On the Possibility of Developing Magnetostrictive Fe-Co/Ni Clad Plate with Both Vibration Energy Harvesting and Mass Sensing Elements

The severe acute respiratory syndrome coronavirus (SARS-CoV-2) has spread rapidly around the world. In order to prevent the spread of infection, city blockades and immigration restrictions have been introduced in each country, but these measures have a severe serious impact on the economy. This paper examines the possibility of both harvesting vibration energy and detecting mass by using a magnetostrictive alloy. Few efforts have been made to develop new magnetostrictive biosensor materials. Therefore, we propose magnetostrictive Fe-Co/Ni clad steel vibration energy harvesters with mass detection, and we numerically and experimentally discuss the effect of the proof mass weight on the frequency shift and output voltage induced by bending vibration. The results reveal that the frequency and output voltage decrease significantly as the mass increases, indicating that the energy harvesting device is capable of mass detection. In the future, device miniaturization and the possibility of virus detection will be considered.


Introduction
The Internet of Things, where everything is connected to the Internet, is aimed at introducing innovation to the whole world. Sensors are installed in facilities and equipment, and analog processes are visualized as digital data and then accumulated and analyzed on the ground via the Internet. This allows the possibility of improving quality, efficiency, and productivity, as well as creating new value and services, and the way of doing business in various fields is about to change. Moreover, the number of sensors is expected to increase significantly in the future (number may reach 1 trillion by 2030) [1]. A few microwatts to milliwatts of power is required for driving the sensors and communicating data [2]. However, when using a battery for a trillion sensors, factors such as the environment, resources, and cost must be taken into consideration. For this reason, energy harvesting, which recovers electric power from unused energy (e.g., vibration, heat, light, and radio waves) present in the natural environment, has received increasing attention. The expectation is that this process will be used to recover electric power for sensor driving and data communication.
Piezoelectric ceramics and polymers are expected to exhibit sensing and energy harvesting properties, and many studies have focused on this possibility [3][4][5][6][7][8]. In addition, magnetostrictive alloys are considered promising energy harvesting materials [9,10], and hence the development and characterization of such alloys have attracted attention [11,12]. In recent years, Fe-Ga/Fe-Co laminated materials [13], Fe-Co/piezoelectric laminated materials [14], Tb-Dy-Fe/Fe-Co laminated materials [15], Fe-Co coatings [16], and Fe-Co short wire/polymer composites [17] have been developed for sensor applications. Stress-induced domain wall motion of Co-based microwires [18], inverse magnetostrictive characteristics of Fe-Co wire/Al-Si composites under impact loading [19], and the twisting effect on the energy conversion of Fe-Co wire/Al-Si [20] and Fe-Co wire/polymer [21] composites have also been studied. In addition, an Fe-Co bolt with a sensor function has been developed [22].
In general, vibration energy harvesting devices often use cantilevers, which are capable of harvesting power resulting from bending vibration [23,24]. A large amount of power is obtained by utilizing the resonance phenomenon of the cantilevers. For this reason, many studies have focused on the bending vibration of energy harvesting magnetostrictive cantilevers [25][26][27][28][29].
The expectation is that magnetostrictive materials will serve as biosensors [30]. Guo et al. [31] developed a wireless magnetostrictive biosensor immobilized with E2 glycoprotein to detect the classical swine fever virus (CSFV) E2 antibody. They used Metglas alloy 2826 (Fe 40 Ni 40 P 14 B 6 ) and found a linear relationship between the resonance frequency shift and the logarithm of CSFV E2 antibody concentrations ranging from 5 ng mL −1 to 10 µg mL −1 .
Recently, a completely new function has been added to composite materials with the aim of realizing multiple functions at the same time. Research and development of multifunctional composite materials are progressing, and research trends are evolving toward new applications and market expansions of these materials. One strategy for achieving such materials includes simultaneously imparting a magnetostrictive material with both an energy harvesting function and a mass detection function [32].
In the present work, a preliminary study of the Fe-Co/Ni vibration energy harvesting cantilever with mass detection is performed. Finite element analysis was carried out to predict the resonant frequency and output voltage in the Fe-Co/Ni cantilever under bending vibration for various weights of a proof mass. The effects of the mass location and distribution on the frequency shift were examined. The output voltage change due to the mass change was also discussed, and the potential of mass detection was shown by changing the output voltage. The frequency shift and output voltage change due to the mass change were then measured, and the test results were compared with numerical values. This comparison expects a good agreement between the model prediction and test data at the microgram level. The results reveal that the vibration energy harvesting device utilizing the resonance phenomenon can be used as a mass sensor. The findings of this work also provide new insights into the possibility of developing self-powered virus sensors.

Numerical Procedure
The effects of the location and distribution of a mass on the sensitivity are investigated via finite element analysis. The basic equations for a magnetostrictive material are outlined here. Considering the rectangular Cartesian coordinate system O-x 1 x 2 x 3 , the governing equations are given as follows [33]: where σ ij , B i , and u i are the stress tensor, magnetic flux density vector, and displacement vector, respectively; ρ is the mass density; and c is the damping coefficient. A comma followed by an index denotes partial differentiation with respect to the space coordinate x i or the time t, and the summation convention for repeated tensor indices is applied. The constitutive laws are given as follows [34]: where ε ij is the strain tensor; H i is the magnetic field intensity vector; and s H ijkl , d m kij , and µ ij are the constant magnetic field elastic compliance, piezomagnetic constant, and magnetic permittivity, respectively. The material constants are characterized by the following symmetry conditions: The strain tensor and the displacement vector are related as follows: The magnetic field intensity is expressed as follows: where ϕ is the magnetic potential.
Let us now introduce a compact matrix notation. This notation consists of replacing ij or kl by p or q, where i, j, k, and l take the values of 1, 2, and 3 and p and q take the values of 1, 2, 3, 4, 5, and 6 according to Table 1. Thus, The material properties of Fe-Co and Ni with piezomagnetic effect are transversely isotropic with x 3 being the axis of symmetry [35]. Constitutive Equations (3) and (4) for the magnetostrictive material are given as follows: where For Fe-Co and Ni used in this study, the constant magnetic field elastic compliances are written in terms of the Young's modulus E, shear modulus G, and Poisson's ratio ν as The relationship between engineering constants is given by Many theoretical studies on magnetostrictive biosensors have been performed [32]. Similarly, for simple shapes, solutions for the resonance frequency and the frequency change due to a mass change have been discussed. The fundamental resonant frequency f 0 of a thin plate with length l, width w and thickness h (h, w l) vibrating in the longitudinal mode is given as follows [36]: If the mass increase is small compared with the initial mass ρlwh of the plate, then the mass change, in accordance with the measured resonance frequency shift, is determined from the following equation [37]: Equation (17) indicates that the resonance frequency decreases linearly with increasing mass on the plate surface. However, evaluating the frequency change from Equation (17) is impossible for the cantilever under bending vibration, and hence, we used the finite element analysis software ANSYS to perform the evaluation. A magnetostrictive clad plate cantilever with the Fe-Co layer (length l, width w, and thickness h/2) perfectly bonded to the top surface of the Ni layer (length l, width w, and thickness h/2) is shown in Figure 1. The proof mass layer (length L, width W = w, and hight H) with weight m was attached to the cantilever. Dimensions w, h, and l were measured along the x 1 = x, x 2 = y, and x 3 = z axes, respectively. The origin of the coordinate system is located at the left-side center of the clad plate. The plate was clamped with z = 0 denoting the fixed center. The z-direction was the easy axis of magnetization for both the Fe-Co and Ni layers. The imposed base excitation was given by the displacement u y0 exp(iωt) of the clamped end, where u y0 is the amplitude of the applied displacement and ω = 2πf is the angular frequency. Furthermore, the mass change induced changes in the magnetic flux density and frequency of the clad plate were calculated via finite element analysis.
Moreover, through Faraday's law, the output voltage was obtained from the magnetic flux density change as follows: (18) where N is the number of turns of a coil. Tables 2 and 3 list the material properties of the Fe-Co and Ni layers.
where N is the number of turns of a coil. Tables 2 and 3 list the material properties of the Fe-Co and Ni layers.

Experiment
When a clad plate with Fe-Co and Ni bonded via thermal diffusion is subjected to bending vibration, the vibration power output obtained is larger than that realized from a traditional Fe-Co plate [26]. A cantilever beam of Fe-Co/Ni clad plate thinner than those used in previous studies [26,38] was fabricated in the present study. The length, width, and thickness were 50 mm, w = 6.2 mm, and h = 0.2 mm, respectively.
To measure the output voltage V out of the Fe-Co/Ni clad plate, a vibration power generation test was executed using a vibrator. The clad plate cantilever with a proof mass of m = 1, 2, 4, 7, or 10 mg was mounted on the vibration shaker (ET-132, Labworks Inc., Costa Mesa, CA, USA), and the imposed displacement vibration was applied with the shaker. The proof mass was a masking tape made of paper. A cantilever without the mass was also used. The free length of the cantilever was l = 33 mm. The peak-to-peak output voltage V pp = 2V out associated with various values of the frequency f was recorded using a data logger (NR-500 series, Keyence Corporation, Osaka, Japan). The number of turns of the coil, resistance of the coil, and the sampling period were~4200, 7.47 kΩ, and 100 µs, respectively. Figure 2 shows the specimen and experimental setup.

Experiment
When a clad plate with Fe-Co and Ni bonded via thermal diffusion is subjected to bending vibration, the vibration power output obtained is larger than that realized from a traditional Fe-Co plate [26]. A cantilever beam of Fe-Co/Ni clad plate thinner than those used in previous studies [26,38] was fabricated in the present study. The length, width, and thickness were 50 mm, w = 6.2 mm, and h = 0.2 mm, respectively.
To measure the output voltage Vout of the Fe-Co/Ni clad plate, a vibration power generation test was executed using a vibrator. The clad plate cantilever with a proof mass of m = 1, 2, 4, 7, or 10 mg was mounted on the vibration shaker (ET-132, Labworks Inc., Costa Mesa, CA, USA), and the imposed displacement vibration was applied with the shaker. The proof mass was a masking tape made of paper. A cantilever without the mass was also used. The free length of the cantilever was l = 33 mm. The peak-to-peak output voltage Vpp = 2Vout associated with various values of the frequency f was recorded using a data logger (NR-500 series, Keyence Corporation, Osaka, Japan). The number of turns of the coil, resistance of the coil, and the sampling period were ∼4200, 7.47 kΩ, and 100 μs, respectively. Figure 2 shows the specimen and experimental setup.   Figure 3 shows the measured peak-to-peak output voltage Vpp versus frequency f for the Fe-Co/Ni clad plates with a proof mass of m = 0, 1, 2, 4, 7, and 10 mg. The resonance frequency of the Fe-Co/Ni clad plate without the proof mass was ∼107 Hz. It was expected that for the first mode, the maximum output voltage generated from the Fe-Co/Ni clad plate without the proof mass would be ∼85 mV. As the weight of the mass increases, the frequency decreases, and the maximum output voltage increases slightly. Table 4 presents a comparison of the output voltage density of the Fe-Co/Ni clad plate with the magnetostrictive harvesters [21,25,27,29,39,40]. Although the output voltage density depends on the bias magnetic field, excitation conditions, number of coil turns, etc., the performance of the Fe-Co/Ni clad plate is almost comparable to those of other magnetostrictive harvesters. Figure 4 shows the measured and calculated frequency shift Δf (due to the proof  Figure 3 shows the measured peak-to-peak output voltage V pp versus frequency f for the Fe-Co/Ni clad plates with a proof mass of m = 0, 1, 2, 4, 7, and 10 mg. The resonance frequency of the Fe-Co/Ni clad plate without the proof mass was~107 Hz. It was expected that for the first mode, the maximum output voltage generated from the Fe-Co/Ni clad plate without the proof mass would be~85 mV. As the weight of the mass increases, the frequency decreases, and the maximum output voltage increases slightly. Table 4 presents a comparison of the output voltage density of the Fe-Co/Ni clad plate with the magnetostrictive harvesters [21,25,27,29,39,40]. Although the output voltage density depends on the bias magnetic field, excitation conditions, number of coil turns, etc., the performance of the Fe-Co/Ni clad plate is almost comparable to those of other magnetostrictive harvesters. Figure 4 shows the measured and calculated frequency shift ∆f (due to the proof mass) as a function of the load P or weight m of the mass. The damping ratios ζ = c/c c (c c : critical damping coefficient) of the Fe-Co/Ni clad plate with a proof mass of m = 0, 1, 2, 4, 7, and 10 mg were obtained by the half power method and were 0.0084, 0.0094, 0.0085, 0.0091, 0.0087, and 0.0094. The length L and height H of the mass were 1 mm and 0.1 mm, respectively. The frequency shift decreases linearly with increasing load or weight. In addition, the mass can be detected from changes in the resonance frequency of this clad steel plate.

Results and Discussion
Materials 2021, 14, x FOR PEER REVIEW 7 of 13 mass) as a function of the load P or weight m of the mass. The damping ratios ζ = c/cc (cc: critical damping coefficient) of the Fe-Co/Ni clad plate with a proof mass of m = 0, 1, 2, 4, 7, and 10 mg were obtained by the half power method and were 0.0084, 0.0094, 0.0085, 0.0091, 0.0087, and 0.0094. The length L and height H of the mass were 1 mm and 0.1 mm, respectively. The frequency shift decreases linearly with increasing load or weight. In addition, the mass can be detected from changes in the resonance frequency of this clad steel plate.    A recent study [41] has shown that optimizing the location and distribution of the load provides the highest sensitivity. Figure 5 shows the calculated resonance frequency f 0 of the Fe-Co/Ni clad plates where the distance between the center of the proof mass and the fixed end is a = 0.5, 9.5, 19, 28.5, and 37.5 mm. The length L and height H of the mass were 1 mm and 0.1 mm, respectively. The calculated frequency shifts ∆f due to the mass of weight m = 10 mg are shown in the figure. The resonance frequency increases (as expected) with decreasing distance of the proof mass from the fixed end, whereas the frequency shift decreases. Figure 6 shows the calculated resonance frequency f 0 and frequency shift ∆f due to the mass with weight m = 10 mg of the Fe-Co/Ni clad plates. The f 0 and ∆f values were calculated for various values of a (the distance between the proof mass and the fixed end) and L (the length; L = 12, 4, and 1 mm) of the proof mass. When the proof mass is near the fixed end, the frequency increases with the mass as the size of the mass increases even if the weight is the same. The frequency changes only slightly when the proof mass is in the center of the cantilever. When the mass is near the free end, the frequency is reduced by the mass regardless of the mass size.    A recent study [41] has shown that optimizing the location and distribution of th load provides the highest sensitivity. Figure 5 shows the calculated resonance frequenc f0 of the Fe-Co/Ni clad plates where the distance between the center of the proof mass an the fixed end is a = 0. 5, 9.5, 19, 28.5, and 37.5 mm. The length L and height H of the mas were 1 mm and 0.1 mm, respectively. The calculated frequency shifts Δf due to the mas of weight m = 10 mg are shown in the figure. The resonance frequency increases (as ex pected) with decreasing distance of the proof mass from the fixed end, whereas the fre quency shift decreases. Figure 6 shows the calculated resonance frequency f0 and fre quency shift Δf due to the mass with weight m = 10 mg of the Fe-Co/Ni clad plates. The and Δf values were calculated for various values of a (the distance between the proof mas and the fixed end) and L (the length; L = 12, 4, and 1 mm) of the proof mass. When th proof mass is near the fixed end, the frequency increases with the mass as the size of th mass increases even if the weight is the same. The frequency changes only slightly whe the proof mass is in the center of the cantilever. When the mass is near the free end, th frequency is reduced by the mass regardless of the mass size.      The results obtained indicate that the Fe-Co/Ni clad plate with energy harvesting capability can detect the weight of the proof mass. In particular, a weight of ~1 mg can be detected from a change in the output voltage of 12 mV. The output voltage of the magnetostrictive material increases proportionally to the number of coil turns [42]. Therefore, the detected weight decreases with the increasing number of coil turns.
The principle of magnetostrictive biosensors is as follows [43]: Due to the magnetostrictive effect, an alternating current (AC) magnetic field applied to the magnetostrictive laminated plate would result in a bending vibration and generate a physical resonance. Consider the surface of the plate covered with a biomolecular recognition element such as an antibody. The fundamental resonance frequency f0 of the plate without antigen   The results obtained indicate that the Fe-Co/Ni clad plate with energy harvesting capability can detect the weight of the proof mass. In particular, a weight of ~1 mg can be detected from a change in the output voltage of 12 mV. The output voltage of the magnetostrictive material increases proportionally to the number of coil turns [42]. Therefore, the detected weight decreases with the increasing number of coil turns.
The principle of magnetostrictive biosensors is as follows [43]: Due to the magnetostrictive effect, an alternating current (AC) magnetic field applied to the magnetostrictive laminated plate would result in a bending vibration and generate a physical resonance. Consider the surface of the plate covered with a biomolecular recognition element such as an antibody. The fundamental resonance frequency f0 of the plate without antigen The results obtained indicate that the Fe-Co/Ni clad plate with energy harvesting capability can detect the weight of the proof mass. In particular, a weight of~1 mg can be detected from a change in the output voltage of 12 mV. The output voltage of the magnetostrictive material increases proportionally to the number of coil turns [42]. Therefore, the detected weight decreases with the increasing number of coil turns.
The principle of magnetostrictive biosensors is as follows [43]: Due to the magnetostrictive effect, an alternating current (AC) magnetic field applied to the magnetostrictive laminated plate would result in a bending vibration and generate a physical resonance. Consider the surface of the plate covered with a biomolecular recognition element such as an antibody. The fundamental resonance frequency f 0 of the plate without antigen binding decreases to f 1 owing to the fact that antigen binds to the antibody immobilized on the sensor surface. This shift of the resonance frequency can be monitored by using a pickup coil. Our Fe-Co/Ni clad plate serves as the bending vibration energy harvesting device, and without antigen adsorption, the harvested power will be able to supply as a source of transmitting power in order to forward information from the sensor. Furthermore, this plate for energy harvesting is subjected to bending vibration and serves as the biosensor without the need for an AC magnetic field (see Figure 8a). In addition, our biosensor may be able to detect the mass from the reduced output voltage ∆V = V 0 − V 1 , which will significantly reduce the detection time (Figure 8b). The purpose of this study is to confirm the principles of vibration energy harvesting and mass detection. Hence, the "mass" of the mass sensing element is not specifically identified. In future research, experiments will be conducted on the mass of the virus. The comparison between two types of traditional biosensors [32,44] and our future biosensor is given in Table 5.
binding decreases to f1 owing to the fact that antigen binds to the antibody immobilized on the sensor surface. This shift of the resonance frequency can be monitored by using a pickup coil. Our Fe-Co/Ni clad plate serves as the bending vibration energy harvesting device, and without antigen adsorption, the harvested power will be able to supply as a source of transmitting power in order to forward information from the sensor. Furthermore, this plate for energy harvesting is subjected to bending vibration and serves as the biosensor without the need for an AC magnetic field (see Figure 8a). In addition, our biosensor may be able to detect the mass from the reduced output voltage ΔV = V0 − V1, which will significantly reduce the detection time (Figure 8b). The purpose of this study is to confirm the principles of vibration energy harvesting and mass detection. Hence, the "mass" of the mass sensing element is not specifically identified. In future research, experiments will be conducted on the mass of the virus. The comparison between two types of traditional biosensors [32,44] and our future biosensor is given in Table 5.  According to a recent study, quartz crystal sensors exhibiting the piezoelectric effect can be modified with mixed self-assembled monolayers (SAMs) and can be explored for the label-free detection of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) [45]. The role played by engineered surface chemistry of personal protective equipment in avoiding the spread of the novel SARS-CoV-2 virus in hospitals was also highlighted [46]. These engineered surfaces could be reused after desorption. Future work could consider the implementation of these mixed SAMs on the Fe-Co/Ni clad plates (Figure 8c).  According to a recent study, quartz crystal sensors exhibiting the piezoelectric effect can be modified with mixed self-assembled monolayers (SAMs) and can be explored for the label-free detection of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) [45]. The role played by engineered surface chemistry of personal protective equipment in avoiding the spread of the novel SARS-CoV-2 virus in hospitals was also highlighted [46]. These engineered surfaces could be reused after desorption. Future work could consider the implementation of these mixed SAMs on the Fe-Co/Ni clad plates (Figure 8c).

Conclusions
In this study, the effect of mass on the bending vibration power generation behavior of a magnetostrictive clad plate was investigated, and the biosensor was reasonably designed based on this principle. Besides, the feasibility was verified by both experiment and numerical simulation method. The voltage output via this vibration decreases with the increasing weight of the mass, owing to the fact that the resonance frequency is shifted by the mass. Through various results, it was confirmed that the detection of the microgram level can be achieved. What is more, the optimization of the biosensor was also conducted to reach the best performance in, for example, detecting the position and size of an antibody. Compared with the traditional detection method, the benefit of the detection from changes of the output voltage instead of the frequency shift is that it does not require fast Fourier transform or discrete Fourier transform analysis and will shorten the detection time. Therefore, real-time detection can be realized, and it is easier to read the results. Since AC magnetic field is not necessary for this detection system, the device can be made wirelessly. Moreover, the materials used in this study are relatively cheap, and the manufacturing process is simple, which is very helpful for wide application. However, the sensitivity of this detection system is not sufficient due to the nanogram scale of viruses. Further research is needed and is currently underway to confirm this possibility.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.