Analytical modeling of flexural vibrations and electromechanical coupling in a piezoelectric-coupled bladeless wind energy harvesting

This paper presents a three-dimensional analytical electromechanical model for the flexural vibrations of a fixed–free composite cantilever consisting of a long isotropic solid cylinder partially encased by a piezoelectric cylindrical tube. The model is motivated by piezoelectric bladeless wind energy harvesters, where vortex-induced vibrations are converted into electrical energy through electromechanical coupling. Unlike conventional beam-based models, the proposed formulation provides a closed-form analytical solution for the coupled mechanical and electrical fields. The governing equations of linear elasticity and piezoelectricity are solved using the method of separation of variables together with continuity, mechanical, and electrical boundary conditions. The analytical solution predicts the displacement, stress, electric potential, and voltage response under aerodynamic loading. Numerical examples for a PZT-4 piezoelectric tube are presented to investigate the influence of structural geometry on the electromechanical response. The results reveal two wave propagation regimes corresponding to coupled electromechanical and purely elastic waves with different phase velocities. A direct analytical relationship between the generated voltage and the lift force is established, while the influence of the tube aspect ratio on the electrical response is clarified. The proposed model provides a theoretical framework for the analysis and design of piezoelectric bladeless wind energy harvesting systems.