Nonlinear vibration in resonant silicon bridge pressure sensor: Theory and experiment

Nonlinear dynamics of a resonant silicon bridge pressure sensor with resistive heating excitation has been investigated. Nonlinear vibration model of the microbridge resonator in the sensor is developed by Euler-Bernoulli beam modeling. Besides nonlinear geometric effect, the model also takes the measured pressure, the heating effect of the resistive heating excitation, and the residual stress into account. Approximate solutions for this model are derived via Galérkin procedure and perturbation methods. From the solution, a bending parameter is extracted to quantitatively evaluate the bending of the microbridge amplitude-frequency response. Dependence of the bending parameter on the sensor operating conditions is examined analytically and experimentally. Analytical and experimental results show good agreement qualitatively. Frequency output error of the sensor due to nonlinear vibration is also calculated. And several suggestions on sensors design and operation with respect to nonlinear effects are proposed.