This paper aims to improve the existing electromechanically coupled analytical model that was developed for defect-induced phononic crystals (PnCs) designed for piezoelectric energy harvesting (PEH). The work outlined in this paper improves the model by considering lateral movements, which are not negligible when the slenderness ratio of the rods is small. Based on the Rayleigh-Love rod theory, the proposed method uses the generalized Hamilton's principle to derive two governing equations in the mechanical and electrical domains. An explicit form of the solutions to the governing equation is then used to derive an improved electromechanically coupled transfer matrix. Based on the transfer matrix method and the S-parameter method, the proposed electromechanically coupled analytical model enables the prediction of defect bands and PEH performance. To evaluate the predictive capabilities under a small slenderness ratio of the rods, the results from the proposed Rayleigh-Love rod-theory-based analytical model are compared with those found by the existing analytical model based on classical rod theory and by a finite element model. The novelties of the research outlined in this paper are as follows: 1) the proposed method considers, for the first time, lateral inertia in analytical modeling of defect-induced PnCs for PEH purposes and 2) three coefficients are newly presented to quantify the effects of lateral motions on the electromechanically coupled transfer matrix.

本文旨在改进现有的机电耦合分析模型，该模型是为专为压电能量收集 (PEH) 设计的缺陷诱导声子晶体 (PnC) 开发的。本文概述的工作通过考虑横向移动来改进模型，当杆的长细比很小时，横向移动是不可忽略的。该方法基于 Rayleigh-Love 棒理论，使用广义哈密顿原理推导出机械和电气领域的两个控制方程。然后使用控制方程解的显式形式导出改进的机电耦合传递矩阵。基于传递矩阵法和S参数法，所提出的机电耦合分析模型能够预测缺陷带和 PEH 性能。为了评估杆的小长细比下的预测能力，将提出的基于 Rayleigh-Love 杆理论的分析模型的结果与基于经典杆理论的现有分析模型和有限元模型的结果进行比较. 本文概述的研究的新颖之处如下：1) 所提出的方法首次考虑了用于 PEH 目的的缺陷诱导 PnCs 分析建模中的横向惯性和 2) 新提出的三个系数来量化影响机电耦合传递矩阵上的横向运动。将提出的基于 Rayleigh-Love 杆理论的分析模型的结果与基于经典杆理论的现有分析模型和有限元模型的结果进行比较。本文概述的研究的新颖之处如下：1) 所提出的方法首次考虑了用于 PEH 目的的缺陷诱导 PnCs 分析建模中的横向惯性和 2) 新提出的三个系数来量化影响机电耦合传递矩阵上的横向运动。将提出的基于 Rayleigh-Love 杆理论的分析模型的结果与基于经典杆理论的现有分析模型和有限元模型的结果进行比较。本文概述的研究的新颖之处如下：1) 所提出的方法首次考虑了用于 PEH 目的的缺陷诱导 PnCs 分析建模中的横向惯性和 2) 新提出的三个系数来量化影响机电耦合传递矩阵上的横向运动。