Wave propagations and high-frequency vibrations in intrinsically mode-reconfigurable resonator by a spatial polarization tailoring

This article investigates wave propagation and high-frequency vibrations in intrinsically mode-reconfigurable acoustically coupled resonators. By leveraging the electrically switchable polarization direction of piezoelectric films, we achieve complementary excitations in the fundamental thickness-extensional and second thickness-extensional modes, with a frequency ratio approaching two. Dispersion equations for bulk wave propagation in mode-reconfigurable resonators under two polarization states are derived and solved using the bisection method. Through analysis of mode shapes, including mechanical displacements, electric potential, stresses, and electric displacement, we reveal the underlying mechanical mechanism enabling complementary harmonic excitations when the piezoelectric films are poled in the same or opposite directions. Furthermore, mode-coupled vibrations in resonators operating with different harmonic modes are studied based on the higher-order stress balance principle. Frequency spectrograms characterizing mode-coupling intensities under different polarization states are obtained, allowing us to identify desirable harmonic vibration modes with weak coupling for radio-frequency applications. Additionally, desirable length-to-thickness ratios are determined to guide structural designs of mode-reconfigurable resonators. These findings provide critical insights into the operational mechanisms and vibration control strategies in mode-reconfigurable resonators, advancing their implementation in tunable radio-frequency systems.