Modeling of PMUTs with Non-Uniform Membrane Based on The Variational Principle

This paper presents a new modeling approach for piezoelectric micromachined ultrasonic transducers (PMUTs) with clamped annular edge based on the variational principle. A piecewise cubic polynomial approximation method is used to effectively fit the eigenmodes of both uniform and non-uniform PMUTs at their first resonant frequency, achieving a relative accuracy of less than 0.1% when compared to the theoretical model for uniform membrane design. Additionally, the paper highlights the significance of patterning the piezoelectric layer to optimize eigenmode vibration shape of the PMUT membrane, enhance the effective acoustic transmission, and improve the electrode excitation efficiency. These findings offer valuable insights for optimizing PMUT design.