitive sensor whose fixed plate features an array structure. Measurements of the first natural vibration frequencies and those predicted by the Newton-Lagrange model are in good agreement. The reduced Young´s modulus given by these experiments is fifteen percent higher than the one generally reported in the literature. It is concluded that capacitive devices are well suited for the study of silicon diaphragm vibrations.<>