Dynamics of pendula system interacting with an electromagnetic shaker: Effects of parameter mismatch

This paper investigates the dynamics of a two-coupled pendula system subjected to non-ideal vertical harmonic excitation generated by an electromagnetic shaker. The novelty of this study lies in establishing the dynamic bases for coupled pendula systems capable of sustaining stable rotational motions under non-ideal harmonic excitations, such as those characterising ocean wave conditions. This approach broadens the operational frequency range of pendulum-based wave energy converters (WECs) and enhances their robustness for efficient energy harvesting in harsh marine environments. The study aims to identify different types of dynamic responses for a wide range of parametric excitation, with particular emphasis on the effects of a parameter mismatch. The investigation focuses on the existence, stability, and robustness of phase-synchronised rotational motions, motivated by potential applications in wave energy harvesting devices. A four mechanical and half electrical degrees-of-freedom model incorporating interactions between the pendula and an electromagnetic shaker is developed. System responses are analysed with time histories, phase portraits, and Poincaré-based maps to determine the ranges of excitation amplitude and frequency supporting stable synchronised rotations. Results show that small asymmetries in pendulum lengths can shift the system response between co-existing attractors, inducing transitions from oscillatory to rotational regimes, in cases of non-identical pendula. These findings highlight the potential of using parameter asymmetry to extend the operational range of synchronised rotations in practical applications. Finally, the numerical model is validated experimentally, showing a good agreement with the observed qualitative dynamics and the boundaries of rotational responses. It was found representing damping as a function of variable pendulum velocity can improve predictive fidelity in future developments.