Vol.:(0123456789) 1 3 Journal of the Brazilian Society of Mechanical Sciences and Engineering (2020) 42:520 https://doi.org/10.1007/s40430-020-02607-9 TECHNICAL PAPER A bistable electromagnetic energy harvester for low‑frequency, low‑amplitude excitation Mohammed Ali Abdelnaby 1  · Mustafa Arafa 2 Received: 31 December 2019 / Accepted: 1 September 2020 / Published online: 15 September 2020 © The Brazilian Society of Mechanical Sciences and Engineering 2020 Abstract In this work, we propose a bistable vibration energy harvester that can be used for non-resonant low-frequency, low-amplitude excitation. The design exploits magnetic bistability created between a pair of repelling magnets. Unlike base-excited beams, our design relies on placing one magnet on the tip of a cantilever beam having a fxed base, while transversely moving an opposite magnet thereby displacing the beam across its two stable positions with an amplifed motion to harvest greater amounts of power by electromagnetic induction. A theoretical model is developed to simulate the dynamic behavior of the system at diferent excitation frequencies, amplitudes and magnetic gaps in order to assess the efect of the design parameters on the performance. It was found that the proposed design is benefcial and outperforms conventional linear oscillators for a broad range of frequen- cies, except at the linear resonance frequency. The results are supported experimentally over a range of load resistance. Keywords Bistable · Energy harvesting · Low-frequency · Low-amplitude List of symbols A Excitation amplitude (mm) AR Amplifcation ratio B Magnetic fux density (T) b Beam width (m) [c] Damping matrix (Ns/m) {F} Total force vector (N) f Excitation frequency (Hz) F m Bistable force (N) F em Electromagnetic damping force (N) h Beam thickness (m) I Electric current (A) [k] Stifness matrix (N/m) l Beam length (m) l c Coil inductance (H) l w Coil wire length (m) [m] Mass matrix (kg) R c Coil resistance (Ω) R l Load resistance (Ω) y External excitation (m) [z] Nodal degrees of freedom β Proportional damping coefcient ω Excitation frequency (rad/s) δ Gap between magnets (m) 1 Introduction Vibration-based energy harvesting has been recognized as an enabling technology for self-powered devices owing to its per- ennial existence in natural sources and engineering equipment [1–4]. One promising application is powering wireless sensor nodes in structural health monitoring applications [5–8]. Dif- ferent harvester designs have been presented in the literature to convert vibrational energy to useful electrical power through the use of electromagnetic and piezoelectric materials [1–4]. Many studies rely on cantilever confgurations with a proof mass because of the ease of manufacturing and the ability to tailor the resonant frequency [9, 10]. However, deviations from operating at resonance lead to signifcant reduction in the output power [11, 12]. Frequency tuning has been investigated as a viable approach to match a device’s natural frequency to that of the excitation through applying axial preload [13, 14], as well as passive and active stifness tuning [15–17]. The use of nonlinear dynamics to widen the frequency range of the energy Technical Editor: Pedro Manuel Calas Lopes Pacheco. * Mohammed Ali Abdelnaby muhmmad.aly@akhbaracademy.edu.eg 1 Department of Production Engineering and Printing Technology, Akhbar Elyom Academy, Cairo, Egypt 2 Mechanical Engineering Department, American University in Cairo, Cairo, Egypt