Second Order Models of Circular Pressure Detecting Elements and a Dynamical Model of Pressure Sensor Systems

Abstract

The second order approximate model (i.e., equivalent vibrating piston model) is obtained for the circular pressure detecting elements such as an edge-clamped membrane and a similar thin plate. The spring constant of the model is defined by the force for making the unit average-displacement of the detecting element. The mass of the model is not the real value of the element, but the effective mass modified by the first order eigenvalue of the element. For a membrane the effective mass is given by 8m^m/α_m1²(≈1.3833m_m) where m^m is the real mass and α^ml is the eigenvalue. For a plate the effective mass is 192m_p/α_p1⁴(≈1.8400m_p) where m_p is the real mass and α_p1 is the eigenvalue.
A dynamical model for pressure sensor systems, which is composed of the radiation impedance of the vibrating piston in a infinite baffle plate contacted with gas or liquid, the second order model mentioned above and the impedance of an air cavity behind the vibrating piston, is also presented in order to analyze the static and dynamic characteristics of the system. The natural frequencies, the static displacement gain and the static pressure gain of the pressure sensor systems are obtained by the use of the dynamical model.