Abstract

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.