Theory of vibrating diaphragm-type pressure sensor

Abstract

In the present paper, we discuss the theory of vibrating diaphragm-type pressure sensors. Starting with the von Karman equation, the series solution of the problem of nonlinear bending of circular thin plates under the action of uniform pressure and uniform initial edge tension (preloaded) at the periphery is obtained. Based on this solution, small vibrations in the vicinity of the static equilibrium configuration are discussed. Here, a series method is suggested in which the characteristic value problem is reduced to a third-order algebraic characteristic value problem with explicit expression, and thus the characteristic value problem of axisymmetric free vibration is solved precisely. The characteristic curve of natural frequency vs pressure is obtained, which is of great interest for practical engineering applications.