Analytical modeling of tribo/piezoelectric transducers for energy harvesting from slow plant movements

• A new model to estimate output energy by a cantilevered piezoelectric single-layer. • A new model to estimate output energy by a cylindrical triboelectric transducer. • Harness energy from the small movements of plant leaves and branches in the wind. • Analytical tests show the potential of the biomimetic energy harvesting devices. • Applications in smart agriculture and the conservation of historic gardens. This paper introduces two new analytical approaches to estimate the electromechanical energy conversion capability of two different systems: one that uses a cantilevered piezoelectric transducer with a single layer of piezoelectric material and the other that employs a sliding triboelectric transducer with cylindrical elements. The first one proposes a simplified model of a cantilever piezoelectric beam, focusing on its first vibration mode, and incorporates a simplified assumption for the neutral axis position in a single-layer beam, providing a theoretical foundation for designing self-powered sensing systems. The second model introduces, for the first time in the literature, a predictive framework for voltage generation from sliding cylindrical structures made of triboelectric materials. Both systems are designed to be moved by the small oscillations of the leaves and branches of plants shaken by wind. Three sheets of piezoelectric material were developed to simulate leaves of three different sizes. Analytical test results show a theoretical generation of 1.8 mV for the medium-size leaf and 7 mV for the branches. The triboelectric transducer operates at an oscillation frequency of 1 Hz. Through the synergy between the two types of transducers, a theoretical power of 0.27 nW has been estimated for small oscillations (2.2 mm) imposed on the leaves, with branch oscillations occurring at a frequency of 1 Hz. These results will highlight the suitability of the proposed environmentally friendly and mimetic energy harvesting devices, sparking interest across various sectors, including smart agriculture, distributed measurement systems, and the preservation of cultural heritage and historical gardens