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decrease in resonance frequency, there is still a significant increase due to the auxetic effect. Strain distributions in x and y directions were shown in Figs. 12 and 13, respec- tively. Maximum strain in x-direction for re-entrant case was around 3.5 uS and it is 20 uS for anti-tetra-chiral case. They were 0.9 uS and 0.08 uS for non-auxetic rectangular and plain cases, respectively. The more important part was in y-direction of the strain distribution. The maximum strain in y-direction occurred in PVDF were mostly in positive

Figure 8 decrease in resonance frequency, there is still a significant increase due to the auxetic effect. Strain distributions in x and y directions were shown in Figs. 12 and 13, respec- tively. Maximum strain in x-direction for re-entrant case was around 3.5 uS and it is 20 uS for anti-tetra-chiral case. They were 0.9 uS and 0.08 uS for non-auxetic rectangular and plain cases, respectively. The more important part was in y-direction of the strain distribution. The maximum strain in y-direction occurred in PVDF were mostly in positive

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Fig. 2 Poling directions and resistance connection The piezoelectric patches were assumed to be perfectly bonded on the surface of the substructure. The poling direc- tion was controlled by rotating the coordinate axis by 180° in Z direction to obtain a series connection between mate- rials. The top surface of the upper piezoelectric material was assigned as the terminal surface, and the bottom of the lower piezoelectric material was assigned as the ground. was assigned as the terminal surface, and the bottom of the
Fig. 2 Poling directions and resistance connection The piezoelectric patches were assumed to be perfectly bonded on the surface of the substructure. The poling direc- tion was controlled by rotating the coordinate axis by 180° in Z direction to obtain a series connection between mate- rials. The top surface of the upper piezoelectric material was assigned as the terminal surface, and the bottom of the lower piezoelectric material was assigned as the ground. was assigned as the terminal surface, and the bottom of the
The other two surfaces were assigned as the terminal sur- faces. A resistor between the terminal and the ground was created to form a circuit, as illustrated in Fig. 2, and the terminal was selected to measure the electric potential generated by the piezoelectric harvester. An experimental study was performed for two substructures of re-entrant and NS-A geometries which will be defined later. Damping for these substructures were calculated by logarithmic decre- ment method and imported to the FEA. An average value for stiffness parameter (7.4 X 107°) of Rayleigh damping was calculated for these substructures and that value was used throughout all the FEA simulations.
The other two surfaces were assigned as the terminal sur- faces. A resistor between the terminal and the ground was created to form a circuit, as illustrated in Fig. 2, and the terminal was selected to measure the electric potential generated by the piezoelectric harvester. An experimental study was performed for two substructures of re-entrant and NS-A geometries which will be defined later. Damping for these substructures were calculated by logarithmic decre- ment method and imported to the FEA. An average value for stiffness parameter (7.4 X 107°) of Rayleigh damping was calculated for these substructures and that value was used throughout all the FEA simulations.
Table 1 Material properties of materials used in the research The schematic in Fig. 4 depicts the experimental setup for validating the piezoelectric energy-harvesting model. The setup consists of steel and PLA substructures with piezo- electric materials bonded on each side of the beam at the same position. One side of the beam was connected to a shaker while the other side was free. To generate the vibra- tion signal, a function generator was connected to the shaker, and the signal was passed through an amplifier. A Laser Vibrometer (Optomet Nova Speed) was used to measure the acceleration applied to the beam. The piezoelectric materi- als were connected to each other in series and attached to a resistor to create an external circuit. When the function gen- erator applied a predefined vibration signal to the shaker, the piezoelectric material generated AC voltage. The generated voltage and acceleration signals were sent to an oscilloscope for measurement and analysis. Voltage data was normalized for 1 g of acceleration and then power was calculated from normalized voltage data and resistor used.
Table 1 Material properties of materials used in the research The schematic in Fig. 4 depicts the experimental setup for validating the piezoelectric energy-harvesting model. The setup consists of steel and PLA substructures with piezo- electric materials bonded on each side of the beam at the same position. One side of the beam was connected to a shaker while the other side was free. To generate the vibra- tion signal, a function generator was connected to the shaker, and the signal was passed through an amplifier. A Laser Vibrometer (Optomet Nova Speed) was used to measure the acceleration applied to the beam. The piezoelectric materi- als were connected to each other in series and attached to a resistor to create an external circuit. When the function gen- erator applied a predefined vibration signal to the shaker, the piezoelectric material generated AC voltage. The generated voltage and acceleration signals were sent to an oscilloscope for measurement and analysis. Voltage data was normalized for 1 g of acceleration and then power was calculated from normalized voltage data and resistor used.
Fig.5 Different substructures used in first case, a re-entrant, b anti-tetra-chiral, c rectangular, d plain Figure 6 shows the power responses of PVDF for the dif- ferent beam geometries and Table 3 shows the maximum harvested power at the natural frequency. Compared to the plain structure, the utilization of auxetic structures has increased the power gain more than 10 times. Maximum power was harvested from re-entrant structure. On the other hand, the power response from the rectangular non-auxetic structure has a maximum power response nearly same that of the anti-tetra-chiral geometry. This indicates that a non- auxetic structure with an area decrease in the geometry can also deliver the power increase achieved by utilizing auxetic This study examined the performance of various beam shapes and piezoelectric materials for harvesting energy across various frequency ranges. First, the optimum resist- ance values were calculated for each case. Because the maximum power can be harvested at the resonance fre- quency, the optimum resistance values were calculated at the resonance of the structure. The resonance frequencies and optimum resistance values calculated for the different beams were listed in Table 2.
Fig.5 Different substructures used in first case, a re-entrant, b anti-tetra-chiral, c rectangular, d plain Figure 6 shows the power responses of PVDF for the dif- ferent beam geometries and Table 3 shows the maximum harvested power at the natural frequency. Compared to the plain structure, the utilization of auxetic structures has increased the power gain more than 10 times. Maximum power was harvested from re-entrant structure. On the other hand, the power response from the rectangular non-auxetic structure has a maximum power response nearly same that of the anti-tetra-chiral geometry. This indicates that a non- auxetic structure with an area decrease in the geometry can also deliver the power increase achieved by utilizing auxetic This study examined the performance of various beam shapes and piezoelectric materials for harvesting energy across various frequency ranges. First, the optimum resist- ance values were calculated for each case. Because the maximum power can be harvested at the resonance fre- quency, the optimum resistance values were calculated at the resonance of the structure. The resonance frequencies and optimum resistance values calculated for the different beams were listed in Table 2.
Fig.4 Experimental set-up for energy harvesting investigation. The auxetic structures (Fig. 5 a, b) shown in the figure have negative Poisson’s ratio. The others have positive Poisson’s ratio. Results for PLA Beam Case This study examined the performance of various beam
Fig.4 Experimental set-up for energy harvesting investigation. The auxetic structures (Fig. 5 a, b) shown in the figure have negative Poisson’s ratio. The others have positive Poisson’s ratio. Results for PLA Beam Case This study examined the performance of various beam
Table 2 Resonance frequencies and optimum resistance values The strain distribution in the x and y directions on the PVDF bonded on auxetic and non-auxetic cases were shown in Figs. 7 and 8. It is clear that all cases were generally in tension in x direction. When looking at the Fig. 7, strain in re-entrant case has a maximum value of 9 mikrostrain (uS =um/m) where plain one has only 2 uS. On the other hand, 7 wS of maximum strain was found for rectangular case. On the other hand, in y-direction, for rectangular and plain cases, the strain was in (—) range generally, and it was a bit uncertain (— and + range together) for re-entrant and anti-tetra-chiral cases. The average strain and stress values
Table 2 Resonance frequencies and optimum resistance values The strain distribution in the x and y directions on the PVDF bonded on auxetic and non-auxetic cases were shown in Figs. 7 and 8. It is clear that all cases were generally in tension in x direction. When looking at the Fig. 7, strain in re-entrant case has a maximum value of 9 mikrostrain (uS =um/m) where plain one has only 2 uS. On the other hand, 7 wS of maximum strain was found for rectangular case. On the other hand, in y-direction, for rectangular and plain cases, the strain was in (—) range generally, and it was a bit uncertain (— and + range together) for re-entrant and anti-tetra-chiral cases. The average strain and stress values
Table 3 Maximum power responses of the structures for PLA case
Table 3 Maximum power responses of the structures for PLA case
case, however, the values were closed to each other for rec- tangular and auxetic cases. In auxetic cases, it was expected that the stress in y-direction is very high when compared to non-auxetic structure. Therefore, it is hard to say that the negative Poisson’s ratio of auxetic geometry really affected the power response of the harvester. Power boost compared to the plain structure was highly due to the area reduction and non-linear geometry. One reason for this can be ineffi- cient energy transfer from substructure to the piezoelectric material due to low stiffness of the substructure material. In that case, substructure cannot bend the piezoelectric material
case, however, the values were closed to each other for rec- tangular and auxetic cases. In auxetic cases, it was expected that the stress in y-direction is very high when compared to non-auxetic structure. Therefore, it is hard to say that the negative Poisson’s ratio of auxetic geometry really affected the power response of the harvester. Power boost compared to the plain structure was highly due to the area reduction and non-linear geometry. One reason for this can be ineffi- cient energy transfer from substructure to the piezoelectric material due to low stiffness of the substructure material. In that case, substructure cannot bend the piezoelectric material
Table 4 Average stress and strain values for different cases with PLA beam
Table 4 Average stress and strain values for different cases with PLA beam
effectively and decreases the energy transfer from the beam to the piezoelectric material. It can be increased by using more stiff material in substructure such as steel. Steel Beam Case For a second case (Table 5), a steel substructure was used with same geometries. The stiffness of the steel beam is higher than the PLA beam due to the higher elasticity modulus. This was expected to increase the energy trans- fer from the beam to the piezoelectric material, in example, with same geometries. The stiffness of the steel beam
effectively and decreases the energy transfer from the beam to the piezoelectric material. It can be increased by using more stiff material in substructure such as steel. Steel Beam Case For a second case (Table 5), a steel substructure was used with same geometries. The stiffness of the steel beam is higher than the PLA beam due to the higher elasticity modulus. This was expected to increase the energy trans- fer from the beam to the piezoelectric material, in example, with same geometries. The stiffness of the steel beam
range for re-entrant and anti-tetra-chiral cases which shows the effect of negative Poisson’s ratio. The average strains and stresses occurred on PVDF can also be seen in Table 6.
range for re-entrant and anti-tetra-chiral cases which shows the effect of negative Poisson’s ratio. The average strains and stresses occurred on PVDF can also be seen in Table 6.
It is clear that the only average positive strain in y-direction was obtained in re-entrant case. In other cases, the average strains in y-direction were in negative range. On the other hand, re-entrant structure gave very high x and y-direction stresses on PVDF when looking at the Table 6. The y-direc- tion stress obtained by re-entrant geometry was closed to the x-direction strain which is a sign of the effect of the auxetic geometry.
It is clear that the only average positive strain in y-direction was obtained in re-entrant case. In other cases, the average strains in y-direction were in negative range. On the other hand, re-entrant structure gave very high x and y-direction stresses on PVDF when looking at the Table 6. The y-direc- tion stress obtained by re-entrant geometry was closed to the x-direction strain which is a sign of the effect of the auxetic geometry.
The new structures were inspired by re-entrant structure which was used in vertical direction and named as NS-A, NS-B and NS-C as shown in Fig. 14. NS-A was directly utilized by using one cell of re-entrant structure. NS-B was obtained by taking out some area from NS-A to decrease the stiffness and increase deflection. For NS-C, two cells of re- entrant structure were used. These structures aim to magnify the stretch of the beam in x direction rather than changing the direction of the strain in y-direction. Because the strain in x-direction is very high compared to the strain in y-direc- tion for bending motion of the beam, increasing the strain in x-direction are expected to affect the harvested energy more. These harvesters were analyzed under identical conditions as those in Case 1, and their maximum power responses were compared to the results of the re-entrant geometry, which exhibited the best performance in previous part. The resonance frequencies and optimum resistance values were given in Table 7. It can be seen that minimum reso- nance frequency was achieved by NS-B which has maxi- mum area reduction and lower stiffness due to its geom- etry. Figure 15 shows the power responses obtained from the offered structures when PLA was used as beam mate- rial under optimum external resistances. It is obvious from the figure that maximum power was gained with the use of NS-B. All the new structures harvested more power from
The new structures were inspired by re-entrant structure which was used in vertical direction and named as NS-A, NS-B and NS-C as shown in Fig. 14. NS-A was directly utilized by using one cell of re-entrant structure. NS-B was obtained by taking out some area from NS-A to decrease the stiffness and increase deflection. For NS-C, two cells of re- entrant structure were used. These structures aim to magnify the stretch of the beam in x direction rather than changing the direction of the strain in y-direction. Because the strain in x-direction is very high compared to the strain in y-direc- tion for bending motion of the beam, increasing the strain in x-direction are expected to affect the harvested energy more. These harvesters were analyzed under identical conditions as those in Case 1, and their maximum power responses were compared to the results of the re-entrant geometry, which exhibited the best performance in previous part. The resonance frequencies and optimum resistance values were given in Table 7. It can be seen that minimum reso- nance frequency was achieved by NS-B which has maxi- mum area reduction and lower stiffness due to its geom- etry. Figure 15 shows the power responses obtained from the offered structures when PLA was used as beam mate- rial under optimum external resistances. It is obvious from the figure that maximum power was gained with the use of NS-B. All the new structures harvested more power from
NS-B giving nearly 42 nW. Power response of NS-A is very low compared to others in this case with a 0.12 nW, how- ever, all the new geometries gave very high power responses compared to the plain beam (Table 9). In the last part of the study, an experimental study was performed to show the effect of the new design in power generation and the results were compared to the FEA results. Here, 3D printed PLA based substructure was used with PVDF bonded on both sides.
NS-B giving nearly 42 nW. Power response of NS-A is very low compared to others in this case with a 0.12 nW, how- ever, all the new geometries gave very high power responses compared to the plain beam (Table 9). In the last part of the study, an experimental study was performed to show the effect of the new design in power generation and the results were compared to the FEA results. Here, 3D printed PLA based substructure was used with PVDF bonded on both sides.
Table6 Average stress and strain values for different cases with steel beam
Table6 Average stress and strain values for different cases with steel beam
As the experimental set-up is only capable of applying a maximum external load of 1 MQ, it was used as load in this case. The results were given in Fig. 17 comparing the results to the FEA. Resonance frequencies were found to be at 355 and 300 Hz in experiments for re-entrant and NS-A structures, respectively. When, they are compared to the FEA results of these structures which were 273 and 328 Hz, it can be seen that there is a difference below 10%. This result could be due to the non-perfect fixture of the beam to the shaker. The maximum power values are lower in the FEA cases due to the same reason as well as solution
As the experimental set-up is only capable of applying a maximum external load of 1 MQ, it was used as load in this case. The results were given in Fig. 17 comparing the results to the FEA. Resonance frequencies were found to be at 355 and 300 Hz in experiments for re-entrant and NS-A structures, respectively. When, they are compared to the FEA results of these structures which were 273 and 328 Hz, it can be seen that there is a difference below 10%. This result could be due to the non-perfect fixture of the beam to the shaker. The maximum power values are lower in the FEA cases due to the same reason as well as solution
step difference in FEA and experiments. Maximum powers were found to be 2.9 and 3.33 nW for re-entrant and NS-A structures, respectively, in experiments. There is a differ- ence below 8% between these values and FEA results which are 2.75 and 3.05 nW for re-entrant and NS-A structures, respectively. On the other hand, the trends are very closed to each other and the differences in FEA and experiment nearly same in all cases and they are in acceptable rates. Therefore, it can be said that FEA results matched well with experiments.
step difference in FEA and experiments. Maximum powers were found to be 2.9 and 3.33 nW for re-entrant and NS-A structures, respectively, in experiments. There is a differ- ence below 8% between these values and FEA results which are 2.75 and 3.05 nW for re-entrant and NS-A structures, respectively. On the other hand, the trends are very closed to each other and the differences in FEA and experiment nearly same in all cases and they are in acceptable rates. Therefore, it can be said that FEA results matched well with experiments.
Fig. 14 New structures offered a NS-A, b NS-B, ¢ NS-C Conclusion Table 7 Resonance frequencies and optimum resistance values for new structures
Fig. 14 New structures offered a NS-A, b NS-B, ¢ NS-C Conclusion Table 7 Resonance frequencies and optimum resistance values for new structures
15 times of rectangular geometry and 1000 times of plain one. Also, average strain in y-direction turned into posi- tive range, as expected from an auxetic structure. How- ever, the values were lower than that of the PLA case, as the increase in stiffness reduced the vibration amplitude and consequently strain levels. For the second part of the
15 times of rectangular geometry and 1000 times of plain one. Also, average strain in y-direction turned into posi- tive range, as expected from an auxetic structure. How- ever, the values were lower than that of the PLA case, as the increase in stiffness reduced the vibration amplitude and consequently strain levels. For the second part of the
study, new structures inspired by re-entrant geometry was utilized aiming to increase the strain in x-direction, rather focusing on strain in y-direction. These geometries outperformed the plain beam and re-entrant structure in PLA and steel cases. Nearly 5 times of re-entrant case and 65 times of plain case was achieved by NS-B structure for PLA beam and NS-A and NS-C also performed better from compared the structures. In steel case, the increase was better reaching 45 times of re-entrant case. Finally, some of the structures were produced and experimentally validated in the last part of the study. As final remarks for this study, it can be said that utilizing auxetic geometries can increase power response in energy harvesting appli- cations with transverse vibrations, however, this increase is affected by the stiffness match between piezoelectric material and substructure. On the other hand, using ver- tical re-entrant geometries in energy harvesters, power can be increased in significantly comparing to the auxetic geometries. Even the increase in power can be unique to the applied case, the idea of using vertical re-entrant geometries can give inspiration on further studies. Also, these structures can be modified for desired application by changing dimensions of the geometry. Different struc- tures give unique performances in different cases and there is not an optimum geometry for all cases. How- ever, new shapes offered in this study have a potential for increased power response for piezoelectric energy harvesting applcations when they are used considering Table 8 Maximum power responses of the structures for PLA case Table 9 Maximum power responses of the structures for steel case
study, new structures inspired by re-entrant geometry was utilized aiming to increase the strain in x-direction, rather focusing on strain in y-direction. These geometries outperformed the plain beam and re-entrant structure in PLA and steel cases. Nearly 5 times of re-entrant case and 65 times of plain case was achieved by NS-B structure for PLA beam and NS-A and NS-C also performed better from compared the structures. In steel case, the increase was better reaching 45 times of re-entrant case. Finally, some of the structures were produced and experimentally validated in the last part of the study. As final remarks for this study, it can be said that utilizing auxetic geometries can increase power response in energy harvesting appli- cations with transverse vibrations, however, this increase is affected by the stiffness match between piezoelectric material and substructure. On the other hand, using ver- tical re-entrant geometries in energy harvesters, power can be increased in significantly comparing to the auxetic geometries. Even the increase in power can be unique to the applied case, the idea of using vertical re-entrant geometries can give inspiration on further studies. Also, these structures can be modified for desired application by changing dimensions of the geometry. Different struc- tures give unique performances in different cases and there is not an optimum geometry for all cases. How- ever, new shapes offered in this study have a potential for increased power response for piezoelectric energy harvesting applcations when they are used considering Table 8 Maximum power responses of the structures for PLA case Table 9 Maximum power responses of the structures for steel case
Related topics:
Piezoelectric Energy Harvesting
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