Piezoelectric energy harvester with double cantilever beam undergoing coupled bending-torsion vibrations by width-splitting method

We propose piezoelectric energy harvester (PEH) with double-cantilever-beam (DCB) undergoing coupled bending-torsion vibrations by combining width-splitting method and asymmetric mass, in order that more ambient energy could be harvested from environmental vibration with multiple-frequency excitation. The geometrical dimensions are optimized for PEHDCB, when the maximum of output peak voltages Up-max and resonance frequency difference (Δf0) between the first and second modes are chosen as optimization objectives based on orthogonal test method. The energy harvesting efficiency is evaluated by the proportion of half-power bandwidth and quality factor, and the experimental and simulation results are compared to verify reliability. The Up-max1 and Pp-max1 are increased 25.2% and 57.3% for PEHDCB under the multi-frequency excitation, when the split-width method is applied into PEH with single-cantilever-beam (SCB) undergoing coupled bending-torsion vibrations. The deviations of Up-max1 and f0 are at the ranges of 4.9–14.2% and 2.2–2.5% for PEHDCB under the different mass ratios, and the measurement reliability is acceptable considering incomplete clamping, damping and inevitable assembly effects. The energy harvesting efficiency of PEHDCB presented is much higher than that of the conventional PEHSCB from environmental vibration with multiple-frequency excitation.

In recent years, harvesting ambient energy using piezoelectric effect is considered to be an important energy conversion technology applicable to future industries along with photovoltaics 1 , thermoelectrics 2 , radio frequencies 3 , and triboelectric technology 4 . Vibration-based piezoelectric energy harvester is a potential candidate to replace existing power sources such as the batteries which have a limited energy storage capacity and lifetime for some applications 5 . Based on Taguchi orthogonal method, the variation in the excitation frequency, the thickness of piezoelectric layers and the acceleration of the bimorph piezoelectric energy harvester (PEH) were optimized by maximum output peak voltage (U p-max ) and signal-to-noise ratio as the optimization objectives 6 , and the ultimate goal is that one could obtain the U p-max with lesser trials 7 . Most of PEHs with the different beam shapes, such as the rectangles [8][9][10][11] and triangles 12,13 have been focused on the energy harvesting characteristics from bending vibration, and the main problem is the significant dropping of output power when the excitation frequency slightly away from the natural frequency of the harvesters. The durability of PEH is importance to sustainable power wireless sensors, and some researchers have focused on the fatigue analysis for PEH under different excitation cycles 14 and levels of base excitation 15 .
PEH can effectively harvest electric power from torsional vibration by attaching a simple cantilever beam structure on the top surface of a rotating shaft generate 16 . A unimorph cantilever beam undergoing bendingtorsion vibrations has been proposed by asymmetry increasing under a transverse harmonic base excitation to narrow the resonance frequency difference (Δf 0 ) between first and second modes, therefore it allows the harvesting of electrical power from multiple-frequency excitation 17  www.nature.com/scientificreports/ harvester for capturing wind energy at low wind speed is of lower natural frequency and smaller electromechanical coefficient than those of the conventional vortex-induced piezoelectric energy harvester 18 . The effect of width-splitting on the harvested power was theoretically and experimentally investigated for a fixed dimension piezoelectric materials of PEH undergoing bending vibration, and the width-splitting method could be used to increase the harvested voltage 19 and power 20 over a wider range of excitation frequencies. The single piezoelectric beam with the similar total width was folded equally and then split a given dimension of piezoelectric materials with the predefined dimensions into the array of smaller-width beams, and there is a substantial increase in harvested power 21 . There are many reports on the evaluation methods of half-power bandwidth and quality factor for PEHs undergoing bending vibration 19,21 , however relatively few researches are focus on the evaluation method for PEH undergoing coupled bending-torsion vibrations. The best performance occurs at a single or very narrow frequency range for most resonating harvesters, and then a critical issue is how to adjust the resonance frequency (f 0 ) flexibility and maximize harvesting power because of environment vibrations composed of some broadband random or multiple-frequency excitation 22,23 . In a word, the width-splitting method could be used to improve energy harvesting performances of PEH undergoing bending vibration, however one could not know whether it is applicable to harvest more ambient energy from multiple-frequency excitation by using PEH undergoing coupled bending-torsion vibrations. In this paper, PEH with single-cantilever-beam (SCB) is equally split into PEH with double-cantilever-beam (DCB) in order to harvest ambient energy from multiple-frequency excitation, which is verified comparing with the experimental and simulation results of the U p-max and Δf 0 . After the geometrical dimensions including the split gap d, primary beam L and substrate thickness t s were determined by using U p-max and Δf 0 combination in multi-factors analysis based on orthogonal test method, we had fabricated PEHSCB and PEHDCB undergoing coupled bending-torsion vibrations. The mechanical vibration experiments were performed by shaker to measure U p vs frequency (U p -f) curves of PEHs undergoing coupled bending-torsion vibrations, and the half-power bandwidth proportion and materials mechanical quality factors are used to evaluate the harvesting efficiency from the multiple-frequency excitation. We expect that the research could significantly offer some useful guidelines to design high-performance PEH, which could harvest more ambient energy under multiple-frequency excitation.

Design and simulation
Construction of PEHDCB split from PEHSCB. The single/double T-shaped brass shims and commercial piezoelectric ceramic PZT bulks were provided by Wuxi Hui Feng Electronics Co. Ltd, and the material properties parameters [24][25][26] are listed in Table 1. PZT element was formed of PZT wafer, top and bottom electrodes, before PEHSCB was designed by bonding the elements on the primary beam via conductive adhesive, as shown in Fig. 1a. PEHDCB is constructed by splitting equally the primary beam of PEHSCB, as shown in Fig. 1b, and the split gap d determined by the width-splitting method 19,21 is listed in Table 2.  www.nature.com/scientificreports/ There are two variable mass blocks M 2 and M 1 placed at tip of the crossbeam, and M 2 /M 1 is defined as the mass ratio m * and when the mass ratio changes, the mass sum of mass blocks remains unchanged at both of the beam ends. The geometrical dimensions of PEHSCB include the length L, width b, thickness t s , piezoelectric ceramic thickness t p for the primary beam and the length L 1 , L 2 , width a, mass ratio m* for the crossbeam, and all of them are listed in Table 2. The polarization direction of piezoelectric ceramic PZT-53 bulk is marked by the red arrows along Z-axis. Learning from the series connection structure 27 , two PZT elements split from the primary beam of PEHSCB are poled oppositely in the perpendicular to length direction to form the series connection shown in Fig. 1b. In Cartesian coordinate system (X, Y, Z), one ends of the single and double beams are fixed, and the crossbeams are at free end.
Simulation. Modeling on PEHSCB and PEHDCB. The U p and f 0 of PEHs are simulated by using the commercial analysis package ANSYS. The 8-node hexahedral coupled-field element SOLID5 and the 8-node linear structural element SOLID45 are used for piezoelectric materials and non-piezoelectric materials, and piezoelectric circuit element CIRCU94 is used for load resistor. The displacement degrees of freedom are constrained to be zero for fixed end of the primary beam of PEH. The electrode connections are made by using the "couple" commands 28 . As for PEHDCB, the potentials of top surface of substrate layer are coupled with bottom surface of piezoelectric layer, and they are individually coupled for top surfaces of two piezoelectric layers. The potential is constrained to be zero for one top surface of piezoelectric layers, and a load resistor is connected between the top surfaces of two piezoelectric layers, as shown in Fig. 1. The output voltage across load resistor is solved for the potential of top surface of piezoelectric layer, when T-shaped beam is loaded with the inertial acceleration 9.8 m/s 2 .
In order to obtain a convergent solution by using mesh refinement 29 , the modal stress diagrams at the first mode of PEHDCB are performed by considering the four different mesh densities 0.7, 0.6, 0.5 and 0.4 mm, and they are respectively given as in Fig. 2a,b,c,d. Obviously, the difference of the maximum stress is less than 6% for the last two mesh densities, as shown in Fig. 2c,d, therefore it could be regarded as a convergent solution when mesh density 0.5 mm.
The modal stress analysis. In order to satisfy the yield strength of piezoelectric materials and brass 30 , the modal analyses on PEHs with asymmetric mass are performed under the mesh density 0.5 mm, and the modal stress diagrams are presented in Fig. 3a Optimization on asymmetry PEHs with the different mass ratios. To investigate the effect of m * on the harvesting performance of PEHSCB, the U p -f curves were simulated under the different mass ratios m * = 19, 9, 4 and 1.5 when b = 12 mm, L 1 = L 2 = 22 mm, and they are described as Fig. 4a. With the asymmetry increase of m * from 1.5 to 19, the U p-max1 and f 01 at the first mode decrease from 33.6 to 29.0 V and 88 to 72 Hz. On the contrary, the U p-max2 and f 02 at the second mode increase from 5.1-11.6 V and 118 to 177 Hz. As for m * > 1, all of the f 01 and f 02 are far lower than the nature frequency 200 Hz and the Δf 0 is narrowed. Therefore it allows the harvesting of electrical power from the multiple-frequency excitation, and they are agreement with the previous results 17 . Drawing the U p-max and f 0 at the certain m * from Fig. 4a, the U p-max vs m * and f 0 vs m * curves are described as Fig. 4b for the first mode and Fig. 4c for the second mode. Both of the U p-max1 and f 01 decrease with the asymmetry increase of m * , as shown in Fig. 4b, however the f 02 increases and the U p-max2 increases to reach a peak value at m * = 9 and then decreases by contrary, as shown in Fig. 4c. The optimization mass ratio m * is determined as 9 by considering the trade-off between U p-max and f 0 , in order that PEHSCB could achieve not only the higher U p-max but also both the lower f 01 and f 02 . According to the previous analysis method 31 , we analogously determine the mass ratios m * = 9 to investigate harvest ambient energy of PEHDCB undergoing coupled bending-torsion vibrations from a multiple-frequency excitation as follow.
Effect of single-factor on PEHDCB. To understand the effect of single geometrical parameter on energy harvesting performance of PEHDCB, the U p -f curves were simulated under the different split gaps d, such as 2, 3, 4, 5 and 6 mm, and they are described as Fig. 5a when m * = 9, b = 12 mm, L 1 = L 2 = 22 mm. With the d increase from 2 to 6 mm, the U p-max1 , f 01 and f 02 increase from 31.8 to 37.3 V, 75 to 80 Hz and167 to 177 Hz however the U p-max2 decreases from 14.6 to 13.3 V. The dependencies of U p-max and f 0 on m * are analogously discussed as shown in Fig. 4b,c, and the U p-max and f 0 vs d curves are described as Fig. 5b for the first mode and Fig. 5c for the second mode. With the increase of d, both of the U p-max1 and f 01 increase monotonously, however the U p-max2 decreases and the f 02 increases by contrary. By adjusting the split gap d, PEHDCB can harvest energy more evenly at the two first modes, and it is in an agreement with the reported result 32 .
The U p -f curves were simulated under the different primary beam lengths L, such as 26, 27, 28, 29 and 30 mm, L 1 = L 2 = 22 mm, and they are described as Fig. 6a when m * = 9, b = 12 mm. The d dependencies of U p-max and f 0 are analogously discussed, as shown in Fig. 5b,c, and the U p-max and f 0 vs L curves are described as Fig. 6b for the www.nature.com/scientificreports/ first mode and Fig. 6c for the second mode. With the increase of L, the U p-max1 monotonously increases but the U p-max2 slightly decreases at the second mode, however both of the f 01 and f 02 decrease. It indicates that the primary beam length can be adjusted by considering the trade-off between the U p-max and f 0 , in order that PEHDCB could harvest energy more evenly under the multiple-frequency excitation.
The U p -f curves were simulated under the different substrate thicknesses t s , such as 0.4, 0.5, 0.6, 0.7 and 0.8 mm, and they are described as Fig. 7a, when m * = 9, b = 12 mm, L 1 = L 2 = 22 mm. Analogously, the U p-max and f 0 vs t s curves are described as Fig. 7b for the first mode and Fig. 7c for the second mode. With the increase of t s , the U p-max1 increases to reach the peak at t s = 0.6 mm however the U p-max2 decreases monotonously. Both the f 01 and f 02 increase. It could guide to choose a suitable t s to achieve high U p-max and low f 0 of PEHDCB under the multiple-frequency excitation.
Multi-factor analysis via orthogonal test method. Generally, the effect of single-factor on performance of PEHDCB could not be taken into account the cross factor effect 33 , therefore we carry out the multifactors analysis to optimize energy harvesting performance of PEHDCB by using orthogonal test method. The orthogonal factor/level list and the L 25 (5 6 ) corresponding orthogonal list are shown in Tables 3 and 4.
There are the three geometrical dimensions d, t s and L corresponding to 5 levels in Table 3. Distinguished from the traditional orthogonal test method 8 , the U p-max1 , U p-max2 and Δf 0 were chosen as the optimization objectives to analyze the influences of the three factors on the performance, and the last three factors are kept empty corresponding to the L 25 (5 6 ) lists in Table 4 34 . As for the optimal combination of Case 21 in Table 4, the U p-max1 and U p-max2 are 37.3 V and 13.3 V, and the Δf 0 is 97.0 Hz. Correspondingly, the d, L and t s are optimally determined as 6, 30, and 0.4 mm, in order that PEHDCB achieves not only high U p-max but also narrow Δf 0 for easily harvesting electrical power from the multiple-frequency excitation 17 .

Experiment
Experimental measurement. The mechanical vibration experiment was carried out to verify the validity and accuracy of simulation result, and the schematic diagram and power measurement circuit are given in Fig. 8a,b for the measurement setup 27 . In order to investigate the effect of width splitting method on the www.nature.com/scientificreports/ energy harvesting performances, PEHDCB was constructed by splitting equally the primary beam, and both of PEHSCB and PEHDCB were fabricated according to the optimal combination Case 21 in Table 4, as shown in Fig. 8c,d. After clamped by the fixtures, PEHSCB and PEHDCB were fixed on the shaker (JZk-5, Sinocera Piezotronics, Inc., Jiangsu, China), and the acceleration was obtained through the accelerometer (CA-DR-005, Sinocera Piezotronics, Inc., Jiangsu, China) placed on the top of the shaker. The sinusoidal vibration from the function generator (Tektronix AFG 3021B, Tektronix) was amplified by the power amplifier (YE5871A, Sinocera Piezotronics, Inc., Jiangsu, China), and the shaker was applied at 2.1 A and 1 V to generate the mechanical energy.
All the output peak voltages of PEHSCB and PEHDCB were measured at the certain resistance of 100 kΩ by Digital Oscilloscope (Tektronix TDS 1002, Tektronix), and the output power was calculated by using the formula where R L the load resistance. Generally, the proportion of half-power bandwidth and the quality factor (Q = f 0 /δ f ) are used to evaluate the collection efficiencies of PEHDCB under a single-frequency excitation and multi-frequency excitation 19,21 , and the δ f is the 3 dB bandwidth of PEHDCB 35 . Test and verify on energy harvesting efficiency of PEHSCBs. The energy harvesting efficiency of PEHSCB undergoing coupled bending-torsion vibrations is better than that of PEHSCB undergoing bending vibration in the simulation results 24 , therefore we hope to verify the previous results by comparing with the Δf 0 and proportion of half-power bandwidth in the mechanical vibration experiment as follow. The output peak voltages were measured under b = 12 mm, L 1 = L 2 = 22 mm, R L = 100 kΩ, and the U p -f and P-f curves are given in Fig. 9a,b for PEHSCBs undergoing coupled bending-torsion vibrations with m * = 9 and bending vibration with m * = 1. Here, the simulation results are represented by the solid lines, and the experimental results are described by the dots for the latter and the triangles for the former. From Fig. 9a, the f 01 of PEHSCB with m * = 9 is lower than that of PEHSCB with m * = 1, which indicates that PEH undergoing coupled bending-torsion vibrations is more suitable for harvesting the electrical power from the ambient vibration composed of low frequency 36 . On the other hand, the Δf 0 is 90.0 Hz for PEHSCB undergoing coupled bending-torsion vibrations, however it is far much narrower than that of PEHSCB undergoing bending vibration. Obviously, the coupled bending-torsion vibrations could decrease the Δf 0 to allow the harvesting of electrical power from the multiple- The energy harvesting efficiency could be generally evaluated by the half-power bandwidth value 19,21 , but the proportion of half-power bandwidth should be more suitable to evaluate the harvesting efficiency for PEH at the multiple-frequency excitation 25 . Here, the proportions of half-power bandwidth are 5.2% at the first mode and 3.8% and at the second mode for PEHSCB with m * = 9, and the proportion of half-power bandwidth is 5.1% at the first mode for PEHSCB with m * = 1. Obviously, the proportion of half-power bandwidth of PEHSCB undergoing coupled bending-torsion vibrations is superior to that of PEHSCB undergoing bending vibration at the first mode, meanwhile the former could far more easy to harvest the electrical power from the ambient vibration because of the resonance lack for the latter at the second mode. The energy harvesting efficiency of PEHSCB undergoing coupled bending-torsion vibrations must be much better than that of PEHSCB undergoing bending vibration, since the environmental vibrations are generally composed of the multiple-frequency.
Effect of width splitting method on the energy harvesting performances. In order to verify the effect of width splitting method on the energy harvesting performances 19,21 , the U p-max and P p-max of PEHDCB are compared with those of PEHSCB, meanwhile the quality factors related with Δf 0 are compared because of damping change induced width splitting method. The U p-max were measured for PEHDCB with d = 6 mm, b = 12 mm, L 1 = L 2 = 22 mm, m * = 9, R L = 100 kΩ, and the U p -f and P-f curves are given in Fig. 10a   www.nature.com/scientificreports/ Energy harvesting performances of asymmetry PEHDCBs. The U p -f curves of the PEHDCBs were measured under the different mass ratios m * , such as 1.5, 4, 9 and 19, and they are given in Fig. 11, when b = 12 mm, L 1 = L 2 = 22 mm, d = 6 mm, R L = 100 kΩ. Here, the simulation and experimental results are represented by the lines and dots, in order that the validity could be confirmed by analyzing the relative deviations of U p-max and f 0 at the first and second modes. Obviously, the maximum relative deviations of U p-max and f 0 are 6.8% and 2.6% for the first mode, and they are 14.2% and 2.5% for the second mode. There are generally the incomplete clamping of the experimental fixture and the unavoidable assembly errors in the manufacture 39 , therefore the simulation results could be not exactly equal to the resonance frequency experiment results for PEHs with the asymmetric mass and width-splitting beam in Figs. 8, 9 and 10. The clamped end of beam is not completely rigid in mechanical vibration experimental, however the fixed boundary conditions in simulation make the beam slightly stiffer. The incomplete clamping and inevitable assembly frequency errors are approximately at the ranges of 2-7% for the nonstable nonlinear energy harvester 40,41 and 5-10% for the piezoelectric energy harvester for harnessing energy from flow-induced vibration 39 , and the U p-max error is approximately at the range of 10-26% for the rotational mechanical plucking energy harvester 42 . The U p-max and f 0 deviations are 14.2% and 2.6% for the PEHDCBs under the different mass ratios, as shown in Fig. 11, therefore the results are acceptable for the mechanical vibration experiment. Drawn from Fig. 11, the U p-max and m * are served as the vertical and horizontal ordinates to understand the effect of asymmetric mass on energy harvesting performance, and the U p-max1 and U p-max2 vs m * curves are described as Fig. 12. With the asymmetric increase of m * from 1.5 to 9, the simulation/experimental U p-max1 values decrease from 41.0 V/38.2 V to 36.5 V/34.8 V, and the simulation/experimental U p-max2 values increase to the reach peak values of 13.3 V/12.8 V and 12.1 V/11.1 V. Obviously, the energy harvesting efficiency is slightly decreased under the multiple-frequency excitation when the mass ratio m * is larger than 9. Considering the trade-off of U p-max1 and U p-max2 , PEHDCB with m * = 9 can harvest energy more evenly, and it is similar with the reported result 43 . In a word, there is a useful strategy to enhance the U p-max1 and U p-max2 by adjusting the

Conclusion
In summary, the optimization geometrical parameters of PEHDCB are determined by considering the U p-max and Δf 0 in the multi-factor analysis based on the orthogonal test, and the Δf 0 narrowed of PEHDCB undergoing coupled bending-torsion vibrations results in harvesting the more electrical power from the ambient vibration composed of low frequency. The quality factors Q 1 and Q 2 of PEHDCB undergoing coupled bending-torsion vibrations are larger than those of PEHSCB under the multi-frequency excitation, and the U p-max1 and P p-max1 at the first mode are increased 25.2% and 57.3% for PEHDCB. The width-splitting method could be successfully used to improve the energy harvesting performances, and the measurement reliability is acceptable considering the incomplete clamping, damping and inevitable assembly effects. Considering the trade-off of U p-max1 and U p-max2 , the asymmetry PEHDCB with the mass ratio determined as 9 can harvest energy more evenly, and the results are effective to predict the energy harvesting performances for PEHDCB undergoing coupled bendingtorsion vibrations under the multi-frequency excitation. As for the purpose to explore the effect of width splitting method on the energy harvesting performances in this work, we should consider the parameters related with damping change such as the width splitting size d into electromechanical coupling dynamic equation, and one could obtain a closed form solution and comparing to give better insights on how the harvested power varies by varying the parameters in future research.   www.nature.com/scientificreports/