An accurate design method for the piezoelectric energy harvesters based on the two-dimensional Green’s functions under a tangential line force

Piezoelectric-coated structures constitute the predominant configuration in contemporary energy harvesting systems, necessitating precise modeling methodologies for their electromechanical coupling behavior under mechanical loading. This study develops an analytical framework for orthotropic piezoelectric-coating substrate systems, deriving two-dimensional Green’s functions in closed-form elementary functions through fundamental solution theory. The formulation specifically addresses tangential line force loading on the coated surface, establishing a mesh-free solution paradigm. The proposed methodology enables reconstruction of full-field electromechanical responses under arbitrary mechanical loading through superposition principles integrated with Gaussian quadrature techniques. Numerical validation demonstrates superior computational attributes, achieving solution accuracy relative to finite element benchmarks while reducing computation time. A critical application lies in coating thickness optimization, where parametric studies reveal a nonlinear correlation between piezoelectric layer geometry and energy conversion efficiency. The framework’s analytical sensitivity coefficients facilitate gradient-based optimization algorithms, yielding efficiency enhancement over conventional empirical designs. These advancements establish a rigorous theoretical foundation for performance prediction in piezoelectric energy harvesters while providing engineers with computationally efficient design tools for thin-film device engineering applications. Mathematics Subject Classification. 74F10.