Free vibration for a micro resonant pressure sensor with cross-type resonator

In this paper, a cross resonator pressure sensor is proposed to improve the detection accuracy of capacitor-detecting sensor. Considering electrostatic force and molecular force, the multi-field coupled dynamic equation of the sensor is established. By solving the dynamic equation, the equations for the mode function and the natural frequencies of the resonator are obtained. Using these equations, the natural frequency and mode function of the sensor are given. Changes of natural frequency of sensor with main parameters are studied. Influence of molecular force on the natural frequency is analyzed. Results show that within a considerable range of pressure, the natural frequencies increase approximately linearly with pressure. Under small pressure, small initial distance between resonator and base, and lower order modes, effects of the Van der Waals force on the natural frequencies are quite obvious.