Energy harvesting dynamic analysis of a piezoelectric beam under axially moving and spinning motions based on the Green’s functions

Abstract

Beams subjected to axial and spinning motions exhibit complex vibration characteristics that can be utilized for piezoelectric energy harvesting. This study investigates the harvesting performance of an axially compressed piezoelectric beam under coupled axial-spinning motions by establishing a continuous electromechanical model that, for the first time, incorporates both translational and rotational effects. Based on Euler–Bernoulli beam theory, the extended Hamilton principle, and PZT-5A constitutive relations, closed-form solutions of forced vibrations are derived using the Green’s function method and Laplace transform, and validated against experimental and benchmark results to ensure accuracy. The results reveal a remarkable synergistic effect: coupled axial-spinning motions significantly amplify voltage output by orders of magnitude and broaden the effective frequency bandwidth compared with single-motion cases, thereby overcoming the limitations of low amplitude and narrowband response in conventional harvesters. Parametric analyses further demonstrate the decisive influence of load resistance, axial velocity, spinning speed, and piezoelectric constants on system behavior and harvesting efficiency. This work not only develops a closed-form analytical framework for piezoelectric harvesters under dual-motion excitations but also establishes clear physical insights and design guidelines, providing a solid theoretical foundation for the development of high-performance energy harvesting devices in drilling, aerospace, precision machinery, and rotating engineering applications.