Dynamical transitions between periodicity, quasiperiodicity, and chaos drive performance changes in a hybrid galloping energy harvester

Abstract

This research investigates the relationship between complex dynamical transitions and average output power (AOP) in a hybrid galloping energy harvester (HGEH) featuring a vertically aligned D-shaped bluff body. The model of the HGEH is developed using Hamilton's principle. Based on the derived equations, the nonlinear dynamical behaviors and AOP variations are systematically analyzed with respect to four parameters associated with base excitation and wind energy. Nine distinct patterns of dynamical transitions between periodicity, quasiperiodicity, and chaos are identified, playing a crucial role in inducing jumps in periodic frequencies. Between two transitions, the HGEH remains in periodic vibration with a stable frequency over a broad parameter range, determining an upper limit for AOP growth. In most cases, the occurrence of quasiperiodic and/or chaotic vibrations in transitional regions causes abrupt, often opposing shifts or zigzags in the AOP curve. As a result, while the overall trend of the AOP curve shows a rise with varying parameters, the emergence of dynamical transitions makes the curve go like “resting between climbing stairs”. Furthermore, when wind speed varies, the maximum AOP is frequently achieved at peak points corresponding to period-3 vibrations. This study may provide valuable insights for optimizing HGEHs with D-shaped bluff bodies to enhance broadband concurrent energy harvesting.