Mathematical analyses of distributed-parameter piezoelectric energy harvester equations are presented for parameter identification and optimization. The focus is placed on the single-mode voltage and vibration frequency response functions (FRFs) per translational base acceleration. Asymptotic trends of the voltage output and the tip displacement FRFs are investigated and expressions are obtained for the extreme conditions of the load resistance. The relationship between the linear voltage asymptotes and the optimal load resistance is discussed. Resonance frequencies of the voltage and the tip displacement FRFs are obtained accounting for the presence of mechanical losses. Closed-form expressions are extracted for the optimal electrical loads of maximum power generation at the short-circuit and open-circuit resonance frequencies of the voltage FRF. Analytical relations are given also for the identification of modal mechanical damping both from the voltage and the vibration FRFs using a single data point. Vibration attenuation and amplification due to resonance frequency shift is also addressed. An experimental case study is presented to validate some of the major equations derived here.
AntonS. R.SodanoH. A.A review of power harvesting using piezoelectric materials (2003–2006). Smart Mater. Struct., 2007, 16, R1–R21.
2.
Cook-ChennaultK. A.ThambiN.SastryA. M.Powering MEMS portable devices – a review of non-regenerative and regenerative power supply systems with emphasis on piezoelectric energy harvesting systems. Smart Mater. Struct., 2008, 17, 043001.
3.
ErturkA.InmanD. J.Issues in mathematical modeling of piezoelectric energy harvesters. Smart Mater. Struct., 2008, 17, 065016.
4.
RoundyS.WrightP. K.A piezoelectric vibration based generator for wireless electronics. Smart Mater. Struct., 2004, 13, 1131–1144.
5.
duToitN. E.WardleB. L.KimS.Design considerations for MEMS-scale piezoelectric mechanical vibration energy harvesters. J. Integr. Ferroelectr., 2005, 71, 121–160.
6.
RennoJ. M.DaqaqF. M.InmanD. J.On the optimal energy harvesting from a vibration source. J. Sound Vibr., 2009, 320, 386–405.
7.
ErturkA.InmanD. J.An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations. Smart Mater. Struct., 2009, 18, 025009.
8.
SodanoH. A.ParkG.InmanD. J.Estimation of electric charge output for piezoelectric energy harvesting. Strain, 2004, 40, 49–58.
9.
duToitN. E.WardleB. L.Experimental verification of models for microfabricated piezoelectric vibration energy harvesters. AIAA Journal, 2007, 45, 1126–1137.
10.
ElvinN. G.ElvinA. A.A general equivalent circuit model for piezoelectric generators. J. Intell. Mater. Syst. Struct., 2009, 20, 3–9.
11.
KimM.HoegenM.DugundjiJ.WardleB. L.Modeling and experimental verification of proof mass effects on vibration energy harvester performance. Smart Mater. Struct., 2010, 19, 045023.
12.
ErturkA.InmanD. J.Assumed-modes formulation of piezoelectric energy harvesters: Euler–Bernoulli, Rayleigh and Timoshenko models with axial deformations. In Proceedings of the ASME 2010 ESDA 10th Biennial Conference on Engineering Systems, Design and Analysis, Istanbul, Turkey, 12–14 July 2010.
13.
RuppC. J.EvgrafovA.MauteK.DunnM. L.Design of piezoelectric energy harvesting systems: a topology optimization approach based on multilayer plates and shells. J. Intell. Mater. Syst. Struct., 2009, 20, 1923–1939.
14.
De MarquiC.Jr.ErturkA.InmanD. J.An electromechanical finite element model for piezoelectric energy harvester plates. J. Sound Vibr., 2009, 327, 9–25.
15.
ElvinN. G.ElvinA. A.A coupled finite element circuit simulation model for analyzing piezoelectric energy generators. J. Intell. Mater. Syst. Struct., 2009, 20, 587–595.
16.
YangY.TangL.Equivalent circuit modeling of piezoelectric energy harvesters. J. Intell. Mater. Syst. Struct., 2009, 20, 2223–2235.
17.
MannB. P.SimsN. D.Energy harvesting from the nonlinear oscillations of magnetic levitation. J. Sound Vibr., 2009, 319, 515–530.
18.
RamlanR.BrennanM. J.MaceB. R.KovacicI.Potential benefits of a non-linear stiffness in an energy harvesting device. Nonlin. Dynam., 2009, 59, 545–558.
19.
CottoneF.VoccaH.GammaitoniL.Nonlinear energy harvesting. Phys. Rev. Lett., 2009, 102, 080601.
20.
GammaitoniL.NeriI.VoccaH.Nonlinear oscillators for vibration energy harvesting. Appl. Phys. Lett., 2009, 94, 164102.
21.
ErturkA.HoffmannJ.InmanD. J.A piezomagnetoelastic structure for broadband vibration energy harvesting. Appl. Phys. Lett., 2009, 94, 254102.
22.
ArrietaA. F.HagedornP.ErturkA.InmanD. J.A piezoelectric bistable plate for nonlinear broadband energy harvesting. Appl. Phys. Lett., 2010, 97, 104102.
23.
DaqaqM. F.Response of uni-modal Duffing-type harvesters to random forced excitations. J. Sound Vibr., 2010, 329, 3621–3631.
24.
StantonS. C.McGeheeC. C.MannB. P.Nonlinear dynamics for broadband energy harvesting: investigation of a bistable inertial generator. Physica D, 2010, 239, 640–653.
25.
BartonD. A. W.BurrowS. G.ClareL. R.Energy harvesting from vibrations with a nonlinear oscillator. ASME J. Vibr. Acoust., 2010, 132, 021009.
26.
StantonS. C.ErturkA.MannB. P.InmanD. J.Nonlinear piezoelectricity in electroelastic energy harvesters: modeling and experimental identification. J. Appl. Phys., 2010, 108, 074903.
27.
ChoiW. J.JeonY.JeongJ. H.SoodR.KimS. G.Energy harvesting MEMS device based on thin film piezoelectric cantilevers. J. Electroceram., 2006, 17, pp. 543–548.
28.
AntonS. R.ErturkA.InmanD. J.Multifunctional self-charging structures using piezoceramics and thin-film batteries. Smart Mater. Struct., 2010, 19, 115021.
29.
GambierP.AntonS. R.KongN.ErturkA.InmanD. J.Combined piezoelectric, solar and thermal energy harvesting for multifunctional structures with thin-film batteries. In Proceedings of the 21st International Conference on Adaptive Structures and Technologies, State College, Pennsylvania, 4–6 October 2010.
30.
Standards Committee of the IEEE Ultrasonics, Ferroelectrics, and Frequency Control SocietyIEEE Standard on Piezoelectricity, 1987, IEEE, New York.
31.
AntonS. R.ErturkA.InmanD. J.Strength analysis of piezoceramic materials for structural considerations in energy harvesting for UAVs. Proc. SPIE, 2010, 7643, 76430E.
32.
EwinsD. J.Modal testing: theory, practice and application, 2000 (Research Studies Press, Baldock, UK).
33.
CloughR. W.PenzienJ.Dynamics of structures, 1975 (John Wiley and Sons, New York).
