Law Of Electromagnetic Induction Research Articles

Nonlinear Dynamic Response of Galfenol Cantilever Energy Harvester Considering Geometric Nonlinear with a Nonlinear Energy Sink

The nonlinear energy sink (NES) and Galfenol material can achieve vibration suppression and energy harvesting of the structure, respectively. Compared with a linear structure, the geometric nonlinearity can affect the output performances of the cantilever beam structure. This investigation aims to present a coupled system consisting of a nonlinear energy sink (NES) and a cantilever Galfenol energy harvesting beam with geometric nonlinearity. Based on Hamilton’s principle, linear constitutive equations of magnetostrictive material, and Faraday’s law of electromagnetic induction, the theoretical dynamic model of the coupled system is proposed. Utilizing the Galliakin decomposition method and Runge–Kutta method, the harvested power of the external load resistance, and tip vibration displacements of the Galfenol energy harvesting model are analyzed. The influences of the external excitation, external resistance, and NES parameters on the output characteristic of the proposed coupling system have been investigated. Results reveal that introducing NES can reduce the cantilever beam’s vibration while considering the geometric nonlinearity of the cantilever beam can induce a nonlinear softening phenomenon for the output behaviors. Compared to the linear system without NES, the coupling model proposed in this work can achieve dual efficacy goals over a wide range of excitation frequencies when selecting appropriate parameters. In general, large excitation amplitude and NES stiffness, small external resistance, and small or large NES damping values can achieve the effect of broadband energy harvesting.

Remote measurement of transient heat flux based on the thermomagnetic effect

Abstract Heat flux is a physical quantity that characterises the strength of heat transfer per unit area. Heat transfer occurs with a temperature difference. Herein, a remote heat flux measurement method based on the thermomagnetic effect is proposed. Using Bloch’s law, Faraday’s law of electromagnetic induction, and Fourier’s law, a temperature measurement model from heat flux to magnetisation of the magnetic film and finally to the induced electromotive force in the Helmholtz coil is established. A compression corner was fabricated, and the heat flux measurement method was experimentally verified in a Mach 6 shock tube wind tunnel. In addition, a Schlieren experiment was performed for comparison. In the experiments, the temperature resolution of the magnetic film reached 0.36 K, and the temperature response reached 100 kHz. The range of the proposed heat flux measurement method is up to 5 MW m m − 2 , and the measurement error is less than 10%. At a resolution of 10 μs, the change in heat flow is mapped when there is a transition for the magnetic film from flat to turbulent flow, which shows the different effects of hypersonic heat flux on the boundary layer and attachment position. The magnetic thin film shows the potential for heat flux estimation in our experiment.

Characteristics of Electric Field Induced by Oscillating Metal Underwater Vehicle

To analyze the induced electric field characteristics generated by the rotation and shaking of underwater metal vehicles, a mathematical model of the induced electric field generated by the underwater metal vehicles was derived using Faraday’s electromagnetic induction law. A mathematical model of the induced electric field on the electrode pairs of metal vehicles shaking in different coordinate system planes was established through in-depth analysis. Based on this, a three-component output model of the induced electric field output by the three-axis sensor was obtained when the measurement system was shaking at all three angles. At a constant speed, the induced electric field interference output by the measurement system is a static signal. The value of the static electric field is proportional to the vehicle’s speed and the value of the geomagnetic field, and the value of each component is related to the direction of movement and the value of the geomagnetic field component. The simulation results show that when the navigation body is moving at a constant speed, the induced electric field is a static electric field with a magnitude of mV/m. In a stable state, the induced electric field noise generated by changes in pitch, roll, and heading sway is at the nV/m level and does not have a significant impact on detection. The correctness of the theoretical model has been verified through experiments on offshore speedboat platforms, and it is feasible to use metal navigation bodies for ship electric field detection.

Analysis of DC bias characteristics of transformer by using fixed-point time-step FEM and dynamic J–A hysteresis model

The injection of the Direct Current (DC) bias component will lead to oversaturation of the transformer core and affect its safe operation. In this paper, the vector magnetic potential A and winding current I are used as the variables solved in the time-step finite element method to simulate the nonlinear transient magnetization characteristics of the transformer under DC bias, and the fixed-point reluctivity is introduced to deal with the nonlinear iterative problem. The field-circuit coupling relationship is established through the electromagnetic induction law, and the two-dimensional time-step finite element model of the transformer core is found. The dynamic J–A hysteresis model is used to deal with the hysteresis effect of iron cores. The fixed-point reluctivity of difference form is introduced to solve the problem of uneven transition and multi-value of magnetization curve with hysteresis in the iterative process. The determination scheme for the equivalent thickness of the core model and the initial iterative value are discussed. A laminated core transformer is made for experiments, and the accuracy and applicability of the model proposed in this paper are verified by comparing the calculation and experimental results. The influence of different voltages and different DC bias components on the electromagnetic characteristics of the transformer is analyzed.

Non-contact electromagnetic controlled metamaterial beams for low-frequency vibration suppression

To address the challenge of suppressing extremely-low frequency vibration and noise in precision instruments and equipment, a novel non-contact metamaterial beams is proposed in this paper. The resonators of the metamaterial beams integrate negative stiffness mechanism and electromagnetic damping tuning system. Based on the magnetic dipole theory and the electromagnetic induction law, the mechanical model of magnetic resonator is established. The band structure and transmission spectrum of the metamaterial beams are obtained by transfer matrix method. Besides, the results of numerical simulations are used to verify the accuracy of theoretical results. The result shows that the negative stiffness can be controlled by nonlinear magnetic force among the magnets. Based on this mechanism, the bandgap frequency can be reduced to a minimum of 50Hz. Then, the method of combining electromagnetic damping and negative impedance circuit is proposed to form a tuning system which can reduce the initial frequency of the bandgap to 4Hz. Interestingly, the proposed bandgap control mechanism achieves the extremely-low bandgap while broadens the bandwidth relatively, which overcomes the deficiency of traditional quasi-zero-stiffness metamaterials that reduce the bandgap frequency while causing the bandwidth to narrow. This study is expected to provide valuable ideas for the application of metamaterials in the field of low-frequency vibration and noise reduction.

Traditionally Originated Modern Technology Motivated Passive Downdraft Cooling System: An Eco-friendly Triple Harvest Solution

With rising heat waves and climate change, the big cities are meshing up with the buildings woven in urban fabric that are becoming power-guzzling air-conditioning machines that increase energy demand multi-fold. This has the side effect of heating up the environment because the return heat from air conditioners mixes with the surrounding air. This dents the microclimate and makes the micro and macro systems worse, as this process is continuous without break. So it will be a disaster for the environment in the future. To mitigate the problem, the paper borrows traditional wisdom to merge with smart technology and create comfortable built spaces in hot-dry and hot-humid weather conditions, based on the principles of evaporative cooling, the venturi effect, and the faraday law of electromagnetic induction. The output of adopting these principles creates comfort conditions for air ventilation with improved air quality and a natural air-conditioning system, ensuring the luxury of contact-free cool air in habitable spaces. The process is based on interoperability, which is built into the system to self-generate and consume renewable energy. The integration of information into the system is a spontaneous cycle of production and consumption of energy. This ensures its self-sufficiency, which bridges the research gap in the design of an upgraded passive downdraft cooling system with three self-sufficient and effective benefits in a single system.

Design of parallel coil arrays with identifiable eigenfrequency elements for wearable human-machine interactions

Wearable electronic devices are considered as a promising platform for efficient human-machine interactions (HMI) in the advancing era of the Internet of Things (IoT). However, the limited capacity often necessitates the arraying of individual devices, which inevitably increase the number of connecting wires, communication channels, and physical chaos. Herein, we propose a high-capacity HMI interface which is composed of parallel-arranged flexible coils, a magnetized composite and a pair of electrodes for electrical connection. When the coils were deformed, the inherent oscillation occurs spontaneously once the mechanical constraint was released. Upon this, the magnetic flux variation caused by the oscillation results in induced current within the coil as defined by the law of electromagnetic induction. Assisted by theoretical model of cantilever beams, eigenfrequency could be effectively regulated and the integration of distinct coils permits a single device to transmit multiple commands and information. Taking advantage of the design, spatial position sensing, virtual piano playing and robotic control have been demonstrated as practical applications, which are mainly based on one communication channel and a pair of electrodes. We expect that the eigenfrequency-dependent mechanism can provide an inspiring solution for the design of high-capacity, effective, and comfortable HMI interfaces in the future.

A magnetic-mechanical strong coupling FEM model and vibration characteristic analysis of transformer core under DC bias

The vibration of a transformer core induced by magnetostriction is closely related to the environment and safety of devices. The DC bias excitation leads to the over saturation of the transformer core and causes more severe vibration. In this paper, a magnetic-mechanical strong coupling model based on a fixed-point time-periodic 2D finite element method with excitation voltage and DC bias current as the input is established in which the vector magnetic potential A, winding current I, and displacement in the core u are simultaneously taken as solution variables, and the fixed-point reluctivity is introduced to deal with the nonlinear problem of the core. In this model, the magnetic field and mechanical field are associated with the piezomagnetic equations and variational principle, and the circuit and magnetic fields are connected through the law of electromagnetic induction. The equivalent thickness of the core model and the determination of the initial value are discussed. A test transformer with a laminated core is made for experimental measurement. The accuracy and efficiency of the model proposed are verified by comparing the calculated results with the experimental results, and the influence of DC bias components on the magnetic characteristics and vibration of the transformer core is analyzed.

Hand-held rolling magnetic-spring energy harvester: Design, analysis, and experimental verification

Aiming at the random and low-frequency characteristics of human motion, a hand-held rolling magnetic-spring energy harvester is proposed to scavenge energy from handshaking. The harvester applies the rolling movement of a magnetically suspended magnet and possesses the merit of low damping. The dynamic model is established and the open-circuit voltages are predicted by combining Faraday's law of electromagnetic induction and finite element analysis. By calculating magnetic flux through coils, the effect of the coil’s position on energy harvesting efficiency is studied through numerical and experimental approaches. Experimental results under harmonic excitations indicate that the coil positioned directly below the stable equilibrium position of the moving magnet has the best output capability, and a maximum open-circuit voltage of 1.33 V and a half-power bandwidth of 1.61 Hz is achieved at 0.3 g. Under handshaking excitation, an instantaneous peak power of 20.15 mW is achieved, along with a maximum average power of 2.22 mW. The corresponding volume and mass power densities are respectively 26.04 μW/cm3 and 23.28 μW/g. Furthermore, handshaking excitation in 5 s to charge a capacitor of 470 μF could enable the watch, time display, timer, and hygrothermograph to operate for 1100 s, 513 s, 86 s, and 35 s respectively, demonstrating the brilliant application foreground of the proposed harvester.

Transduction of UV-light energy into alternating-current electricity via a neglected internal photoelectric effect of metal foil-based nanogenerator

Massive free electrons in metals could escape from the metal surface to generate a convection current when colliding with high-energy photons (e.g. UV light). Namely, metals with specific work functions could transduce light energy into direct-current (DC) electricity via the famous external photoelectric effect. However, obtaining alternating-current (AC) electricity via a non-Faraday’s law of electromagnetic induction directly using metal foil is challenging. Inspired by our recent work, we herein for the first time report a subtle method to directly transduce UV light energy into AC electricity by metal foil nanogenerators and propose a new mechanism regarding the transduction of UV light into AC electricity entitled the neglected internal photoelectric effect (NIPE). According to the NIPE, a zinc foil-based NIPE nanogenerator (NIPEG) can output an optimal open-circuit voltage (Voc) and a short-circuit current (Isc) of 108 V and 320 μA, respectively. The maximum output power and the photoelectric conversion efficiency of the fabricated nanogenerator approach 23.9 W m−2 and 77.02%, respectively. Meantime, the electrical energy stored in the capacitor connected to the Zn foil-based nanogenerator after rectification is several orders of magnitude higher than that of the conventional Cu/PTFE/PET/Cu-based triboelectric nanogenerator and Cu/PTFE/Al-based water droplet nanogenerator. The herein approach potentially offers a novel energy harvesting and conversion avenue to develop self-powered and wearable electronic devices.

Theoretical justification of faraday's experimental law

So far, the fundamental laws of nature can only be obtained experimentally. Among them is Faraday's law of electromagnetic induction in mathema-tical representation as Maxwell's second law of the elec-tric field. Theoretically, it is impossible to obtain it on the basis of the laws of electrodynamics. Therefore, in the work, a bold attempt is made to theoretically obtain its analogue in the gravitational field, and then, on the basis of electromechanical analogies, to return to the electric field. What has been successfully done. But before that, there was a need to mathematically rehabili-tate the electromechanical analogies themselves, the reputation of which had suffered in the process of the reverse extension of the law from electricity to gravity under the name of gravito(electro)magnetism. Such immersion in the world of two disciplines - electricity and mechanics − is fundamental for a deeper understanding of physical processes, and at the same time for their quantitative detection.

Detection of Surface and Back-Surface Defects on Metal Plate via Rectangular Wave Eddy Current Testing Using Magnetoresistive Sensor

Eddy current testing (ECT) at different frequencies can identify surface and back-surface defects caused by the skin effect. Traditional ECT uses a pickup coil to measure the magnetic-field signal caused by eddy current. However, according to Faraday’s law of electromagnetic induction, the voltage signal detected at low frequencies is weak; thus, the signal is susceptible to interference from noise. By contrast, magnetoresistive (MR) sensors have high sensitivity at low frequencies. Therefore, we developed a rectangular wave eddy current testing system using an MR sensor. The system uses rectangular wave excitation, which can generate both low- and high-frequency signals, and the MR sensor detects the magnetic-field components. A 12-mm-thick aluminum plate with an artificial circular defect 10 mm in diameter and 4 mm in height was used as a specimen. The measurement results indicated that the developed system can accurately and quickly distinguish between surface and back-surface defects.

Design of a multicylinder crank-slider wind energy harvester utlizing Faraday's law of electromagntic induciton

Advancement in smart electronic devices such as smartphones, smart watches, tablets have impacted the requirement of supplying continuous energy for powering and functioning of these devices. There have been several research studies performed on harvesting energy from mechanical vibrations, wind, fluid flow, solar and geothermal etc. using various mechanisms. Piezoelectric mechanism provides high power density of energy conversion from mechanical vibrations or wind into electric voltage or charge, however, due to the lower power output of these devices, many devices must be summoned in order to generate actual usable power for small scale electronic devices. In this paper, we have designed, developed, and extensively tested a multicylinder wind energy harvester that converts rotational motion into linear motion which further converts it into electric voltage using Faraday's law of electromagnetic induction. The multicylinder design and modified crank allow the device to output higher power while operating at lower wind speeds such as 2.4 m/s. Furthermore, this device included a rectifier to convert from AC to DC, a capacitor to clean the output signal, and a 5 V regulator that can be used to charge a USB connected smartphone or other smart devices. Under a regulated low wind speed of 2.4 m/s and across a 305 Ω load, the device had a rotational frequency of 0.76 Hz and a power output of 1.2 mW whereas at the wind speed of 4.9 m/s the rotational frequency was 7.25 Hz and the output 421.9 mW. At a rotational frequency of 6 Hz the device was used to charge a 3.7 V 46 mAh smart watch at 1% charge in 1.4 min. We also used an optimized 305 Ω load in wind speeds reaching 10.1 m/s in real world conditions at which point the harvesters' output peaked at 1.21 W resulting in a power density of 19.98 W/m3. Authors believe that these results are promising for understanding, investigating, and providing continuous power solutions to small scale smart electronic devices.

Analytical solution and optimal design for the output performance of Galfenol cantilever energy harvester considering electromechanical coupling effect

The theoretical model of a Galfenol cantilever energy harvester is investigated for vibration energy harvesting. Compared with the numerical solution, the analytical solution can better capture the intrinsic effects of the physical parameters on the performance of the harvester. In this work, an electromechanical coupled distributed-parameter model of the Galfenol cantilever energy harvester is established based on Hamilton’s principle, linear constitutive equations of magnetostrictive material, and Faraday’s law of electromagnetic induction. The definitions and expressions of the electric damping and modified frequency are proposed due to the electromechanical coupling. The explicit analytical expressions of the average harvested power across the load resistance and tip vibration displacement of the Galfenol energy harvesting model are derived using the methods of Galliakin decomposition and electromechanical decoupling. The accuracy of the derived analytical results is verified by the experimental data and numerical solutions. The vibration response and energy harvesting performance of the Galfenol energy harvesting model are investigated by varying the excitation frequency, external resistance, and excitation acceleration amplitude. The analytical results show that, with the increase of the external load resistance and excitation frequency, the harvested power increases first and then decreases, indicating the existence of the optimal resistance and excitation frequency. From the explicit analytical expressions of the average harvested power, the optimal external load resistance or excitation frequency could be easily found to achieve the maximum harvested power for any fixed excitation frequency or external load resistance. The concept of proposing the electric damping and modified frequency for the Galfenol cantilever energy harvester simplifies the solution process for the output performances benefiting from the exact relationship between the output performances and the electromechanical coupling parameter derived in this work.

Theoretical and experimental investigation of magnet and coil arrays optimization for power density improvement in electromagnetic vibration energy harvesters

Power density is a critical evaluation indicator of electromagnetic vibration energy harvesters and has become one of the research hotspots. Therefore, it is of great significance to establish a simple and accurate theory to optimize and guide the design of an energy harvester for power density enhancement. Indeed, an alternating magnet array has a high flux gradient, which is one of the key factors for power enhancement. Under volume constraints, the coil output power is highly related to the magnet configuration, as the latter determines the magnitude of the flux gradient as well as the total flux mutation. Motivated by this, in this paper, an electromagnetic vibration energy harvester based on a coil array and a magnet array is proposed. The magnetic field distribution of rectangular magnets is analyzed. Then, a theoretical model based on Faraday's law of electromagnetic induction is derived to efficiently calculate the open-circuit voltage of coils with different numbers of magnets. After that, the optimal magnetic configuration is obtained based on the developed model without the need of measuring the parasitic damping of the energy harvester. Simulations and experiments verify the correctness of the theory. The results show that at an acceleration of 1 g and frequency of 41.2 Hz, the output power and power density reach a maximum of 3.71 mW and 106.68 μW/cm3, respectively, when the number of magnets m = 6, which is 2.58 times higher than the case of m = 3 and 2.06 times higher than the case of m = 12. The model proposed in this paper applies to the optimization of magnet array configurations of any volume, demonstrating the great benefits of power density enhancement.

Electrophysical Mechanism of Appearance of the Phenomenon of Superficial Effect in a Metallic Conductor with the Alternating Electric Current

An electrophysical mechanism explaining the origin of an uneven distribution of the field strength of the intrinsic alternating electromagnetic field (EMF) over the thickness of the bulk homogeneous nonmagnetic metal conductor with a rectangular cross-section with an alternating current i0(t) of different peak-temporal parameters is suggested. This mechanism, justifying the manifestation of the surface effect in the specified conductor, is based on the Faraday–Maxwell law of electromagnetic induction. It is mathematically shown that inductive alternating conduction currents and their alternating EMF arising in the conductor material due to the action of an alternating conduction current i0(t) and, accordingly, an intrinsic alternating magnetic flux Ф0(t) at dФ0(t)/dt>0 weaken the intrinsic alternating EMF strength distributed inside the conductor, and at dФ0(t)/dt<0 they maintain the EMF strength diminishing with time and the material depth.

Micromagnetic stimulation (µMS) dose-response of the rat sciatic nerve

Objective. The objective of this study was to investigate the effects of micromagnetic stimuli strength and frequency from the Magnetic Pen (MagPen) on the rat right sciatic nerve. The nerve’s response was measured by recording muscle activity and movement of the right hind limb. Approach. The MagPen was custom-built to be stably held over the sciatic nerve. Rat leg muscle twitches were captured on video, and movements were extracted using image processing algorithms. EMG recordings were also used to measure muscle activity. Main results. The MagPen prototype, when driven by an alternating current, generates a time-varying magnetic field, which, according to Faraday’s law of electromagnetic induction, induces an electric field for neuromodulation. The orientation-dependent spatial contour maps of the induced electric field from the MagPen prototype have been numerically simulated. Furthermore, in this in vivo work on µMS, a dose-response relationship has been reported by experimentally studying how varying the amplitude (Range: 25 mV p-p through 6 V p-p) and frequency (range: 100 Hz through 5 kHz) of the MagPen stimuli alters hind limb movement. The primary highlight of this dose-response relationship (repeated over n rats, where n = 7) is that for a µMS stimuli of higher frequency, significantly smaller amplitudes can trigger hind limb muscle twitch. This frequency-dependent activation can be justified by Faraday’s Law, which states that the magnitude of the induced electric field is directly proportional to the frequency. Significance. This work reports that µMS can successfully activate the sciatic nerve in a dose-dependent manner. The impact of this dose-response curve addresses the controversy in this research community about whether the stimulation from these μcoils arise from a thermal effect or micromagnetic stimulation. MagPen probes do not have a direct electrochemical interface with tissue and therefore do not experience electrode degradation, biofouling, and irreversible redox reactions like traditional direct contact electrodes. Magnetic fields from the μcoils create more precise activation than electrodes because they apply more focused and localized stimulation. Finally, unique features of µMS, such as the orientation dependence, directionality, and spatial specificity, have been discussed.

The influences of external magnetic field on the reflection and transmission waves at the interface of two dipolar gradient elastic solids

The elastic wave propagation and the reflection and transmission at interface with consideration of the microstructure effects and the Lorentz force simultaneously are investigated in the present work. The microstructure effects are modelled by the dipolar gradient elasticity and the Lorentz force due to the external magnetic field is derived by the electromagnetic induction law and Maxwell equation. The numerical results are provided for incident P wave, incident SV wave and incident SH wave, respectively. It is found that the microstructure effects induce the dispersive feature of elastic waves but the external magnetic field do not contribute to the dispersion with only influence on the amplitude of speed. The surface waves are more sensitive to the external magnetic field and the microstructure effects compared with the bulk waves.

Design and modeling of a novel triple-magnet magnetic dynamic vibration absorber

A novel Triple-magnet Magnetic Dynamic Vibration Absorber (TMDVA) with Eddy Current Damping (ECD) and Coulomb damping is proposed in this paper. A multi-storey structure is selected as the vibration reduction object. First, the equivalent dynamics model of the TMDVA multi-storey structure vibration reduction system is established. Then the nonlinear magnetic force model is built according to the magnetizing current theory. Next, an ECD accurate calculation model is developed and derived based on Faraday’s law of electromagnetic induction. Because of the model, the ECD coefficient can be designed and adjusted arbitrarily. The full text indicates that adjusting the ECD coefficient properly can not only improve the vibration reduction effect of the TMDVA, but also reduce the sensitivity of the vibration reduction effect to the excitation amplitude as well as enhance the broadband vibration reduction performance and the robustness of the TMDVA. With its simple structure, the TMDVA is easy to be implemented and miniaturized. And the low frequency vibration reduction effect of the TMDVA is better than other existing magnetic dynamic vibration absorbers. Taken together, the TMDVA has potential application value in passive vibration reduction of engineering structures.

Electromagnetic induction: How the “flux rule” has superseded Maxwell's general law

As documented by textbooks, the teaching of electromagnetic induction in university and high school courses is primarily based on what Feynman labeled as the “flux rule,” downgrading it from the status of physical law. However, Maxwell derived a “general law of electromagnetic induction” in which the vector potential plays a fundamental role. A modern reformulation of Maxwell's law can be easily obtained by defining the induced electromotive force as ∮l(E→+v→c×B→)·dl→, where v→c is the velocity of the positive charges which, by convention, are the current carriers. Maxwell did not possess a model for the electric current. Therefore, in his law, he took v→c to be the velocity of the circuit element containing the charges. This paper aims to show that the modern reformulation of Maxwell's law governs electromagnetic induction, and the “flux rule” is not a physical law but only a calculation shortcut that does not always yield the correct predictions. This paper also tries to understand why Maxwell's law has been ignored, and how the “flux rule” has taken root. Finally, a section is dedicated to teaching this modern reformulation of Maxwell's law in high schools and elementary physics courses.