Automated mode chart generation for finite element analysis of piezoelectric resonators using principal component analysis based on clustering

Abstract

This paper presents a new clustering method for identifying the vibration mode shapes of piezoelectric resonators using image processing and principal component analysis (PCA). The finite element method (FEM) is an indispensable tool for analyzing the vibration-displacement distribution of resonators and suppressing spurious vibration modes. Although the FEM exports eigenfrequencies as a list, including spurious vibration modes, recognizing the vibration shape of each eigenfrequency requires manual operation by operators to view the displacement distribution and identify the vibration shapes. The proposed method consists of a preprocessing step based on a threshold selection before the PCA step. Preprocessing significantly simplifies the vibration displacement distribution and reduces the amount of data required for post-processing PCA. The mode chart of the AT-cut quartz crystal resonator obtained using the proposed method agreed with Koga’s experimental results. The proposed method enables the generation of mode charts with reduced processing and computational resources.