Guided wave propagation in piezoelectric bars with parallelogram cross-section: An improved double orthogonal polynomial approach

Hui Qiao, Xianhui Wang, Xiaoming Zhang and Weihong Ren

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 248, issue C, 644-667

Abstract: In this study, we propose an improved double Legendre polynomial series approach (IDLPSA) to analyze the elastic wave propagation characteristics in piezoelectric bars with parallelogram cross-sections, a novel geometric configuration that significantly enhances electromechanical coupling and energy distribution compared to traditional rectangular cross-sections. The IDLPSA introduces two key innovations: (1) the direct imposition of boundary conditions through partial integration and local coordinate transformation, which transforms the problem into a stable and easily solvable linear eigenvalue system, and (2) the development of an analytical integration technique that replaces time-consuming numerical integration, drastically improving computational efficiency. Validation against COMSOL simulations confirms the accuracy and efficiency of the proposed method. Notably, the parallelogram cross-section design demonstrates a remarkable increase over 100% in the electromechanical coupling coefficient at specific frequencies. Furthermore, at low frequencies, increasing the tilt angle of the parallelogram enhances the energy proportion of the quasi-E0 mode while maintaining a high electromechanical coupling factor, offering a promising approach for optimizing acoustic device performance. This work not only provides a highly efficient and accurate analytical framework for studying complex piezoelectric structures, but also opens new avenues for designing high-performance acoustic devices with improved energy conversion efficiency. The findings hold significant practical application value for advancing piezoelectric technology and academic research significance for exploring wave propagation in non-traditional geometries.

Keywords: Guided waves; Legendre polynomial; Piezoelectric bars with parallelogram cross-section; Dispersion; Electromechanical coupling factor (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:248:y:2026:i:c:p:644-667

DOI: 10.1016/j.matcom.2026.04.033

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