CONVERTING FORCED VIBRATIONS INDUCED IN PIEZOELECTRIC CANTILEVER PLATE INTO NANO ELECTRICAL POWER

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1 International Journal of Mechanical Engineering and Technology (IJMET) Volue 9, Issue 11, Noveber 2018, pp , Article ID: IJMET_09_11_017 Available online at ISSN Print: and ISSN Online: IAEME Publication Scopus Indexed CONVERTING FORCED VIBRATIONS INDUCED IN PIEZOELECTRIC CANTILEVER PLATE INTO NANO ELECTRICAL POWER Dr. Hate Hadi Obeid Assist. Professor Departent of Mechanical Eng. / University of Babylon ABSTRACT In current paper, uniorph cantilever lainated plate was constructed using piezoelectric aterial and aluinu etal to study their ability to generate energy under action of wind load. The Euler Bernoulli ethod was used to investigate the behavior of power harvesting structures theoretically. The cantilever plate structure exained under siple haronic and rando point loads. The obtained results showed that, the haronic excitation gives power ore than rando excitation and the frequency is of contrariwise effect on the harvested power. The cantilever plate structure that was analyzed under haronic action and rando. The obtained results showed that, the structure gives powers ( W in Pin-force ethod, W in Enhanced pin-force ethod and W in Euler Bernoulli ethod) within 3 second. KEYWORDS: Uniorph Cantilever plate, PZT, Euler Bernoulli, Rando Force, Finite Eleent Analysi Cite this Article Dr. Hate Hadi Obeid, Converting Forced Vibrations Induced in Piezoelectric Cantilever Plate into Nano Electrical, International Journal of Mechanical Engineering and Technology, 9(11), 2018, pp INTRODUCTION Most fors of energy and power can be converted fro for to another. Of course, energy exists in any fors, such as solar energy, water flow, wind, teperature gradients, vibrations, sound waves, etc. The energy generated fro natural resources refers to the ter renewable energy. Its indicated in 2006 that ore than 18% of the global consued power cae fro different fors of renewable power which is considered non-negligible ratio [P. Basset,200]. The production of renewable energies lies between the enorous of Mega Watts to low of Nano Watts range according to the ethod of generation. figure (1) Shows three divisions of renewable energies based upon the generated power ratings such that they are depending upon their applications i.e editor@iaee.co

2 Dr. Hate Hadi Obeid Figure 1 Different renewable energies sources and applications Enorous power generation sources rated in egawatts. Low power generation sources rated in icro to iliwatt. Nanotechnology power Sources. Through the rest years it was possible to convert energy associated with vibration induced in structures to electrical one based on properties of piezoelectric aterials. The Brothers Pierre and Jacques Curie in 1880 were the first to prove and deonstrate the effect of piezoelectric to convert vibration energy into electrical one. Briefly, in the piezoelectric aterial a dipole deforation and charge foration occur when subjected to loads and inducing stresses. On the contrary, stresses are induced when a voltage is generated through piezoelectric aterial of a polarized attitude. The polarity will be lost in piezoelectric aterial when teperature is raised above Curing [ Ikeda,1990], Priya,2007] and [ Sodano,200]. A piezoelectric aterial is that generates an electric voltage drop when subjected into squeezed or stretched load and stresses are induced. On other hand, shrink or expand deforations are induced when an electric charge is applied on the PZT. These effects are generated in crystal structural that have central un syetry. Let us first understand the coon dielectric aterial to illustrate the piezoelectric effect. High perittivity dielectrics [Jyoti K. Ajitsaria,2008] can be forulated as: Figure 2 Piezoelectric Transducers [Priya,2007] editor@iaee.co

3 Converting Forced Vibrations Induced in Piezoelectric Cantilever Plate into Nano Electrical And 1 2 The electric displaceent (denoted by D), which is the charge density or charge to area ratio of the capacitor: And the electric field forulated as: 3 Equations (1) to (4) are valid for isotropic dielectrics. PZT ceraic aterial is considered isotropic in the state of unpolarizing, but they ay be considered anisotropic in the state of poling. For anisotropic aterial, the electric field and electric displaceent can be forulated in three diensions vector for. That lead to the dependent of the dielectric displaceent and electric field ratio on the direction or capacitor orientation with respect to the crystal axes. Then the electric displaceent is written as an equation of state variables [Jyoti K. Ajitsaria,2008] as: Electric displaceent is acting or generated in parallel with the electric field. That let the electric displaceent vector (Di), is the product of suations of field vector (Ej) and dielectric constant, ij [Jyoti K. Ajitsaria,2008] as: 6 Most of the constants of dielectric for PZT ceraics are characterized to be opposed to single crystal PZT aterial, then they are eliinated to zeros [Jyoti K. Ajitsaria, 2008]. The reaining non-zero ters are forulated as:. According to ANSI/IEEE [1988], [ANSI / IEEE Standard,1988], the PZT bender constitutive equations are forulated as: The boundary conditions that ay be used are assigned as: Constant stresses (T), Constant strains (S), Constant electrical displaceents (D) and Constant field (E). 2. MODELING OF PZT SENSER PZT sensor odel is considered to be a laination of PZT and etal bended as shown in figure (3). Euler-Bernoulli propose atheatical odel of the PZT etal laination plate response. The bonding is assued to be not perit of slipping between layers. Neutral axis can be assigned using odulus weighted algorith, [Wang,K,2001] editor@iaee.co

4 Dr. Hate Hadi Obeid Figure 3 Euler Bernoulli odel of PZT - etal [Wang,K,2001] The location of neutral axis can be specified as: [Eggborn,2003] The average strain ϵ a that induced in PZT is estiated and then used to find the generated voltage drop as: Substitution of Equation (9) into (10) lead to obtain the induced average strain as: [Eggborn,2003] The voltage on the PZT poling surfaces is also can be obtained in relation to the stress as: [Wang, K,2001] The substitution of equation (13) into (14) and applying hooks law leads to the voltage as: [Eggborn,2003] 3. CANTILEVER PTZ PLATE POWER HARVESTING Figure (4) shows a cantilever rectangular laination plate proposal odel. The odel is considered to be thin plate satisfying the conditions of the geoetric ratios between the diensions according to [Wang,K,2001]. The lainated plate is consisting of aluinu etal and PTZ bonded together perfectly as assued such that he PZT covers all the top surface of the aluinu plate. The PZT elastic odule is (62 109)Pa, while that for the aluinu is (71 109)Pa. the analysis is required to estiate an equivalent Young s Modulus for the lainated plate as: [Wang,K,2001] editor@iaee.co

5 Converting Forced Vibrations Induced in Piezoelectric Cantilever Plate into Nano Electrical Where is the plate s Young s Module, and is the plate thickness. The equivalent odulus Estiff is estiated as ( )Pa. For the purpose of estiating natural frequencies of lainated plate, Ritz ethod was used as applied by Blevins (1987). For a vibrating elastic plate, equation of axiu potential energy is given as: Where w(x,y) is the lateral deforation (displaceent) through x and y doains, equivalent Poisson s ratio for lainated plate with a value of 0.28, Beer [1992]. is the Where D is the flexural rigidity of aluinu plate, t is thickness of the PZT and aluinu referred as the plate thickness. The generated voltages are estiated by applying equation (1), a sall difference will be appeared due to the variable, which take into the account a ratio of lainated plate total thickness to thickness of PZT, which is a part of the total thickness (t). The plate s flexural vibration equation is: Where: plate s vibrational displaceent w(x,y) can be estiated as, Young [190] Where is an indexed coefficient that satisfying boundary conditions of cantilever plate. Then, the ode shapes Plate can specify for each ode. The first three odes are intended for that purpose. The first ode shape is represented as shown in Figure () which is uch siilar to the ultiplication two orthogonal beas with proper boundary conditions through x and y axis. The plate has claped-free boundary conditions in x axis: 10 editor@iaee.co

6 Dr. Hate Hadi Obeid And free-free boundary conditions in y axis: The claped-free odes are given by the equation Table 1 gives coefficients and, where (a) is the length of plate. The free-free odes through y axis are given by the equation: [Young (190)] Also, Table 1gives coefficients and, where b is the width of plate. Equation (23a) represents rigid-body translation while equation (23b) represents rigid-body rotation, and equation (23c) specifies free - free boundary conditions. Table 2 shows the correct cobination of both of Xi(x) and Yi(y). [Young [190] Table 1: The coefficients,, and Young [190] i *π/ 17*π/ *π/2 13*π/ *π/ 2 1*π/ editor@iaee.co

7 Converting Forced Vibrations Induced in Piezoelectric Cantilever Plate into Nano Electrical Table 2 Mode shapes pairings Mode,Φ(x,y) pairings Next, the following integrals is needed to solve: The values of indices i, k, and n are fro 1 to 6 that set equations (24a-f) for (6*6) atrix. Then after soe derivation, Blevins reaches to the characteristic equation: Where the product and for n = ik, while set to zero for n ik. The atrix C is fored fro the equations ( ) by the two equations: It ay be valid for the off-diagonal where n ik. While for diagonal ters n=ik: 4. FINITE ELEMENT MODELLING Finite eleent odel was created to the lainated plate using the ANSIS Package. The eleents SOLID, PLANE13, SOLID98, PLANE223, SOLID226, and SOLID227 were used to create the finite eleent odel. The eleent of (SOLID) have been used as the cantilever bea odel and for the electrical solution the eleent (CIRCU94) have been used and the odel can be shown in figure 6, The eleent of (CIRCU94) used to add resistor to the odel as shown and the point of node ust wiring to the node of the resistor and then the voltage will be copute editor@iaee.co

8 Dr. Hate Hadi Obeid Figure 6 uniorph Cantilever Plate finite eleent odel and odal analysis. HARVESTING ENERGY IN TERM OF DYNAMIC EXCITATION It s about to derive atheatical odel that describing the energy generated in the lainated plate when subjected into dynaic excitation. Two types of excitations will be considered. The first is haronic while the second is rando excitation..1. Haronic Driving Force: The dynaic haronic excitation is given by [Eggborn, 2003] as Where: F0: is the aplitude of load function. : is excitation frequency editor@iaee.co

9 Converting Forced Vibrations Induced in Piezoelectric Cantilever Plate into Nano Electrical is displaceent of the forcing function through bea length,,, is displaceent of the forcing function through width. After applying orthogonality principle, it can be reduce the force odel into: Where: Then it s possible to propose the tie response of the plate through x and y doains as: Researchers had been found when the plate is excited by dynaic load applied at fundaental natural frequency of the plate, only odd odes are excited. Thus, the odal deflections, and that corresponding with the even odes can be eliinated and equal to zero. The nuber of odes used in the deflection calculation is reduced to three. The flexural profile shape of the plate through x and y axis can now be detected using curvature equations of plate as: Then, the total or overall plate curvature can be estiated by the product two separate curvatures together (siilarly as in the plate s ode shapes) as: For eliination of the curvature s dependent on the location through plate doain, average curvature can estiate as: Considering the first five ode shapes, only fifth ode has a dependent on width along y axis. While Second and fourth odes dependent on y but do they aren t contributing to the plate curvature since they aren t excited; therefore, only the first and third odes will be considering leads to a suitable estiation of the average curvature, thus equation (34) can be reduced to: The oent that applied on the plate can be estiated as: Tioshenko [199] 14 editor@iaee.co

10 Dr. Hate Hadi Obeid where get units of N. as: is the oent applied per unit length which can be ultiplied by width of plate to To get axiu harvesting power, the tie response ust be axiizing but does not exceed the allowable safety liit. That ay be occurred under resonance when the plate is excited closer to fundaental natural frequency. In addition to excitation closer to second, third. Fifth natural frequencies..2. Rando Driving Force: The dynaic rando excitation is given by Inan[2000] as: The frequency is that excited within the first five natural frequencies range, ( ) is the phase shift within the range between 0 and π. n is nuber of iterations that generating rando excitation function sufficiently. The range of frequency that considered is 0 to 1000 Hz such that the first two resonant odes are excited and included. [Inan2000] proposed a generalized tie response using ode suation ethod as: given as: The curvature equation for the plate can be described as: The equation used to calculate power fro an AC voltage signal is: Where V is the source voltage, is the Resistance load, is the resistance of source and n is the nuber of tie steps. 6. RESULTS AND DISCUTIONS 6.1. Case study properties: The diensions and the properties of the aluinu plate can be shown in table3 1 editor@iaee.co

11 Converting Forced Vibrations Induced in Piezoelectric Cantilever Plate into Nano Electrical Table 3: the diension and properties of Aluinu plate Aluinu plate properties Unit Value Paraeter Length 0.00 Width 9*10-4 Thickness Kg/3 271 density Pa Young's Modulus The diensions and the properties of the PZT can be shown in table 4 Table 4 the diension and properties of PZT plate PZT properties Unit Value Paraeter 0.10 Length 0.0 Width 2.667*10-4 Thickness Pa Young's Modulus /v Dielectric constant V/N Voltage constant Ω 3900 Internal resistance Table shows the five natural frequencies calculated by the Ritz ethod Young (190). The estiated natural frequencies and ode shapes are using for both haronic and rando excitations. Table The first five natural frequencies Mode Plate with haronic excitation: f i (Hz) ω i (rad/s) Figure 7 shows the estiated harvesting power in addition to the corresponding load ipedance. It s obvious the axiu harvested power occurs when the load ipedance coinciding with the internal resistance of the PZT. The harvesting power estiated with each ethod is indicated in Table 6. The results show that Euler Bernoulli ethod gives lower agnitudes of harvesting power if copared with the other two ethods. Table 6 the power harvest fro plate odel, haronic forces. (µw ) (W ) Method Pin force Enhanced Pin force Euler Bernoulli 16 editor@iaee.co

12 Dr. Hate Hadi Obeid Figure 8 illustrates the power harvest fro the analytical plate odel and the voltage output fro odel Plate with rando excitation: The first five siulation presented in table 7 and the average power estiated will be copute and figures 9, 10, and 11 shows the voltage of the 1st, 2 nd and 3th siulation respectively, of three ethods and the figures 12, 13, and 14 show the power estiation fro first three siulation with tie taking 3 second for three ethods. Figure 8 of the 1st siulation of the plate odel, the voltage alternate signal about 0.V,- 0.V in Euler-Bernoulli ethod.v,-v in the Pin-force and Enhanced Pin-Force. In the figure 9 of the 2nd siulation, the shape of the signal output voltage was changed because the rando excitation was not predicted in value and range of frequency. The sae thing was found in the figures 10, of the 3th siulation, the shape of the output voltage was changed and the value of voltage was changed too. Table 7 The first five siulation of power estiated fro plate (W ) Average power fro external rando force (W ) th siulation (W ) 4th siulation (W ) 3rd siulation (W ) 2nd siulation (W ) 1st siulation Method ( ) =100H z Pin force Enhance d Pin force Euler Bernoull i Figure 7 powers of the three ethods with load ipedance, plate odel 17 editor@iaee.co

13 Converting Forced Vibrations Induced in Piezoelectric Cantilever Plate into Nano Electrical Figure 8 power harvest with tie fro the analytical plate odel, haronic force and output voltage fro odel. Figure 9 PZT voltages calculated fro analytical plate odel, rando forcing, and 1 st siulation Figure 10 PZT voltages calculated fro analytical plate odel, rando forcing, and 2 nd siulation. Figure 11 PZT voltages calculated fro analytical plate odel, rando forcing, and 3 rd siulation editor@iaee.co

14 Dr. Hate Hadi Obeid Figure 12 power harvest with tie fro the analytical plate odel, rando force and 1 st siulation Powe r(w) Peb Powe r(w) Ppin Pow er(w ) Penh Tie (Second) Tie (Second) Tie (Second) Figure 13 power harvest with tie fro the analytical plate odel, rando force and 2 nd siulation. (W) Peb ( Ppin W) Pow er(w ) Penh Tie (Second) Tie (Second)*10 - Tie (Second)*10 - Figure 14 power harvest with tie fro the analytical plate odel, rando force and 3rd siulation. The purpose of this paper is to estiate harvesting power of plate structures, and the best configuration of vibratory plate illustrate to get axiu power, know fro Table (7) we can taken the average power harvesting within 3 second of Euler Bernoulli ethod and copute the power per tie. A ( w) is copute for 3 second and it's be equal to7.6288w per 24 hours. CONCLUSION 1. The power can be harvesting fro any plate structural vibrate by haronic or rando load according like speed of wind and it is easy to get power along tie fro the uniorph plate. A ( W) per 3 second that ean ( W) per day is useful to use as long-life battery. 2. Euler Bernoulli ethod that used analysis of the behavior the of piezoelectric eleents. Such that deflection, voltage, and power generation fro a plate were estiated under action of excitation of either haronic or rando loads. The force used to excite the plate is a siulation to the wind load which ore practical. 3. You can use this study on bridge structural as a large area of plate and big excitation rando load by oving cars to get a harvesting power that not endless editor@iaee.co

15 Converting Forced Vibrations Induced in Piezoelectric Cantilever Plate into Nano Electrical REFERENCES [1] ANSI / IEEE Standard. (1988). IEEE Standard on Piezoelectricity, [2] Ikeda, T. et al.," Fundaentals of Piezoelectricity". New York: Oxford University Press [3] Blevins, R. D. Forulas for Natural Frequency and Mode Shape. 4th Edition, Robert E.Krieger Publishing Co., Florida. 1987, p.24. [4] Beer, F. P. and Johnston, Jr., E. R. Mechanics of Materials, 2nd Ed, McGraw-Hill, Inc.,New York, [] Young, D. Vibration of Rectangular Plates by the Ritz Method. Journal of Applied Mechanics, Deceber 190, pp [6] Stephen P. Tioshenko and S. Woinowsky-Krieger. Theory of Plates and Shells (199). [7] Inan, D. J. Engineering Vibration, 2nd edition, Prentice Hall, [8] Jyoti K. Ajitsaria, MODELING AND ANALYSIS OF PZT MICROPOWER GENERATOR, Deceber 19, 2008 [9] P. Basset et al., Chip-size antennas for iplantable sensors and sart dusts, Proc. of Transducers 0, Seoul, Korea, 200 [10] Priya et al., "Advances in energy harvesting using low profile piezoelectric transducers". Journal of Electro Cera, 19(3), [11] Sodano, H., Inan, D. & Park, G. (200). Coparison of piezoelectric energy harvesting devices for recharging batteries. Intelligent Material Systes and Structures, 16(10), [12] Eggborn, T., Analytical odels to predict power harvesting with piezoelectric aterials, Master s Thesis Virginia Polytechnic Institute and State University, [13] Wang, K. Modeling of Piezoelectric Generator on a Vibrating Bea. For copletion of Class Project in ME 984 Sart Materials, Virginia Polytechnic Institute and State University, April LIST OF ABBRIVATIONS R Resistance source Ω s Elastic Copliance N t Thickness Or Plate Separation t PZT thickness t bea thickness V Voltage v Veb Voltage of Euler Bernoulli ethod v Vpin Voltage of Pin-forced ethod v Venh Voltage of Enhanced pin-force ethods v V RMS Source Voltage v ω Frequency rad/s Relative Dielectric Constant Non Dielectric Constant Of Air = 8.8 * V Dielectric Constant V ε Mechanical Strain σ Mechanical Stress N ρ Density Kg # Ζ Daping Ratio Non editor@iaee.co