A quasi-zero adjustable stiffness magnetoelectric generator of an inverted pendulum for ultra-low frequency blue energy harvesting (2023)

In recent years, marine wireless sensors, communication networks and MEMS have been developed rapidly[1], [2], and most of these devices use batteries and wired cables as power supplies[3], which have the drawbacks of limited life time, potential environment hazards, and difficulty in building cables and maintenance[4], [5]. The use of energy from the marine environment, such as solar[6], [7], [8], [9], [10], wind[11], [12], [13], [14], temperature difference[15], [16], [17], [18] and vibration[19], [20], [21], [22], can provide energy for these systems and has become an important means to address the above problems. Vibration energy is a prevalent form of energy in the marine environment, including wind-driven vibration[23], [24], [25] and fluid vibration[26], [27], [28], [29], and its collection and conversion into human-usable energy has a wide range of prospects. Most blue energy harvesting devices have a response frequency range concentrated at tens of Hz and can only capture vibration energy in specific directions. In fact, ocean wave energy mostly comes from multiple directions and has time-varying characteristics[30], the frequency is often below 10Hz, even 1Hz[31].

Existing wave energy harvesters are mainly based on piezoelectric[32], [33], [34], [35] and triboelectric-electromagnetic[36], [37], [38], [39]. However, most piezoelectric generators use a single cantilever as an energy harvesting component[40], [41], which has the possibility of permanent deformation and device failure. Most electromagnetic generators are driven at higher frequencies[40], [41], [42], [43], [44] and have inflexible responses, make them difficult to apply to low-frequency marine environments. On the one hand, magnetoelectric (ME) composites are composed of magnetostrictive and piezoelectric materials, such as Terfenol-D/PZT/Terfenol-D[45], which have a high magnetic-mechanical-electrical coupling coefficient and high output power density. It is often used in underwater acoustic transducers, medical ultrasonic transducers and various sensors[46], [47], [48], [49] and has been applied to energy harvesting in recent years[50], [51]. Ghodsi et al. proposed a magnetoelectric cantilever with an external bias magnetic field, and the maximum output power density reached 6.81mW/cm³[52]. Kumar et al. studied the effect of the aspect ratio of the piezoelectric element on the collecting performance of the magnetoelectric cantilever and optimized the maximum output power of 380 μW at an excitation frequency of 60Hz[53]. Dai et al. studied the influence of the initial relative position of the array cantilever on the output power, and the maximum output power was 7.13mW when the excitation frequency was 34.8Hz[54]. Li et al. broadened the frequency response range by rotating self-tuning, which was used to power wireless sensors for rotation applications when the excitation frequency was 9.8Hz, the maximum output power was 517 μW[55]. Therefore, the driving frequency of the current magnetoelectric generator (MEG) is generally too high to be suitable for wave energy harvesting. On the other hand, the quasi-zero stiffness (QZS) mechanism can greatly reduce the natural frequency of the device system to accommodate ultra-low frequency wave motion. Drezet designed a single-DOF bistable buckling beam and a permanent magnet-electromagnetic energy harvesting device with negative stiffness, and the maximum normalized output power was 41.3mW/(g²∙cm³) at an excitation frequency of 5.3Hz[56]. Wang designed a single-DOF QZS-TENG based on the negative stiffness of a permanent magnet, and the power reached 4.06mW when the excitation frequency was 3Hz[57]. Liu proposed a single-DOF QZS-PEG based on the negative stiffness of a buckling beam, and the power reached 8.31mW when the excitation frequency was 2.5Hz[58]. Additionally, further introducing an adjustable stiffness mechanism can help adapt to the time-varying characteristics of ocean waves.

In this work, we first demonstrate a QZS based MEG for the efficient acquisition of ultra-low and wide-band frequency wave energy from the ocean. The quasi-zero adjustable stiffness (QZS) mechanism formed by the unique juxtaposition of the double leaf springs and the inverted pendulum can effectively collect the wave energy of ultra-low frequency and wide frequency band. Low frequency applications below 2Hz are systematically studied. Then, the influence of the initial relative position of the alternating magnetic field and ME on the output power is analyzed. Four ME arrays of L-T (length direction deformation of magnetostrictive material, thickness direction deformation of piezoelectric material) mode are surrounded near the mutant magnetic field, which greatly improved the energy harvesting efficiency. Finally, flexible hinges and swing blocks are introduced to successfully achieve multi-directional energy harvesting. To comprehensively evaluate the dynamic performance of the energy harvesting system, the outputs of the QZS-MEGs with different natural frequencies are measured under various vibration frequencies, motion angles, amplitudes and wave heights. This work provides a valuable demonstration of using a quasi-zero adjustable stiffness mechanism and magnetoelectric composites for ultra-low frequency energy harvesting.