Electroelastically coupled stiffness matrix method for phononic crystals with piezoelectric defects and its applications to filters, sensors, and energy harvesters

Abstract

This study presents a comprehensive analytical framework for one-dimensional phononic crystals (PnCs) integrated with piezoelectric defects, leveraging an electroelastically coupled stiffness matrix under longitudinal wave propagation. This matrix effectively captures the mechanical coupling between defects and piezoelectric devices, as well as the piezoelectric coupling within the devices, providing a robust foundation for predicting key behaviors such as band structures, defect mode shapes, and frequency responses. The stiffness matrix method employed in this study overcomes the numerical instabilities inherent in traditional transfer matrix approaches, thereby enhancing the reliability and precision of the framework. The versatility of the proposed framework is evident in its application across diverse engineering domains, including tunable bandpass filters, high-sensitivity ultrasonic sensors, and energy harvesters. The accuracy of the model is validated through finite-element simulations, which demonstrates significantly reduced computation times. To encourage further research and practical implementation, the study provides MATLAB codes. This study establishes the foundation for extending the framework to bending waves, miniaturized PnCs, and oblique wave propagation scenarios.