An Accurate Method for Designing Piezoelectric Energy Harvesters Based on Two-Dimensional Green Functions Under a Tangential Line Force

The piezoelectric coating structure constitutes the main configuration of contemporary energy harvesting systems, and its development requires accurate modeling of electromechanical coupling behavior under mechanical loads. The present work prepares a framework to analyze orthotropic piezoelectric coating–substrate systems; based on the fundamental solution theory, it derives two-dimensional Green functions from closed-form elementary functions. The formulation can establish the mesh-free solution paradigm through addressing tangential line force loading onto a coated surface. This method helps reconstruct full-field electromechanical responses upon arbitrary mechanical loading by integrating superposition principles and Gaussian quadrature technologies. An important application is in optimizing coating thickness, where parametric research suggests that piezoelectric layer geometry is non-linearly correlated with energy conversion efficiency. Notably, analytical sensitivity coefficients of this framework contribute to gradient-based optimization algorithms, which enhances efficiency compared with traditional empirical frameworks.