Figure 4.

Schematic of piezoelectric resonators for (a) stiffened k₃₃-mode and (b) unstiffened k₃₁-mode. The particle vibration displacement is parallel to the direction of polarization in stiffened modes, while for unstiffened modes the particle vibration displacement is perpendicular to the polarization. The red arrows denote the direction of particle vibration displacement u and the blue ones denote the macroscopic polarization P of piezoelectric materials. A 3×6 schematic matrix describing vibration modes is given in (c), where the stiffened modes are underlined and marked as red while the blue ones are unstiffened modes.