Ultralow-frequency Excitation Research Articles

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.

A multidirectional ultralow-frequency rotational energy harvester: Modeling and characterization

Energy harvesting under ultralow-frequency rotation is challenging, especially for frequencies below 1 Hz. This paper proposes a highly robust multidirectional ultralow-frequency rotational energy harvester (MUREH). The impact force generated by periodic gravity provides double excitation for the harvester at ultralow frequencies. The piezoelectric cantilever beam resonates at the intrinsic frequency under ultralow-frequency excitation, achieving frequency up-conversion and energy harvesting abilities under 1 Hz. An electromechanical coupling model is developed to analyze the influence of crucial parameters. Uniaxial and triaxial rotation measurements characterize the performance of the MUREH. At optimum conditions, the MUREH’s root mean square voltage is 4.995 V at 0.8 Hz. The adaptability of attitude randomness is verified by triaxial rotation experiments, with an output of not less than 77 % when tilted less than 45°. Under frequent disturbances, 66 % power is maintained, demonstrating high robustness.

The Modular Gait Design of a Soft, Earthworm-like Locomotion Robot Driven by Ultra-Low Frequency Excitation

In complex and extreme environments, such as pipelines and polluted waters, gait programming has great significance for multibody segment locomotion robots. The earthworm-like locomotion robot is a representative multibody bionic robot, which has the characteristics of low weight, multibody segments, and excellent movement performance under the designed gait. The body segment cell can realize large deformation under ultra-low frequency excitation. The multibody segment robot can locomote under ultra-low frequency excitation with appropriate shifts. In this paper, a modular gait design principle for a soft, earthworm-like locomotion robot is proposed. The driven modules defined by modular gait generation correspond to the peristaltic wave transmissions of the excitation in the robot for different modular gait modes. A locomotion algorithm is presented to simulate the locomotion of the earthworm-like robot under different locomotion gaits. Moreover, the locomotion speeds are obtained for different modular gait modes. The results show that locomotion speed is related to the original state of the body segments and modular gaits. As the initial actuated segments and driven modules (which correspond to the excitation frequency and shift) increase, faster movement speeds can be realized, which resolves the speed saturation of the earthworm-like robot. The proposed modular gait design method gives a new gait generation principle for the improvement of the locomotion performance of soft, earthworm-like robots.

A semi-active quasi-zero stiffness vibration isolator based on magnetorheological elastomer with a fast convergence switch control

Quasi-zero stiffness (QZS) isolators have attracted extensive attention due to their high-static–low-dynamic stiffness. The effectiveness of the traditional QZS (T-QZS) isolators to attenuate low-frequency vibration has been extensively studied. The T-QZS isolator, however, cannot usually provide satisfactory vibration mitigation performance under ultra-low frequency excitation. To tackle this challenge, we propose a semi-active QZS isolator featuring magnetorheological elastomer (SAQZS-MRE isolator). The prominent merit of the proposed design is that the applied MRE material can provide varying stiffness and damping to the proposed SAQZS-MRE isolator, making the isolator suitable for vibration isolation under wide-band low-frequency range. The dynamic viscoelasticity properties of the MRE are experimentally characterized, to formulate the dynamic modeling of the SAQZS-MRE isolator. The open-loop vibration isolation characteristics of the SAQZS-MRE isolator are assessed using the harmonic balance method (HBM). Subsequently, two semi-active control strategies including skyhook and fast convergence switch (FCS) are effectively utilized in the proposed SAQZS-MRE isolator to evaluate their closed-loop performance. The results demonstrate that the SAQZS-MRE isolator with FCS control can eliminate the resonance peak and reduce the initial isolation frequency. In the higher frequency range, it can also improve the vibration isolation performance compared with the SAQZS-MRE isolator with passive control.

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.

Modal Identification of Ultralow-Frequency Flexible Structures Based on Digital Image Correlation Method

Traditional modal testing has difficulty accurately identifying the ultralow-frequency modes of flexible structures. Ultralow-frequency excitation and vibration signal acquisition are two main obstacles. Aiming at ultralow-frequency modal identification of flexible structures, a modal testing method based on Digital Image Correlation method and Eigensystem Realization Algorithm is proposed. Considering impulse and shaker excitation are difficult to make generate ultralow-frequency vibration of structures, the initial displacement is applied to the structure for excitation. The ultralow-frequency accelerometer always has a large mass, which will change the dynamics performance of the flexible structure, so a structural vibration response was obtained through the Digital Image Correlation method. After collecting the free-decay vibration signal, the ultralow-frequency mode of the structure was identified by using the Eigensystem Realization Algorithm. Ground modal tests were conducted to verify the proposed method. Firstly, a solar wing structure was adopted, from which it was concluded that the signal acquisition using Digital Image Correlation method had high feasibility and accuracy. Secondly, an ultralow-frequency flexible cantilever beam structure which had the theoretical solution was employed to verify the proposed method and the theoretical fundamental frequency of the structure was 0.185 Hz. Results show that the Digital Image Correlation method can effectively measure the response signal of the ultralow-frequency flexible structure, and obtain the dynamics characteristics.

A pendulum-plucked rotor for efficient exploitation of ultralow-frequency mechanical energy

Harvesting the pervasive ultralow-frequency (<5 Hz) mechanical energy has been considered as a promising strategy to implement decentralized power sources for the sharply increasing number of low-power electronics, but the low output power impedes the practical application of ultralow-frequency energy harvesting technologies. To address this issue, this paper reports a pendulum-plucked rotor that can transform ultralow-frequency excitations (vibrations and swings) to uni-directional and rapid rotation. This transformation is enabled by an innovative inclined two-layered plectrum, which provides both sufficiently large driving stiffness and low friction resistance. Owing to the uni-directional and rapid rotation, an energy harvester realized with the pendulum-plucked rotor achieves 7.6 mW and 1.25 mW output power under ultralow-frequency swings and vibrations, respectively, which are approximately an order of magnitude higher than those (0.2 mW and 0.15 mW) generated by the conventional swing-based energy harvester under the same conditions. Moreover, the fabricated harvester can capture sufficient human biomechanical energy for powering a wireless temperature sensor and a wireless door bell. This study demonstrates the promising potential of the pendulum-plucked rotor in harnessing the ultralow-frequency mechanical energy as the decentralized power sources.

A dual impact driven frequency up-conversion piezoelectric energy harvester for ultralow-frequency and wide-bandwidth operation

In the view of the limitation of traditional frequency up-conversion piezoelectric energy harvesters (FUC-PEH) which has a narrow operating frequency range and is difficult to adapt to the ultralow frequency excitation, this study presents a dual impact driven FUC-PEH composed of two piezoelectric energy harvester units (PEHUs). The electromechanical model of the FUC-PEH is established based on the single degree of freedom system and piezoelectric coupling factor. An experimental prototype is made and tested under different excitation frequencies and accelerations. The dynamic characteristics and energy output characteristics of the system are analyzed by theoretical calculation and experimental tests. The results show that the proposed energy harvester can provide efficient energy output in a wide frequency range of 3.5 Hz–15 Hz under different excitation accelerations. When the excitation acceleration is 6 m/s2 and the excitation frequency is 9.8 Hz, the average output power of the lower PEHU across optimum load resistance can reach 1.17 mW. When the excitation frequency is 15 Hz, the average output power of the upper PEHU across optimum load resistance can reach 1.86 mW. The theoretical and experimental results show that the proposed energy harvester has potential for powering miniaturized wireless portable devices.

An ultra-low frequency vibration energy harvester with zigzag piezoelectric spring actuated by rolling ball

This paper presents an ultra-low frequency vibration energy harvester using a zigzag piezoelectric spring oscillator, which consists of two piezoelectric zigzag springs and a rolling metal ball. The metal ball rolls and drives the piezoelectric springs to deform to harvest energy when a slight vibration occurs in the external environment. The natural frequency of zigzag spring oscillator piezoelectric energy harvester (ZSO-PEH) is related to the length of the spring and the weight of the ball, correlation analysis is carried out by theoretical derivation and ANSYS simulation. It is found experimentally that the proposed device offers efficient energy output in ultra-low frequency excitation. A maximum output power of 5.68 mW is achieved under the best matching resistance of 5.1 kΩ at the excitation frequency of 3 Hz. The performance of energy harvester can be optimized by adjusting the length of the spring and the mass of the ball. The results show that the proposed piezoelectric energy harvester has the potential to power low-power electronic devices and wireless sensor nodes.

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.

Stochastic resonance in a piecewise bistable energy harvesting model driven by harmonic excitation and additive Gaussian white noise

Strategies for the energy harvesting of low-frequency vibration modes such as sphygmus and human body motions are immature due to the rigorous resonance issue. Stochastic resonance seems to be an appropriate solution to the energy harvesting of low-frequency vibrations. This paper presented the mathematical model of piecewise bistable energy harvesters and solved numerically. Taking the piecewise slope into consideration, the Kramers rate and signal to noise ratio (SNR) of piecewise bistable systems were studied, and the effects of piecewise slope on dynamic output characteristics of piecewise bistable energy harvesters were analyzed. The effect of load resistance on the efficiency of energy harvesting of piecewise bistable energy harvesters compared with their counterparts is evaluated. Furthermore, the influences of ambient periodic excitation and additive noise on the energy harvesting performance of piecewise bistable energy harvesters were investigated. Additionally, the evaluation of piecewise bistable energy harvesters using the measured input signal was completed. The numerical simulations indicate that piecewise bistable energy harvesters with small piecewise slope make great contributions to the enhancement of SNR and energy harvesting; the increases in resonant amplitude of ambient periodic excitation or additive noise intensity cause the transition from monostable to bistable, and piecewise bistable systems with smaller piecewise slope have larger unsaturation for ambient energy harvesting. The maximum electric power can be achieved by using optimal load resistance which can be identified numerically. The evaluation of piecewise bistable energy harvesters by employing the measured input signal shows that piecewise bistable energy harvesters with small piecewise slope perform satisfactory under ultra-low frequency excitation.

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.

A two-degree-of-freedom string-driven rotor for efficient energy harvesting from ultra-low frequency excitations

The aim of this study is to report a two-degree-of-freedom (2-DOF) string-driven rotor to convert ultra-low frequency vibrations to high-speed rotation motion of a rotor, which enables the efficient exploitation of ultra-low frequency mechanical energy. The proposed rotor structure consists of a disk-shaped rotor, a spring and two pieces of string, featuring extremely simple configuration. Based on the proposed rotor, we designed an electromagnetic energy harvester (EMEH) to show the feasibility of utilizing the rotor to achieve improved energy harvesting performance. Experimental results showed that the fabricated harvester with various structural parameters could provide two peak power outputs and generate up to 9.4 mW power when actuated at 3 Hz by a displacement excitation with an amplitude of 8 mm. With the electric power converted from the treadmill vibration by the EMEH, a hygrothermograph could be continuously driven to work with full functionality. Under the manual operation, the harvester could also sustainably charge some portable electronic gadgets. The results of this study exhibit the promising potential of the proposed rotor in efficiently harvesting the ambient ultra-low frequency energy.

A twisting vibration based energy harvester for ultra-low frequency excitations

Ultra-low frequency mechanical excitations are omnipresent in our surrounding environment, but the efficient exploitation of them is generally difficult because they normally drive the widely reported cantilevered harvesters to work under non-resonant conditions. Although the frequency up-conversion strategy has been proposed to mitigate this issue, it usually leads to complicated structures. This paper reports a novel energy harvesting approach based on the twisting vibration of a string-driven rotor. To examine the feasibility of this approach, an electromagnetic energy harvester is designed, which is composed of a lid, a rotor with embedded magnets, a pendant, and a tube with pick-up coils attached to the outer surface. The rotor is suspended between the lid and the pendant through a piece of string, and then actuated by the ambient excitations through the string. Under the excitations produced by a crank-slider mechanism, the designed harvester can generate useful electric outputs that are proportional to the excitation amplitude, the initial angle between the pendant and lid, and the excitation frequency. Moreover, the harvester can also provide 0.034 mW power when it is periodically pulled by the human hand at approximately 1 Hz. This study demonstrates the potential application of the string-driven rotor in collecting energy from ultra-low frequency excitations.

A string-driven rotor for efficient energy harvesting from ultra-low frequency excitations

This Letter reports a string-driven rotor for constructing ultralow frequency energy harvesters. Consisting of a disk-shaped rotor with a shaft, an elastic string, and an inelastic string, the proposed rotor structure can convert ultralow frequency vibrations or linear reciprocating motions to high-speed rotation of the rotor without any sophisticated transmission mechanism. On the basis of the string-driven rotor, an electromagnetic energy harvester is designed, and the corresponding theoretical model is established. Both simulation and experiments demonstrate the high output performance of the harvester under a periodic excitation with an amplitude of 5 mm and at a frequency lower than 5 Hz. The harvester also generates 6.5 mW power when driven by hand at a frequency of approximately 4 Hz. This study exhibits the exciting potential of the string-driven rotor for boosting the efficiency of harvesting energy from pervasive ultralow frequency excitations.

The design of negative stiffness spring for precision vibration isolation using axially magnetized permanent magnet rings

A negative stiffness element is always employed to generate high-static–low-dynamic stiffness characteristic of the vibration isolator, reduce the resonance frequency of the isolator, and improve the vibration isolation performance under low and ultra-low frequency excitation. In this paper, a new compact negative stiffness permanent magnetic spring (NSPMS) that is composed of two axial-magnetized permanent magnetic rings is proposed. An analytical expression of magnetic negative stiffness of the NSPMS is deduced by using the Coulombian model. After analyzing the effect of air-gap width, air-gap position, height difference between the inner ring and outer ring on the negative stiffness characteristic, a design procedure is proposed to realize the negative stiffness characteristic with a global minimum linear component and uniformity stiffness near the equilibrium position. Finally, an experimental prototype is developed to validate the effectiveness of the NSPMS. The experimental results show that combining a vibration isolator with the NSPMS in parallel can lower the natural frequency and improve the isolation performance of the isolator.

Harvesting energy from twisting vibration of a rotor suspended by a piece of string

This letter reports a twisting-vibration based energy harvesting method to generate electricity from ultra-low frequency excitations. Different from the conventional rotational energy harvesters (REHs) that normally use a shaft or bearing structure to support the rotor, the proposed method turns to a piece of string to suspend and drive the rotor. To demonstrate the operational principle and feasibility of this method, we designed a harvester prototype based on the electromagnetic transduction and established the corresponding dynamic model. Both theoretical results and experimental tests exhibit the favorable performance of this method in energy harvesting, which enables the design of REHs with a simpler structure. Moreover, the inherent frequency up-conversion feature makes the proposed method well suited for operating in the natural environment that abounds with ultra-low frequency excitation sources.

Nonlinear Piezoelectric Structure for Ultralow-frequency Band Vibration Energy Harvesting with Magnetic Interaction

In order to realize the energy harvesting structure working for an external perturbation or ultralow-frequency excitation, a continuous structure with adjustable nonlinearity is proposed and analyzed. The novel energy harvesting structure is consisted of a piezoelectric elastic beam and two pairs of magnets. Different from normal assembly of magnets in the same direction of the vibration motion, two pairs of magnets are assembled vertically to the vibration direction to induce adjustable nonlinear restoring force similar as the pre-deformed elastic components in so-called quasi-zero-stiffness system. With the model of magnets, the interaction energy and interaction force are obtained. Considering the the piezoelectric cantilever beam, it can realize a multi-stable vibration structure. The zero equilibrium is stable and the interaction energy there is very high, while there are two symmetry stable equilibriums with very low interaction energy. Thus, for small-amplitude and ultralow-frequency excitations from natural phenomenon such as dropping raining, the structure can have large-amplitude vibration with adjustable output frequency. At last, we realize the proposed vibration energy harvester by designing the structural according to the theoretical analysis. The structure of this study has potentially remarkable applications in intelligent and sustainable power generation.

A nonlinear two-degree-of-freedom electromagnetic energy harvester for ultra-low frequency vibrations and human body motions

Converting the ambient waste energy into electricity has been considered as an effective approach for sustaining low-power devices. One of the key issues is how to generate more electricity from ultra-low frequency excitations that are ubiquitous in our environment. To tackle this problem, this paper presents a two-degree-of-freedom (2-DOF) electromagnetic energy harvester (EMEH) that is realized simply by magnetically levitating a 1-DOF EMEH in a cylindrical housing. Both experiment and simulation exhibit the advantages of the proposed design, including the tunable operating frequencies, improved power output, and extended operating bandwidth. The experimental measurements show that, under a sinusoidal excitation with an amplitude of 0.5 g (1 g = 9.8 m/s2), nearly 40% increase in the magnitude of the power and 152% increase in the operating bandwidth are achieved by the proposed harvester. Under the hand-shaking induced excitation, the 2-DOF EMEH can enhance the voltage of a capacitor (33 μF) from 0 V to 5 V within half a second, showing a charging performance much better than that of the 1-DOF EMEH. Moreover, the 2-DOF EMEH successfully sustains the continuous operation of a hygrothermograph using the energy converted from human body motions, demonstrating its potential application in powering some wearable electronics.

Capturing energy from ultra-low frequency vibrations and human motion through a monostable electromagnetic energy harvester

In the energy-harvesting field, one of the key issues is how to realize efficient energy extraction from ultra-low frequency excitation sources. To offer a solution to this issue, this paper presents a monostable electromagnetic energy harvester (EMEH) that is composed of a magnet-spring resonator encapsulated in a tube, a set of coil wrapped around the tube, and two endmost magnets affixed at the tube's two ends. The three magnets are arranged in such a way that the attractive interaction is applied on both sides of the movable center magnet. Theoretical simulations and experimental tests under harmonic excitations indicate that the proposed EMEH features monostability, exhibits typical softening response, and enables the shift of the operating frequency band toward the left (lower frequency). Under the hand-shaking induced excitation, the proposed EMEH can light up 48 light-emitting diodes (LEDs) or enhance the voltage across a 47 μF capacitor from 0 V to 4 V within 2 s. The experiments conducted on a treadmill show that the fabricated prototype can generate approximately 0.5 mW of power with it attached on the leg vertically under walking and 0.7 mW of power when it is attached on the leg parallelly under running.