Low-frequency Ambient Vibrations Research Articles

A broadband bistable energy harvester with self-decreasing potential barrier effect: Design, modeling and experiments

The conventional bistable energy harvester (CBEH) is difficult to break through the potential barrier for large-amplitude inter-well motion under weak excitation environments, which results in a narrow effective bandwidth. This paper proposes a bistable energy harvester with self-decreasing potential barrier effect (BEH-DPBE) for harvesting low-frequency vibrational energy. A spring is introduced to transform the fixed end of the S-type power generating beam into a movable end, while its oscillator has a dual function of dynamically reducing the potential barrier in the return trip and enhancing the potential energy in the outward trip. The characteristics of the proposed energy harvester are evaluated and analyzed by combining finite element simulations, numerical studies, and experiments. Finally, the effects of key parameters, such as the spring pre-compression, proof mass, and load resistance, are studied. In low-frequency conditions, the effective bandwidth and peak-to-peak voltage of BEH-DPBE are 6.35 Hz (5.98–12.33 Hz) and 10.1 V, respectively. The proposed BEH-DPBE can effectively capture energy in low-frequency ambient vibrations.

Bulk wave manipulation by periodic in-filled barriers in unsaturated soil

Band gaps or attenuation zones existing in periodic structures can filter out elastic waves propagating in both single-phase soils and saturated soils in specific frequency regions, which opens a window for designing new wave barriers to attenuate ambient vibration. However, vibration mitigation in unsaturated soil remains a significant challenge due to soil’s constitutive relation strongly relying on saturation, especially by periodic wave barriers. Based on local resonance mechanism, the performance of a periodic in-filled barrier for isolating low-frequency ambient vibration is studied. The periodic in-filled barrier is filled with a viscous material. Investigations found that the attenuation zones of the periodic wave barrier are robust to saturation and the viscosity of the in-filled material can broaden the frequency range for vibration reduction. More interestingly, periodic wave barriers in unsaturated soils can produce attenuation zones for P1 waves, which is impossible in saturated soils. Therefore, this investigation provides a promising insight for the application of periodic wave barriers to unsaturated soils.

An Impact-Driven Enhanced Tuning Fork for Low-Frequency Ambient Vibration Energy Harvesting: Modeling, Simulation, and Experiment

An Impact-Driven Enhanced Tuning Fork for Low-Frequency Ambient Vibration Energy Harvesting: Modeling, Simulation, and Experiment

Bio-inspired quad-stable piezoelectric energy harvester for low-frequency vibration scavenging

Due to the unique and diverse nonlinear characteristics, bionic structures can effectively broaden the acquisition bandwidth and improve the performance of harvesters. Inspired by dipteran flight motion, a novel bionic quad-stable piezoelectric energy harvester (BQPEH) is designed to collect low-frequency ambient vibration. The novelty of this bionic energy harvester lies in the combination of the “click” mechanism and “snap-through” motion, thus broadening the application scenarios and improving adaptability for the harvesters. A mass block and a post-buckled piezoelectric beam are connected by a rigid bar to create quadruple-well potentials. The static bifurcation analysis is performed to identify the quad-stable region in the parameter space. The dynamic responses of the system are investigated theoretically and numerically under constant and swept-frequency excitations and then verified experimentally. Broadband low-frequency and high-power energy harvesting are obtained through the inter-well motion induced by the combined nonlinearity of the BQPEH. The results indicate the potential of the bionic strategy for powering wireless devices in low-frequency environments and provide a novel concept for the innovative development of energy harvesters.

Investigation of Nonlinear Piezoelectric Energy Harvester for Low-Frequency and Wideband Applications.

This paper proposes a monostable nonlinear Piezoelectric Energy Harvester (PEH). The harvester is based on an unconventional exsect-tapered fixed-guided spring design, which introduces nonlinearity into the system due to the bending and stretching of the spring. The physical–mathematical model and finite element simulations were performed to analyze the effects of the stretching-induced nonlinearity on the performance of the energy harvester. The proposed exsect-tapered nonlinear PEH shows a bandwidth and power enhancement of 15.38 and 44.4%, respectively, compared to conventional rectangular nonlinear PEHs. It shows a bandwidth and power enhancement of 11.11 and 26.83%, respectively, compared to a simple, linearly tapered and nonlinear PEH. The exsect-tapered nonlinear PEH improves the power output and operational bandwidth for harvesting low-frequency ambient vibrations.

A graded metamaterial for broadband and high-capability piezoelectric energy harvesting

This work proposes a graded metamaterial-based energy harvester integrating the piezoelectric energy harvesting function targeting low-frequency ambient vibrations (<100 Hz). The harvester combines a graded metamaterial with beam-like resonators, piezoelectric patches, and a self-powered interface circuit for broadband and high-capability energy harvesting. Firstly, an integrated lumped parameter model is derived from both the mechanical and the electrical sides to determine the power performance of the proposed design. Secondly, thorough numerical simulations are carried out to optimize both the grading profile and wave field amplification, as well as to highlight the effects of spatial-frequency separation and the slow-wave phenomenon on energy harvesting performance and efficiency. Finally, experiments with realistic vibration sources validate the theoretical and numerical results from the mechanical and electrical sides. Particularly, the harvested power of the proposed design yields a five-fold increase with respect to conventional harvesting solutions based on single cantilever harvesters. Our results reveal that by bridging the advantages of graded metamaterials with the design targets of piezoelectric energy harvesting, the proposed design shows significant potential for realizing self-powered Internet of Things devices.

A numerical-experimental dynamic analysis of high-efficiency and broadband bistable energy harvester with self-decreasing potential barrier effect

It is difficult for a conventional bistable energy harvester (CBEH) to form inter-well motion under a weak excitation, resulting in a narrow output bandwidth. In this paper, a bistable energy harvester with a self-decreasing potential barrier effect (BEH-DB) is proposed. It adopts a spring-magnetic oscillator to rectify the cantilever beam bi-directionally causing the potential barrier to be dynamically lowered when returning to the trivial position; while the potential energy is enhanced when moving away from the trivial position. The theoretical model is established by using Euler-Bernoulli's stepped beam and magnetic dipole theories. The influence of system parameters on the performance of the self-decreasing potential barrier is studied by tracking the trajectories on the potential energy surface. The frequency and amplitude sweeps, phase portraits, Poincare maps, and bifurcation analysis are used numerically to investigate the dynamics of the system. The simulation results present a series of complex dynamic behaviors such as intra-well, inter-well harmonic and sub-harmonic orbits, and chaotic motion. The BEH-DB is more easily to be excited to the inter-well orbit to form a large oscillation in an ultra-wide bandwidth, even at the low frequency. Its effective bandwidth and maximum average power are approximately 16.17 Hz and 9.02mW, respectively. Finally, the experiment was carried out, which illustrates that the power generation capacity and bandwidth of the BEH-DB are improved several times that of the CBEH. The experimental results are agreed qualitatively with the numerical simulation. The proposed BEH-DB can be used to harvest energy efficiently and broadly from a low or ultra-low frequency ambient vibration.

Performance-Improved Highly Integrated Uniaxial Tristate Hybrid Nanogenerator for Sustainable Mechanical Energy Harvesting.

Despite advances in the development of individual nanogenerators, the level of output energy generation must be increased to meet the demands of commercial electronic systems and to broaden their scope of application. To harvest low-frequency ambient mechanical energy more efficiently, we proposed a highly integrated hybridized piezoelectric-triboelectric-electromagnetic (tristate) nanogenerator in a uniaxial structure. In its highly integrated approach, a piezoelectric nanogenerator (PENG) based on CsPbBr3 (cesium lead bromide) nanoparticles (NPs) and poly(dimethylsiloxane) (PDMS) nanocomposite was fabricated on a triboelectrically negative nanostructured polyimide (PI) substrate. A cylindrical aluminum electrode grooved with permanent magnets was directed to move along a spring-less metallic guide bounded by these nanocomposites, thus essentially forming two single-electrode mode triboelectric nanogenerators (TENGs). By its optimized material design and novel integration approach of the PENGs, TENGs, and electromagnetic generators (EMGs), this uniaxial tristate hybrid nanogenerator (UTHNG) can synergistically produce an instantaneous electrical power of 49 mW at low-frequency ambient vibration (5 Hz). The UTHNG has excellent charging characteristics, ramping up the output voltage of a 22 μF capacitor to 2.7 V in only 12 s, which is much faster than individual nanogenerators. This work will be a superior solution for harvesting low-frequency ambient energies by improving the performance of hybrid nanogenerators, potentially curtailing the technology gap for self-powered micro/nanosystems for the Internet of Things.

Bow-type bistable triboelectric nanogenerator for harvesting energy from low-frequency vibration

Triboelectric nanogenerators (TENGs) are emerging, leading-edge, and promising devices for converting ambient vibration energy into electrical energy and power for low-power sensors. However, it is difficult to harvest energy from low-frequency ambient vibrations using conventional TENGs. To solve this issue, in this study, we propose a bow-type TENG with a bistable stiffness feature, which enables the conversion of low-frequency vibration energy into electrical energy with high efficiency. The dynamic model of the bow-type TENG was established based on extended Hamilton’s principle and numerically solved to obtain the dynamic responses. Subsequently, a prototype of the bow-type TENG was fabricated and tested to verify the design concept. Moreover, the dependencies of the energy-harvesting performance on the structural parameters were experimentally investigated. The average power had a maximum value of 0.64 mW at 5 Hz in the case of optimal load resistance. The bow-type TENG could power a number of light-emitting diodes (LEDs) to display the word “HNU” under low-frequency excitation. Hence, the bow-type TENG can substantially extend the function of harvesting vibration energy from high to low frequencies.

Resonant Frequency Reduction of Vertical Vibration Energy Harvester by Using Negative-Stiffness Magnetic Spring

This work studies the resonant frequency reduction of vibration energy harvesters so as to adapt low-frequency ambient vibrations. In a typical electromagnetic vibration energy harvester, it is common sense that the resonant frequency decreases with the spring stiffness. However, the mass gravity will result in a large initial deformation of the spring with small stiffness when the energy harvester is vertically installed. To solve the problem, this work proposes a method of resonant frequency reduction by adding a negative-stiffness magnetic spring which is arranged symmetrically at the two sides of the equilibrium point. The theoretical expression of resonant frequency is derived based on magnetic field calculation. Comparisons between the energy harvesters with and without negative-stiffness magnetic spring are implemented through simulations and experiments. The results show that the resonant frequency of the vertical energy harvester can be reduced as expected without an increase of initial spring deformation by using the negative-stiffness magnetic spring. This work can provide an effective approach to designing energy harvesters for applications with low-frequency vibrations.

Long-time measurements of line-integrated plasma electron density using a two-color homodyne optical fiber interferometer

A two-color homodyne Mach-Zehnder (M-Z) optical fiber interferometer with wavelengths of 1.55 and 1.31 µm was developed for long-time measurement of line-integrated plasma electron density. A novel phase difference demodulation algorithm based on a single 3 × 3 optical coupler was implemented in a two-color optical fiber interferometer scheme for the first time. Our laboratory tests showed that this new optical fiber interferometer could determine the phase shift due to the low-frequency ambient vibration and could maintain high phase resolution measurement. The resolution of the new interferometer was less than 0.04rad in 1000s, corresponding to a line-averaged electron density of less than 1.0 × 1019m-2. Actual plasma discharge experiments performed on KTX-CTI, which is a new compact torus injector (CTI) constructed at the Keda Torus eXperiment (KTX), showed that this interferometer has excellent several-second stability.

Review of frequency up‐conversion vibration energy harvesters using impact and plucking mechanism

One of the main challenges in the field of vibration energy harvesting is to extract energy from the low-frequency ambient vibrations. Since the voltage and power production in vibration energy harvesters depends on the relative velocity (frequency), therefore, comparatively high power levels are produced at a high frequency of vibrations. For low-frequency excitation of the base, technique such as frequency up-conversion (FUC) is widely utilised. In FUC method, a very low-frequency vibration is efficiently harvested using the plucking mechanism. FUC harvesters are comprised of a low-frequency mechanism (primary system) and a high-frequency mechanism (secondary system), which are either coupled operationally through freely moving mass, mechanical plucking, magnetic plucking or mechanical impact. The mechanical contact plucking or magnetic plucking mechanism is used for exciting a secondary system that has a much higher frequency for efficiently harvesting more energy. This work provides a detailed review of the FUC energy harvesters that are utilising freely moving mass, plucking mechanism and mechanical impact techniques reported in the literature. Information about the harvesters' architecture, working, fabrication and output performance is performed with an emphasis on input low frequency, input acceleration, converted high frequency, voltage generation, power levels and power density values reported in the literature. Moreover, all techniques developed for low-frequency vibration applications are compared and the effectiveness of each mechanism used for low-frequency energy harvesting is discussed.

A new concept of frequency-excitation-up conversion to improve the yield of linear piezoelectric generators

A new and novel frequency-excitation up-conversion (FEUC) mechanism achieved by converting low-frequency excitation into friction-induced vibration (FIV) is proposed to improve the output power of linear piezoelectric energy harvesters at ultra-low ambient frequencies. For comparison, a conventional resonant energy harvester and an impact-driven energy harvester are created, the output power is measured at the resonant frequency under a 0.5 g driving acceleration. Then, a friction system driven by reciprocating sliding and capable of generating FIV is established. The driving reciprocating is equivalent to the low-frequency ambient vibration, and a single piezoelectric cantilever beam is added to the friction system for energy recovery. The results show that, compared with the impact-driven energy harvester, the vibration frequency can be increased hundreds of times, and the excitation level can be improved several orders of magnitude by the friction nonlinearities. The impedance of the energy harvester is reduced significantly due to a sharp increase in the vibration frequency. In addition, the open-circuit voltage amplitude is not substantially lowered due to the significantly increased excitation level, even though the piezoelectric cantilever beam operates in a high-frequency condition and in the absence of resonance. Therefore, the output power is dramatically improved. The effectiveness and superiority of the FEUC strategy proposed in this work has been demonstrated.

Enhancement of the performance of nonlinear vibration energy harvesters by exploiting secondary resonances in multi-frequency excitations

This study is concerned with utilizing secondary resonances in order to harvest energy from low-frequency excitations. Nonlinearities give rise to secondary resonances, which can potentially activate large-amplitude responses when the excitation frequency is a fraction of the fundamental frequency of the system. Such resonances offer an untapped and unique opportunity for harvesting vibratory energy from excitation sources with low-frequency components. This issue has propelled the current study. Based on multi-frequency excitation, we develop a novel theoretical framework for a piezomagnetoelastic energy harvester to enhance its performance. The proposed scheme is implemented in both monostable and bistable piezomagnetoelastic under low-frequency excitations. It is shown throughout the paper that when the excitation frequencies are certain fractions of the system's fundamental frequency, the combination and simultaneous resonance activate large-amplitude responses. Another advantage of the scheme is that the energy could be harvested from low-frequency ambient vibrations, which is a considerable concern in this field of study. Different responses of the system, such as low-amplitude and high-amplitude limit-cycle oscillations and chaotic motions, are studied through perturbation theory and numerical techniques. Various numerical tools, including phase portrait, Poincare section, and Lyapunov exponent, are used to explore complex dynamical behavior of the system. The performance of the harvester is also compared in different regions. Numeral simulations clearly confirm that the proposed framework dramatically enhances the performance of the energy harvester.

A predictive model for electrostatic energy harvesters with impact-based frequency up-conversion

This paper reports a predictive model for vibration-to-electrical energy harvesters based on an in-plane, gap-closing variable capacitor with frequency up-conversion triggered by the impact between the electrodes. Since the output power is proportional to the output frequency, rectifying low-frequency ambient vibrations (1–50 Hz) to high-frequency electrical signals (200–600 Hz) increases the power output. While such a device has been previously reported experimentally, this is the first time a model able to predict the experimental data has been described. The model is based on lumped approximation. The central area supporting the mobile electrodes, or the shuttle mass, is represented by a point mass suspended by springs and has its own equation of motion. The motion of the electrodes attached to the shuttle is described by a set of two equations, each associated with a distinct dynamic mode. In these equations, the electrodes are represented by an equivalent mass and spring constant. The first equation describes the separate motion of mobile and fixed electrodes. In this mode, the electrodes experience damped free vibration due to the electrostatic and air damping between them. The second equation describes the combined motion when the two set of electrodes move together. In this mode the air damping forces between the collided electrodes is eliminated and the electrostatic force is kept constant. The motion equations are solved simultaneously with Kirchhoff’s law to compute the voltage drop across a resistor in series with the variable capacitor and a DC bias voltage source. Predictions are shown to be consistent with the experimental results, and frequency up-conversion effects are observed with exponentially decaying voltage amplitude as seen in experiments. A parametric study is also carried out to identify main parameters that affect the up-conversion, laying the foundation for future design optimization to maximize the power output.

Scalable pendulum energy harvester for unmanned surface vehicles

This paper proposes a novel pendulum energy harvester design for converting energy of low frequency ambient vibration, such as that found in unmanned surface vehicles (USVs) due to ocean waves, into usable electrical energy. The primary novelty of this design is the mechanical rotation rectifier (MRR) system, which is able to improve on existing designs through the use of spur gears and sprag clutches capable of handling significant torque, in an arrangement which is easily scalable to larger devices. Using a minimal number of offset gears, this system is designed to maintain high efficiency and minimal backlash. The energy harvester was proven to produce a maximum normalised average power output of 20.62 W/g2, corresponding to an average power of 0.72 W and a power density of 0.43 W/kg, at 0.186 g rms acceleration. The resonant frequency of the system is designed at 1 Hz, within the range of the expected natural frequencies of USV motion. The energy conversion efficiency at resonance was 43.5 %. Furthermore, a mathematical model was developed and verified through experimental testing, and was used to simulate the effects of various pendulum lengths, masses and flywheels on the system. This demonstrates the specific negative relationship between pendulum arm length and natural frequency of the system, as well as the positive correlation between pendulum mass and maximum power. Furthermore, higher inertia flywheels are shown to produce significantly smoothed voltages and increased output power, while extending the time it takes for the harvester to reach steady state. It is concluded that this device would be viable for assisting in powering USV communications and extending the exploration life of these vessels.

Modeling and Analysis of Micro-cantilever Plate Piezoelectric Energy Harvester with a Tip Mass

With the development of MEMS (Micro-electro-mechanical Systems) techniques, research interest has deepened in micro piezoelectric harvesting device, which can supply electrical power for wireless sensors from ambient vibration. This paper proposes a nonlinear analysis of a micro-scale PEH (piezoelectric energy harvester), which is modeled by a micro-cantilever plate with two layers and a tip mass attached to the free end. Considering size effect and nonlinear curvature, based on strain gradient and inextensible plate theory, nonlinear dynamic equations of the micro cantilever piezoelectric energy harvester with tip mass are established by virtue of the Hamilton’s principle. The maximum output voltage of piezoelectric energy harvester with different tip mass is calculated respectively using MATLAB software. Comparative analysis confirms that an increase of K (the mass ratio of the tip mass to piezoelectric plate) reduces the natural frequency of energy harvester and significantly enhances the nonlinear phenomenon. In addition, when the mass ratio K exceeds 1, obvious superharmonic resonance phenomena generates, which considerably improves the output voltage of the proposed PEH in a lower frequency band. This study proposes an approach to enhance the output performance of micro-cantilever plate energy harvesters and broaden the bandwidth of PEH to adapt low-frequency ambient vibration.

Design and Numerical Analysis of an Electrostatic Energy Harvester With Impact for Frequency Up-Conversion

Abstract Integration of vibration energy harvesters (VEHs) with small-scale electronic devices may form an attractive alternative for relatively large batteries and can, potentially, increase their lifespan. However, the inherent mismatch between a harvester's high-frequency resonance, typically in the range 100−1000 Hz, relative to the available low-frequency ambient vibrations, typically in the range 10–100 Hz, means that low-frequency power generation in microscale VEHs remains a persistent challenge. In this work, we model a novel electret-based, electrostatic energy harvester (EEH) design. In this design, we combine an out-of-plane gap-closing comb (OPGC) configuration for the low-frequency oscillator with an in-plane overlap comb configuration for the high-frequency oscillator and employ impact for frequency up-conversion. An important design feature is the tunability of the resonance frequency through the electrostatic nonlinearity of the low-frequency oscillator. Impulsive normal forces due to impact are included in numerical simulation of the EEH through Moreau's time-stepping scheme which has, to the best of our knowledge, not been used before in VEH design and analysis. The original scheme is extended with time-step adjustments around impact events to reduce computational time. Using frequency sweeps, we numerically investigate power generation under harmonic, ambient vibrations. Results show improved low-frequency power generation in this EEH compared to a reference EEH. The EEH design shows peak power generation improvement of up to a relative factor 3.2 at low frequencies due to the occurrence of superharmonic resonances.

Low-frequency, broadband piezoelectric vibration energy harvester with folded trapezoidal beam.

To efficiently scavenge the energy from low-frequency ambient vibrations, this paper proposed a piezoelectric energy harvester (PEH) with a six-segment folded trapezoidal beam. The new configuration provides the PEH with a lower natural resonant frequency and closer resonance peaks, which makes the harvester suitable to daily vibrations with more functioning resonance modals. Meanwhile, the folded geometry extends the whole length of beam, and then induce a larger strain in the clamped end, leading to a more favorable output voltage. The experimental results show that the proposed structure obtains 5 resonant peaks in 0-30 Hz and an operating bandwidth of 11 Hz. The highest open-circuit output voltage is 20.78 V, and the optimized output power is 217.201 µW.

Analytical modeling and validation of multi-mode piezoelectric energy harvester

Abstract Energy consumption of electronic devices continues to reduce dramatically, enabling the ambient energy harvesting devices as a solution for powering the wireless sensor nodes (WSNs), micro-electromechanical systems and portable electronics. Over the years, vibration-based piezoelectric harvesting has been emerged as a potential technology to recharge/replace chemical batteries in WSNs. A conventional linear piezoelectric energy harvester (PEH) cannot meet the requirement of broadband vibration resources as it generates useful power only in a narrow bandwidth near the resonant frequency. Several techniques such as passive/active resonance tuning, array of harvester beams, nonlinear designs and multi-degree-of-freedom energy harvesters have been investigated. This paper proposes a generalized multi-mode PEH (MPEH) accompanied with analytical modeling, which generates multiple close peaks of voltage output from low amplitude broadband and low frequency ambient vibration sources. The proposed MPEH comprises of a main cantilevered beam bonded with a patch of piezoelectric layer and attached with multiple branches with tip masses at their free ends. The useful bandwidth and the number of peaks for the MPEH could be tuned conveniently by varying multiple branches and tip masses. The proposed MPEH offers high design flexibility in tuning geometric parameters for achieving target frequencies and generates high power density. The mathematical modeling of generalized MPEH under transverse harmonic base vibrations is presented and the dynamic equations of the multi-modal harvester system are obtained following the Lagrangian method. The derived distributed parametric model of MPEH is more accurate than lumped parametric models of PEHS presented in the literature. The accuracy of the proposed analytical model is validated by two examples with numerical simulation and experimental results. It is shown that the multi-mode PEH has potential to generate sufficient power output from broadband vibration sources to sustain low-power electronic devices.