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

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.