Ultra-low Frequency Vibrations Research Articles

An enhanced electromagnetic energy harvester based on dual ratchet structure with secondary energy recovery

Abstract With the continuous advancement of ultra-low-power electronic devices, capturing energy from the surrounding environment to power these smart devices has emerged as a new direction. However, most of the mechanical energy available for harvesting in the environment exhibits ultra-low frequencies. Therefore, the feasibility of self-powering low-power devices largely depends on the effective utilization of this ultra-low-frequency mechanical energy. Consequently, this work proposes an enhanced electromagnetic energy harvester based on a dual ratchet structure with secondary energy recovery. It converts ultra-low frequency vibrations into fast rotational movements by means of a rack and pinion mechanism, thus achieving high power output while maintaining a simple structure. Experimental tests demonstrate that the proposed harvester exhibits excellent power output under ultra-low-frequency external excitation. Under external excitation with a frequency of 1.5 Hz and an amplitude of 22 mm, with the optimal load matched at 20 Ω, the maximum power output reaches 598 mW, with a power density of 1572.65 μW/cm³. The secondary energy recovery power accounts for 34.4 %, resulting in a 52.56 % enhancement in the energy harvester's output performance. Additionally, hand-cranking tests indicate that the fabricated prototype of the electromagnetic energy harvester can power some common electronic devices, including smartphones, showcasing significant application potential.

A direction-adaptive ultra-low frequency energy harvester with an aligning turntable

Ultra-low frequency vibrations in the ambient environment contain abundant sustainable energy. However, their time-varying and random direction nature poses a prominent challenge for the design of effective energy harvesters. This paper proposes a direction-adaptive ultra-low frequency energy harvester with an aligning turntable to ensure a systematic alignment between the pendulum swinging plane and the excitation direction. The aligning turntable is easily rotated by overcoming friction, thus reducing the deviation angle till zero. Experimental results verify the output power enhancement from several milliwatts to over 1 W owing to the alignment process. Moreover, setting resonance frequency with large amplitude vibration can significantly shorten the alignment time. Decreasing the pendulum swinging natural frequency contributes to a slower alignment process but enhances the system stability.

A multi-stable rotational energy harvester for arbitrary bi-directional horizontal excitation at ultra-low frequencies for self-powered sensing

A rotational multi-stable energy harvester has been presented in this paper for harnessing broadband ultra-low frequency vibrations. The novel design adopts a toroidal-shaped housing to contain a rolling sphere magnet which absorbs mechanical energy from bidirectional base excitations and performs continuous rotational movement to transfer the energy using electromagnetic transduction. Eight alternating tethering magnets are placed underneath its rolling path to induce multi-stable nonlinearity in the system, to capture low-frequency broadband vibrations. Electromagnetic transduction mechanism has been employed by mounting eight series connected coils aligned with the stable regions in the rolling path of the sphere magnet, aiming to achieve greater power generation due to optimized rate of change of magnetic flux. A theoretical model has been established to explore the multi-stable dynamics under varying low-frequency excitation up to 5 Hz and 3 g acceleration amplitudes. An experimental prototype has been fabricated and tested under low frequency excitation conditions. The harvester is capable of operating in intra-well, cross-well, and continuous rotation mode depending on the input excitation, and the validated physical device can generate a peak power of 5.78 mW with 1.4 Hz and 0.8 g sinusoidal base excitation when connected to a 405 Ω external load. The physical prototype is also employed as a part of a self-powered sensing node and it can power a temperature sensor to get readings every 13 s on average from human motion, successfully demonstrating its effectiveness in practical wireless sensing applications.

Branch spiral beam harvester for uni-directional ultra-low frequency excitations

In recent years, there has been a growing interest in piezoelectric energy harvesting systems, particularly for their potential to recharge or replace batteries in energy-efficient electronic devices and wireless sensor networks. Nonetheless, the conventional linear piezoelectric energy harvesters (PEH) face limitations in ultra-low frequency vibrations (1–10 Hz) due to their narrow operating bandwidth and higher resonance frequencies. To address this, researchers explored compact shaped geometries, with spiral PEH being one such design to lower resonance frequencies by reducing structural stiffness. While trying to achieve this lower resonance frequency, spiral designs overlooked that they were spreading the stress across the structure. This was a significant drawback because it reduced the structure's ability to stress the piezoelectric transducer. The issue remains unaddressed, limiting the power generation of spiral beam harvesters. Furthermore, spiral structures also fail to broaden the operating bandwidth, posing additional constraints on their effectiveness. This study introduces a novel solution – the “branch spiral beam harvester,” combining the benefits of both spiral and branch beam designs. The integration of the branch beam concept into the spiral structure aimed to broaden the effective frequency range and establish a concentrated stress area for the placement of the piezoelectric transducer. Finite Element Analysis (FEA) was employed to assess operating bandwidth and stress distribution, while experimental studies evaluated voltage and power generation. Once the workability was confirmed, a statistical optimisation method was introduced to tailor the harvester for specific frequencies in the ultra-low frequency range. Results indicated that the branch spiral beam harvester exhibits a wider operating bandwidth with six natural frequencies in the ultra-low frequency range. It harnessed significantly higher output voltages and power compared to conventional linear PEH. This innovation presents a promising advancement in piezoelectric energy harvesting, offering improved performance without the need for proof masses or additional accessories.

Ultra-low frequency vibration energy harvesting of piezoelectric vibration systems with an adjustable device

Energy harvesting from external Ultra-low frequency vibrations is currently attracting a lot of attention. However, for the same system, it is difficult to satisfy the need for more efficient energy harvesting in a variety of external environments. Accordingly, an adjustable gearing device connected to the energy harvesting system is used herein for adapting energy harvesting to a wide range of external environments. The device uses four symmetrical inclined springs. One end of the springs is connected to a gear and the other end to a mass element. The geometrical parameters of the system can be varied by rotating the gears, thus varying the dynamic stiffness of the system. The kinetic equations of the system are derived and their nonlinear terms are Taylor-expanded. The amplitude-frequency response curve of the system is obtained by solving using the harmonic balance method. Multi-color plots of RMS values of induced voltage and electric power are obtained using the fourth-order Runge-Kutta method. The results show that the device has excellent adjustable performance. Adjusting the rotation angle of the gears can change the soft and hard characteristics of the system's dynamic stiffness and the intrinsic frequency, thus improving the system's energy harvesting performance in different environments.

Design and test of a quasi-zero stiffness isolator with machinable springs

Quasi-zero stiffness (QZS) vibration isolators are widely used for vibration isolation due to their high performance, but their low load-carrying capacity limits their applications. In this paper, a heavy-load-bearing QZS vibration isolator consisting of three compression springs is investigated for isolating ultra-low frequency vibrations. From the theoretical aspect, parameter optimization considering both load mass and isolation performance metric (IPM) is implemented, and a parameter guidance diagram is proposed for parameter design. From the practical point of view, two innovative springs are designed and fabricated by wire-electrical discharge machining (W-EDM), referring to the idea of compliant mechanism. These creative designs are endowed with precise stiffness, large compression and buckling avoidance, which further improve the system properties. Finally, a prototype is made and experiments are carried out to verify the effectiveness of the design. Compared with linear isolators, the experimental results of QZS isolator show better isolation performances in a wider frequency range.

QZS isolators with multi-pairs of oblique bars for isolating ultralow frequency vibrations

QZS isolators with multi-pairs of oblique bars for isolating ultralow frequency vibrations

Linear Segmented Arc-Shaped Piezoelectric Branch Beam Energy Harvester for Ultra-Low Frequency Vibrations.

Piezoelectric energy harvesting systems have been drawing the attention of the research community over recent years due to their potential for recharging/replacing batteries embedded in low-power-consuming smart electronic devices and wireless sensor networks. However, conventional linear piezoelectric energy harvesters (PEH) are often not a viable solution in such advanced practices, as they suffer from a narrow operating bandwidth, having a single resonance peak present in the frequency spectrum and very low voltage generation, which limits their ability to function as a standalone energy harvester. Generally, the most common PEH is the conventional cantilever beam harvester (CBH) attached with a piezoelectric patch and a proof mass. This study investigated a novel multimode harvester design named the arc-shaped branch beam harvester (ASBBH), which combined the concepts of the curved beam and branch beam to improve the energy-harvesting capability of PEH in ultra-low-frequency applications, in particular, human motion. The key objectives of the study were to broaden the operating bandwidth and enhance the harvester's effectiveness in terms of voltage and power generation. The ASBBH was first studied using the finite element method (FEM) to understand the operating bandwidth of the harvester. Then, the ASBBH was experimentally assessed using a mechanical shaker and real-life human motion as excitation sources. It was found that ASBBH achieved six natural frequencies within the ultra-low frequency range (<10 Hz), in comparison with only one natural frequency achieved by CBH within the same frequency range. The proposed design significantly broadened the operating bandwidth, favouring ultra-low-frequency-based human motion applications. In addition, the proposed harvester achieved an average output power of 427 μW at its first resonance frequency under 0.5 g acceleration. The overall results of the study demonstrated that the ASBBH design can achieve a broader operating bandwidth and significantly higher effectiveness, in comparison with CBH.

An asymmetric bistable vibro-impact DEG for enhanced ultra-low-frequency vibration energy harvesting

In order to enhance the performance of bistable energy harvesters with dielectric elastomers (DEs) under ultra-low frequency vibrations, this paper proposes an asymmetric bistable vibro-impact dielectric elastomer generator (ABVI DEG), which mainly consists of a vibro-impact (VI) DEG, two identical pre-compressed springs, two pairs of undeformed springs, and a base. Two kinds of dynamics models of the proposed energy harvester under ultra-low frequency harmonic excitations are developed, and the instantaneous impact model is selected due to its computational efficiency and accuracy. The instantaneous impact model is extended by a series of impact experiments and validated by comparing the dynamical responses of the proposed energy harvester obtained from the two kinds of dynamics models. On this basis, the dynamical behavior and the energy harvesting (EH) performance of the proposed energy harvester under ultra-low frequency harmonic excitations are studied for the initial conditions of the system, different bistable potential wells, and various parameters, which include the pre-stretched ratio of the membranes and the distance between the two membranes. A further comparative study demonstrates the superiority of the proposed energy harvester under the ultra-low frequency harmonic excitation. This work not only provides an insight into dynamical behavior of the proposed ABVI DEG, but helps guide the design and optimization of the proposed EH system in the ultra-low frequency vibration environment.

Diamagnetic-levitation-based Electromagnetic Energy Harvester for Ultralow-frequency Vibrations and Human Motions

Diamagnetic-levitation-based Electromagnetic Energy Harvester for Ultralow-frequency Vibrations and Human Motions

Energy Harvesting from Ultra-low-Frequency Vibrations Through a Quasi-zero Stiffness Electromagnetic Energy Harvester

PurposeTo scavenge vibrational energy from ultra-low frequency vibrations with low excitation levels, this paper presents a novel quasi-zero stiffness electromagnetic energy harvester (QZS-EMEH) by exploiting a rolling magnet system.MethodsBy calculating the nonlinear restoring force exerted on the moving magnet, the parameter region that results in conditions of quasi-zero stiffness is determined, and a theoretical model of the QZS-EMEH is established. Based on the method of harmonic balance, the analytical solution of the QZS-EMEH is derived, and the influence of system parameters on the response characteristics and energy harvesting performance is discussed.ResultsNumerical and theoretical results indicate that the QZS-EMEH can efficiently harness energy in a wide frequency range under low-level excitations. Furthermore, the nonlinear dynamics of the QZS-EMEH are investigated based on the bifurcation diagram, phase orbit, Poincaré map, and basin of attraction, demonstrating that appropriate initial conditions can lead to the high-energy orbit oscillation.ConclusionsFinally, realistic ambient vibration accelerations from a bus and a human body are applied to excite the QZS-EMEH, and the results illustrate that the QZS-EMEH can generate considerable electrical output power and has excellent application prospects.

A tunable multi-arm electromagnetic pendulum for ultra-low frequency vibration energy harvesting

Autonomous electronic devices and sensors are essential to reduce expensive maintenance, increasing job security and reliability, avoiding battery replacements and wired systems. Industrial systems and civil structures vibrate dissipating an important amount of energy that can be harvested to power small devices. This work continues and extends a previous work from the authors (Castagnetti 2019 Meccanica 54 749–60). Here we improved that initial configuration by proposing a tunable multi-arm electromagnetic pendulum for ultra-low frequency vibrations energy harvesting. This configuration features five electromagnetic converters and a magnetic spring, each supported by a pendulum arm with different length: when excited by external vibrations, this six arms frame is free to oscillate around a central pivot. The paper starts from conceptual design, includes a detailed multiphysics dynamic simulation implemented with Matlab Simscape software, presents the prototype development through three-dimensional printing and experimental validation. Systematic experimental tests investigated different pendulum configurations for three stiffness levels of the magnetic spring and confirmed both the ultra-low frequency response (from 2 to 10 Hz), as predicted by the dynamic simulation, and the good voltage and power outputs. Specifically, for the higher stiffness of the magnetic spring, corresponding to an oscillation frequency of about 9.5 Hz, the power output was up to 8.4 mW and the output voltage of about 2 Volt.

Investigation of internal resonance on widening the bandwidth of energy harvester based on a cantilevered double pendulum structure

With the development of small-scale electronic elements and wireless sensor networks, energy harvesting technologies have attracted much attention because they can offer environment-friendly, long-lifetime, and no replacement requirements. However, energy harvesting techniques for collecting ultralow frequency vibrations remain a challenge because of the ultralow frequency, low excitation amplitude, and non-continuous vibrations. This study proposes an ultralow frequency broadband energy harvester based on a double-pendulum structure and cantilevered beam, which utilizes the internal resonance to widen the bandwidth of the energy harvester. The double pendulum oscillator with appropriate parameters can yield two resonance frequencies in an ultralow frequency band (from 1 to 5 Hz). The cantilevered beam can achieve 1:2 internal resonance with the double pendulum oscillator in the second resonance frequency of the double pendulum oscillator. The experiment result shows that the internal resonance vibration piezoelectric energy harvester based on a double-pendulum structure can obtain a bandwidth of 4.4 Hz under 0.4 g excitation.

An ultra-low frequency ball-impacted potential-variable nonlinear energy harvester

Efficient energy harvesting for ultra-low frequency vibrations remains a large challenge. An ultra-low frequency ball-impacted potential-variable nonlinear energy harvester (abbreviated as BPNEH) is proposed in this work to provide a new solution for the challenge. Upon excitation, a horizontal beam, which is magnetically coupled to a vertical one, vibrates back and forth with large amplitudes through ball-impacts, along with a variable potential energy due to the vibration of the coupled vertical one. A prototype of the proposed BPNEH is fabricated to demonstrate the effective contribution of both the ball-impact and the variable potential energy under an ultra-low frequency excitation. Compared to a conventional potential-variable nonlinear energy harvester (abbreviated as PNEH), the RMS voltage of the proposed BPNEH is increased by 78.4 % in 1–8 Hz, along with a sub-peak that appears to the left side of the main peak. This new finding of a double peak phenomenon is further observed and clarified by a theoretical model, where the output voltage of the proposed BPNEH is increased by 209.6 % in 1–10 Hz. In addition, the main factors affecting the sub-peak in the observed double peak phenomenon are also considered and discussed with respect to harvesting more energy. The proposed BPNEH along with the double peak phenomenon is believed to be applicable to ultra-low frequency scenes, especially with large amplitudes, of engineering fields such as wearable devices, structural health monitoring systems, etc.

Inertial-Amplified Mechanical Resonators for the Mitigation of Ultralow-Frequency Vibrations

We propose the design of a vibrational energy-absorption device based on the concept of inertial amplification, by utilizing coupling between translational and rotational motions. A compact and lightweight device, with dimensions being only 10--20 cm and weighing less than 1 kg, can achieve ultralow-frequency resonance response at seismic frequency range, i.e., 0.5--5 Hz. Resonators that can respond at such a low-frequency range are usually bulky structures on the civil-engineering scale; our compact design offers flexibility and options for practical applications. Fabricated functional prototypes verify the very large inertial-amplification factor, up to 137, through vibrational characterizations. Experimentally measured data are consistent with our analytical modeling of the inertial-amplification mechanism. Furthermore, we propose a structurally refined device configuration and demonstrate, through simulations, its capability of vibrational total absorption with a comparatively broadband working frequency range. Our design can be easily adapted for resonance frequencies up to 100 Hz, via further miniaturization of the device dimension and lowering of the inertial-amplification factor. The inertial-amplified resonator represents an unconventional solution to the difficult problem of ultralow frequency vibration mitigation, with compact and lightweight devices that can fit into limited space.

An eccentric mass-based rotational energy harvester for capturing ultralow-frequency mechanical energy

The omnipresent ultralow-frequency vibrations and swings contain a huge amount of mechanical energy, but the low harvesting efficiency hinders their application as a practical power source. To address this issue, this paper reports an innovative eccentric mass-driven rotor (EMDR) that is capable of transforming ultralow-frequency excitations to uni-directional rotation. This motion transformation is enabled by a two-layered cantilevered plectrum that provides a sufficiently large driving stiffness for the anticlockwise rotation of a rotator but a very small sliding friction resistance during its clockwise rotation with respect to the rotator. A rotational energy harvester (REH) based on the EMDR is designed and fabricated, which exhibits remarkably improved electric outputs under ultralow-frequency excitations as compared with the conventional REH without the EMDR. Moreover, the designed REH has a comparatively long duration of electric outputs after the applied excitation vanishes, making it adapt well to the real-world excitations featuring intermittent availability. When the designed REH is attached to the human arm or leg, the generated electric energy under jogging is sufficient for running some small electronic devices. This study demonstrates the promising application foreground of the proposed EMDR in realizing high-output ultralow-frequency energy harvesters.

Superviscous properties of the in vivo brain at large scales

There is growing awareness that brain mechanical properties are important for neural development and health. However, published values of brain stiffness differ by orders of magnitude between static measurements and in vivo magnetic resonance elastography (MRE), which covers a dynamic range over several frequency decades. We here show that there is no fundamental disparity between static mechanical tests and in vivo MRE when considering large-scale properties, which encompass the entire brain including fluid filled compartments. Using gradient echo real-time MRE, we investigated the viscoelastic dispersion of the human brain in, so far, unexplored dynamic ranges from intrinsic brain pulsations at 1 Hz to ultralow-frequency vibrations at 5, 6.25, 7.8 and 10 Hz to the normal frequency range of MRE of 40 Hz. Surprisingly, we observed variations in brain stiffness over more than two orders of magnitude, suggesting that the in vivo human brain is superviscous on large scales with very low shear modulus of 42±13 Pa and relatively high viscosity of 6.6±0.3 Pa∙s according to the two-parameter solid model. Our data shed light on the crucial role of fluid compartments including blood vessels and cerebrospinal fluid (CSF) for whole brain properties and provide, for the first time, an explanation for the variability of the mechanical brain responses to manual palpation, local indentation, and high-dynamic tissue stimulation as used in elastography.

Achieving high-speed rotations with a semi-flexible rotor driven by ultralow-frequency vibrations

Rotational motions are generally enabled by the flow energy for generating electricity or by the electric energy to drive various mechanical motions. Here, we report a fundamentally different approach (which we name “semi-flexible rotor”) that uses omnipresent ultralow-frequency (&amp;lt;5 Hz) vibrations as the energy source to achieve high-speed rotational motions. The semi-flexible rotor comprises mainly a turntable, an elastic support, a lid, and a piece of rope, in which the periodically tensioned and released rope under external excitations provides the torque for spinning the turntable. The feasibility of the proposed approach is confirmed by both experimental measurements and theoretical simulations. As excited by a quasi-harmonic vibration with an amplitude of 10 mm, the rotor achieves a high rotational speed of up to 250 rad/s (2400 rpm) at around 2 Hz, and can provide an average rotational speed higher than 50 rad/s within a frequency range from 0.5 Hz to 5 Hz. The semi-flexible rotor is thus an option for realizing some rotation-based devices (e.g., miniature centrifuges) that work in scenarios without electricity supply or for designing efficient energy harvesters that exploit ubiquitous ultralow-frequency vibrations to generate electricity.

Exploiting ultralow-frequency energy via vibration-to-rotation conversion of a rope-spun rotor

Ultralow-frequency kinetic energy mainly in the form of vibrations is omnipresent in the environment, but its effective exploitation remains a challenge. To tackle this problem, this paper presents a rope-spun rotor structure to transform ultralow-frequency vibrations/linear motions to rapid rotations through a piece of rope. The superior performance of the rotor is demonstrated by applying it to electromagnetic energy harvesting from ultralow-frequency vibrations and irregular human body motions. When the rope-spun rotor based harvester is periodically pushed down 10.5 mm at 1.5 Hz, it produces 9.7 mW electric power. When embedded in a shoe insole, the harvester delivers 8 mW power to a matched load as a male participant walks with the shoe at 6.5 km/h. When positioned under a piece of floorboard, the harvester can charge a supercapacitor (220 mF) from 0 to 3.5 V within 8 min. The harvester can also sustain the continuous operation of multiple electronics simultaneously by scavenging energy from gentle finger tapping motions. This study demonstrates a new mechanism for realizing vibration-to-rotation conversion and a promising way for efficient harvesting of ultralow-frequency energy.

Design and development of a rotational energy harvester for ultralow frequency vibrations and irregular human motions

This paper presents a rotational energy harvester (REH) that is realized based on a rope-driven rotor. Featuring simple structure, low fabrication difficulty and high power density, the proposed REH can do high-speed rotation under ultralow frequency excitations, enabling efficient exploitation of ubiquitous ultralow frequency vibrations and human motions. The REH is modeled, and both simulations and experiments reveal that the performance of the REH has a positive relationship with the cross-sectional area of the elastic rope but a negative correlation with the original length of the elastic rope. Moreover, the output power exhibits a monotonous increase trend when the actuation frequency rises from 1 Hz to 5 Hz. The power generated by the REH under the manual operation at a frequency of around 4 Hz is 5.3 mW, whereas the power converted from the arm swing at a walking speed of 6.5 km/h is 0.65 mW. The REH also produces 0.45 mW power when it is actuated by the treadmill vibration triggered by human jogging. With the energy harvested by the REH from various human motions, the normal operation of some commercial electronics is continuously sustained, which demonstrates the promising potential of the REH in implementing self-powered portable/wearable personal electronics.